Split-planar microwave resonator devices for electron spin resonance

Abstract

In a general aspect, a split-planar microwave resonator device for electron spin resonance is described. In some aspects, a microwave resonator device for electron spin resonance includes parallel first and second substrates that are spaced apart from each other by a separation distance. The microwave resonator device includes a first ground plane disposed on the first substrate; a second ground plane disposed on the second substrate; a first transmission line resonator patterned on the first substrate; and a second transmission line resonator patterned on the second substrate. The first transmission line resonator is configured to produce a first microwave field in a sample region between the first and second substrates; and the second transmission line resonator is configured to produce a second microwave field in the sample region. In some examples, the first and second microwave transmission line resonators are made of superconducting material.

Description

Split-Planar Microwave Resonator Devices for Electron Spin ResonanceCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 575,118, filed April 5, 2024, entitled "Split-Planar Microwave Resonator Devices for Electron Spin Resonance," and to U.S. Provisional Patent Application No. 63 / 664,227, filed June 26, 2024, entitled "Split-Planar Microwave Resonator Devices for Electron Spin Resonance." The above-referenced priority documents are incorporated herein by reference.BACKGROUND

[0001] The following description relates to a split-planar microwave resonator device for electron spin resonance.

[0002] This specification relates to a microwave resonator device for magnetic resonance applications, including electron spin resonance (ESR) applications. Electron spin resonance systems are used to study various types of samples and phenomena. In some magnetic resonance applications, the spins in a sample are polarized by a static, external magnetic field, and a resonator manipulates the spins by producing a magnetic field at a frequency near the spins’ resonance frequencies. In electron spin resonance (ESR) applications, resonators typically operate at microwave frequencies to interact with electron spins in the sample.DESCRIPTION OF DRAWINGS

[0003] FIG. 1 is a schematic diagram showing aspects of an example electron spin resonance (ESR) system.

[0004] FIG. 2 is a side view of an example microwave resonator device.

[0005] FIG. 3 includes circuit diagrams showing equivalent circuit models of the example microwave resonator device shown in FIG. 2.

[0006] FIG. 4 includes effective circuit diagrams showing modes of operation ("Odd and "Even" modes) of an example microwave resonator device represented by the equivalent circuit models shown in FIG. 3.

[0007] FIG. 5 is a block diagram showing aspects of an example resonator unit.

[0008] FIG. 6 is a perspective view of an example microwave resonator device.

[0009] FIGS. 7A-7C are field overlays showing spatial distributions of microwave magnetic fields generated by first and second microwave resonator devices at respective resonance frequencies.

[0010] FIG. 7D is a plot showing resonance frequency in GHz and coupling coefficient as a function of the separation distance d in mm in the first and second microwave resonator devices shown in FIGS. 7A-7C.

[0011] FIG. 8A is a perspective view of the second microwave resonator device in FIGS. 7B-7C.

[0012] FIG. 8B includes plots showing the spin-cavity interaction strength in units of Hertz (Hz) as a function of distance in the Y direction across the sample region in the first and second microwave resonator devices in FIGS. 7A-7C.

[0013] FIG. 8C includes a plot showing the spin-cavity interaction strength in units of Hertz (Hz) along the Z-axis in the sample region of the second microwave resonator device in FIG. 8A as a function of a height for different separation distances d, and a plot showing the spin-cavity interaction strength in the sample region of the first microwave resonator device shown in FIG. 7A as a function of a height to the resonator plane of the first microwave resonator device.

[0014] FIGS. 9A-9B show cross-sectional views of the microwave vector fields along the YZ plane at X=0 in the first microwave resonator device shown in FIG. 7A and the second microwave resonator device shown in FIG. 7B.

[0015] FIG. 10A is a plot showing single-ended scattering parameters (S-parameters) in dB as a function of frequency in GHz for the microwave resonator device shown in FIG. 6.

[0016] FIG. 10B is a plot showing mixed-mode s-parameters in dB as a function of frequency in GHz for differential (odd) and common (even) modes of the microwave resonator device shown in FIG. 6.

[0017] FIG. 11 is a perspective view of an example resonator unit excitation structure.

[0018] FIG. 12A is a plot showing S-parameters, in units of decibels (dB), of the microwave resonator device shown in FIG. 11 as a function of frequency in units of GigaHertz (GHz).

[0019] FIG. 12B shows current distribution over the first terminals of the first and second microwave resonator units.

[0020] FIG. 12C shows a magnetic field distribution in the sample region when the microwave device is operating under an odd mode at 9.7535 GHz.

[0021] FIG. 13 is a flow chart showing aspects of an example process for operating an example microwave resonator device.

[0022] FIGS. 14A-14B include perspective views of an example resonator contained within an example RF package.

[0023] FIGS. 15A-15C include a side view, a perspective view, and a top view of an example microwave resonator device.

[0024] FIG. 16 includes a perspective view of an example microwave resonator device with an ESR sample placed in a sample region.

[0025] FIG. 17A-17B is a perspective view of an example microwave resonator device including feedlines for excitation and readout.

[0026] FIG. 17C is a plot showing scattering parameters (S-parameters) in units of decibels (dB) as a function of frequency in units of GigaHertz (GHz) of the microwave resonator device shown in FIG. 17B.

[0027] FIG. 18 is a perspective view of an example microwave resonator device connected to a microwave transceiver.

[0028] FIG. 19A is a top view of an example microwave resonator device.

[0029] FIG. 19B is a plot showing scattering parameters (S-parameters) in units of decibels (dB) as a function of frequency in units of GigaHertz (GHz) of first and second microwave resonator devices of the microwave resonator device shown in FIG. 19A.

[0030] FIGS. 20A-20B show cross-sectional views of the microwave vector fields along the XY plane at Z=0 in the microwave resonator device shown in FIG. 19A.

[0031] FIGS. 21A-21B is a plot showing scattering parameters (S-parameters) in units of decibels (dB) as a function of frequency in GigaHertz (GHz) of the microwave resonator device shown in FIG. 19A.

[0032] FIG. 22 is a block diagram showing aspects of an example resonator unit.

[0033] FIGS. 23A-23D are simulation results showing circularly polarized magnetic field vectors in a sample region of the example microwave resonator device in FIG. 22 at various phase differences.DETAILED DESCRIPTION

[0034] In some aspects of what is described here, a microwave resonator device for electron spin resonance includes a split-planar microwave resonator device. A split-planar microwave resonator device can include two separate planar transmission line resonators patterned on surfaces of two respective substrates. The two substrates can be oriented parallel to each other, and they can be spaced apart from each other by a separation distance. In some examples, a split-planar microwave resonator device includes two ground planes disposed on the two respective substrates. In certain instances, the two planar transmission line resonators are made of superconducting materials, for example, to enhance the sensitivity of the device and suppress noise.

[0035] In some implementations, microwave fields produced by a microwave resonator device (e.g., by one or both of the two planar transmission line resonators) form a drive magnetic field in a sample region of the microwave resonator device. In some instances, the drive magnetic field generated by the split-planar microwave resonator device may contain multiple microwave resonance frequencies to manipulate the electron spins. In some implementations, the microwave resonator device can be configured to support one ormore microwave resonance modes that share a common spatial volume in the sample region. Each of the two planar transmission line resonators may include multiple conductors that support multiple microwave resonance modes for performing electron spin resonance measurements. In some cases, the techniques and systems described here can be deployed in connection with continuous wave (CW) magnetic resonance (e.g., using CW electron paramagnetic resonance spectroscopy methodology), pulse magnetic resonance (e.g., using pulsed electron paramagnetic resonance (EPR) spectroscopy methodology), inductive detection EPR measurements, EPR spectroscopy, general single frequency pulsed EPR, multiple resonance EPR, or a combination of these.

[0036] In some implementations, a microwave resonator device includes two planar transmission line resonators that are coupled to each other. For example, the two planar transmission line resonators may be configured to support a single desired resonance mode that is well-confined in a relatively large three-dimensional sample region. In some implementations, a microwave resonator device includes two planar transmission line resonators that are uncoupled from each other. For example, the two planar transmission line resonators may be configured to support distinct, independent resonance modes that are each well-confined in a relatively large three-dimensional sample region. The independent resonance modes may be used at the same time.

[0037] In some aspects of what is described here, a microwave resonator device for electron spin resonance is a crossed split-planar microwave resonator device, in which the two planar transmission line resonators have orthogonal (crossed) orientations. In some examples, one of the planar transmission line resonators is oriented to generate control fields in one direction (e.g., the Z direction), and the other planar transmission line resonator is oriented to generate control fields in another direction (e.g., the Y direction). In other aspects, the two planar transmission line resonators have the same orientation. In some examples, both of the planar transmission line resonators are oriented to generate control fields in the same direction (e.g., Z direction or the Y direction).

[0038] In some cases, a microwave resonator device can electromagnetically interact with liquid samples, solid samples, liquid crystal samples, spin-labeled protein samples, or other types of samples to be measured or otherwise analyzed by an electron spinresonance system. Aspects of the systems and techniques described here can be adapted for various types of applications. For example, the systems and techniques described here may be used for structural biology measurements, for instance, to measure structural properties of proteins or protein complexes in a biological sample (e.g., a blood sample, a urine sample, a saliva sample, a sweat sample, or another type of biological sample). Such measurements can be useful in clinical applications, for example, diagnostics, treatments, pharmaceutical drug discovery / development and understanding the structure and function of membrane proteins, and other applications. As another example, an electron spin resonance system may include components that operate in a cryogenic environment (e.g., at 77 K, 4 K, or other cryogenic temperatures below 273 K), or an electron spin resonance system may operate at non-cryogenic temperatures including room temperatures.

[0039] In some implementations, the systems and techniques described here can provide a number of advantages. For example, some of the systems and techniques presented here can improve resonator filling factor and field homogeneity of the microwave resonator device and thus provide improved sensitivity and measurement fidelity. In some instances, the systems and techniques described here can enable efficient exchange of magnetic energy between a sample and the resonator and improve the conversion efficiency to provide larger control field strengths (Rabi frequency) and inductive signal strength. In some examples, the systems and techniques described here can ensure that substantially all spins in the sample experience similar dynamics under control sequences and detection schemes. In some instances, the systems and techniques presented here can be used to perform biological EPR measurements on relatively large sample regions (e.g., in a range of sub microliters to a few tens of microliters) that are concentration limited. For example, the systems and techniques presented here based on the crossed split-planar microwave resonator can be used in inductive detection EPR measurements by providing dedicated and distinct resonators for signal transmission and detection. Some of the systems and techniques presented here can provide high isolation between spectrometer transmission and detection circuitry without requiring protection switches. Some of the systems and techniques presented here can also enable two distinctresonance modes for double-resonance measurements. The microwave fields generated by the two planar transmission line resonators may interact with a spin sample in the sample region independently. Each resonator circuit may also be taken to interact with spectrometer circuitry independently, offering flexibility in defining transmission and detection channels for EPR measurements. In some cases, a combination of these and potentially other advantages and improvements may be obtained.

[0040] FIG. 1 is a schematic diagram showing aspects of an example electron spin resonance system 100. The example electron spin resonance system 100 includes a resonator unit 106, a primary magnet system 112, and a control system 114. The control system 114 further includes computer and signal processing units 102, a spectrometer unit 104, a temperature control unit (TCU) 108, and a field control unit (FCU) 110. In some examples, each of the units of the electron spin resonance system 100 may include an associated electronic circuit and other components, including housing, ports, etc.

[0041] In some cases, the computer and signal processing units 102 communicate with the spectrometer 104, the TCU 108, the FCU 110, the primary magnet system 114, and other units / components of the electron spin resonance system 100. In some instances, the computer and signal processing units 102 can be implemented as a single computer device (e.g., a laptop computer, a workstation, a desktop computer, a server, etc.) or by multiple computer devices. In some cases, the computer and signal processing units 102 can be colocated with the spectrometer 104, the resonator unit 106, and the other units or components of the example electron spin resonance system 100; and may be connected to other units and components of the electron spin resonance system 100, for example, by cables (e.g., coaxial cables, network cables, waveguides, etc.) or other types of local communication channels. In some cases, all or part of the computer and signal processing units 102 is located remotely from the spectrometer 104, and resonator unit 106, and may be directly connected to the units and components of the electron spin resonance system 100, for example, by a network (e.g., the Internet, a virtual private network, a wide area network, etc.) or other types of remote communication channels. Some aspects of the computer and signal processing units 102 may be deployed in a cloud computing environment, or otherwise. In some implementations, the computer and signal processingunits 102 include one or more user interfaces such as, for example, a touchscreen, a pointing device, a keyboard, a microphone, etc., that allow a user to interact with and provide input to the computer and signal processing units 102 of the electron spin resonance system 100. In some implementations, the computer and signal processing units 102 include one or more user interface devices that allow the computer and signal processing units 102 to present information and data (e.g., graphical user interfaces, etc.) for display to a user.

[0042] The computer and signal processing units 102 can include, for example, a central processor unit (CPU) or another type of general-purpose processor that runs software. The computer and signal processing units 102 can include, for example, a graphics processing unit (GPU), a cryptographic processor unit, a field-programmable gate array (FPGA) unit, a digital signal processing (DSP) unit, or another type of data processing apparatus. In some instances, the computer and signal processing units 102 maybe configured to perform digital signal processing and signal averaging. In particular, the computer and signal processing units 102 may be configured to identify a pulse sequence for an electron spin resonance experiment; generate sets of digital intermediate frequency (IF) signal information by modulating respective pulses in the pulse sequence at an intermediate frequency; generate a hardware control sequence based on the pulse sequence; convert the digital IF signal information and the hardware control sequence to the signal processing unit 104; generate digitized magnetic resonance detection signals; demodulate a digitized magnetic resonance detection signal at the intermediate frequency for phase-sensitive detection; etc. In some instances, the computer and signal processing units 102 may be configured to perform other operations. For example, the computer and signal processing units 102 may be configured to generate multiple resonance pulses by modulating pulses in a pulse sequence at different intermediate frequencies and superposing the modulated pulses, for example, for performing a multiple electron spin resonance measurement. In this case, the computer and signal processing units 102 maybe also configured to demodulate the digitized magnetic resonance detection signal at the multiple intermediate frequencies. In some instances, the computer and signal processing units 102 may becontrolled by software to execute a pre-configured program stored in a memory unit of the computer and signal processing units 102.

[0043] The computer and signal processing units 102 may be configured to generate analog electrical signals based on the digital signal values according to the hardware control sequence; and to transmit the analog electrical signals to the resonator unit 106 via the spectrometer 104. The computer and signal processing units 102 can further receive an electron spin resonance detection signal at a second resonance frequency from the resonator unit 106 via the spectrometer 104. The electron spin resonance detection signal includes a signal with amplitude, phase, and frequency modulation at an intermediate frequency and can be digitized by operation of the computer and signal processing units 102. In some instances, the computer and signal processing units 102 may be configured to perform other operations.

[0044] In some instances, the spectrometer 104 includes microwave or radio frequency hardware components (e.g., switches, mixers, amplifiers, attenuators, etc.) that manipulate microwave or radio frequency signals. For instance, the spectrometer 104 may be configured to process S-band (2-4 GHz), C-band (4-8 GHz), X-band (8 - 12 GHz), Ku-band signals (12-18 GHz), K-band signals (18-26.5 GHz), Q-band signals (33-50 GHz), V-band signals (50-75 GHz), W-band signals (75-110 GHz), or signals in other microwave frequency bands. In some examples, the spectrometer 104 may include a low phase noise microwave synthesizer to generate system master oscillator signals and analog spectrometer local oscillator signals, an IQ mixer device to upconvert analog IF electrical signals to single sideband signals that can be applied to the resonator unit 106 and to provide local oscillator suppression and image suppression, and a bandpass filter device to suppress noise bandwidth on a transmitter side. In some instances, the spectrometer 104 may include other circuit components. In certain cases, the spectrometer 104 can receive the analog IF electrical signals from the computer and signal processing units 102 and output a magnetic resonance control signal (e.g., upconverted and single band electrical signals). In some implementations, the magnetic resonance control signal has a frequency in a radio frequency or microwave regime. In the example shown in FIG. 1, the magnetic resonance control signal from the spectrometer 104 is passed to the resonator unit 106.

[0045] In some instances, the spectrometer 104 can be digitally controlled by the digital control signals from the computer and signal processing units 102. In some instances, the spectrometer 104 may include one or more switch devices. In some implementations, at least a portion of the spectrometer 104 operates at an elevated temperature, e.g., room temperature, outside of a cryogenic environment. In some instances, some components of the spectrometer 104 may operate in a cryogenic environment, for example, the same or different cryogenic environment where the resonator unit 106 resides. In some examples, the spectrometer 104 may be digitally controlled to perform fast switching between pulse and continuous-wave modes of operation. In some instances, the spectrometer 104 may include other components or may be configured to perform other operations.

[0046] In some instances, the spectrometer 104 may include an amplifier device (e.g., a cryogenic LNA device). In some implementations, the spectrometer 104 can include a mixer device for down-converting electron spin resonance detection signals received from the resonator unit 106 to an intermediate frequency ( / F), by mixing the electron spin resonance detection signals with a local oscillator frequency (L0). The spectrometer 104 may also include a filter device that removes unwanted frequency components, for example, a bandpass IF filter device that rejects frequencies near a frequency value of fL0— f1Ffrom the mixer device and suppresses noise outside the receiver bandwidthThe spectrometer 104 may also include other components such as, for example, an IF amplifier device, a lowpass filter device, and other circuit components. In some instances, the spectrometer 104 may include various stages of filtering and amplification to reduce noise bandwidth. The spectrometer 104 shown in FIG. 1 can accept both low-level spin signal inputs and high-level pulse transient digitizing inputs. In some examples, the spectrometer 104 may be controlled to switch between modes of operation, for example, between an electron spin resonance measurement mode and a pulse transient digitizing / correcting mode.

[0047] In some instances, the spectrometer 104 may be configured to process S-band (2-4 GHz), C-band (4-8 GHz), X-band (8 - 12 GHz), Ku-band signals (12-18 GHz), K-band signals (18-26.5 GHz), Q-band signals (33-50 GHz), V-band signals (50-75 GHz), W-band signals (75-110 GHz), or signals in other microwave frequency bands. For example, thespectrometer 104 may include a single stage of up-conversion or down-conversion with a single microwave synthesizer device that is configured to generate LO signals at respective microwave frequency bands. For another example, the spectrometer 104 may include two or more stages of up-conversion or down-conversion with two or more microwave synthesizer devices and two or more corresponding mixer devices.

[0048] In the example shown in FIG. 1, components of the spectrometer 104 are electromagnetically coupled to (e.g., by coaxial cables, waveguides, etc.), and adapted to communicate with the resonator unit 106. For example, the spectrometer 104 can be adapted to provide a voltage or current electrical signal that drives the resonator unit 106. In the example shown in FIG. 1, the spectrometer 104 can also acquire magnetic resonance data based on control signals delivered to the resonator unit 106. For example, the spectrometer 104 may receive electron spin resonance detection signals generated by an interaction between the resonator unit 106 and samples at the resonator unit 106 based on the electron spin resonance control signals received at the resonator unit 106.

[0049] In some implementations, the electron spin resonance system 100 includes a superheterodyne spectrometer system. Generally, a superheterodyne spectrometer generates electron spin resonance control signals by mixing intermediate frequency (IF) signals with local oscillator (LO) signals to produce a high frequency (e.g., RF or microwave) signal that can then be further processed and passed on to the resonator unit 106; a superheterodyne spectrometer processes high-frequency electron spin resonance detection signals (e.g., spin signals) from the resonator unit 106 by mixing the high- frequency signals with LO signals to produce an IF signal, which can then be further processed and digitized for analysis by the data processing apparatus 102.Superheterodyne operation can allow for increased sensitivity, selectivity, and signal-to- noise ratio, among other advantages. By generating control information and processing detected signals at IF frequencies, superior control and data processing can be achieved in some cases. Also, by using one or more tunable local oscillators, the superheterodyne spectrometer can tune to multiple distinct spin resonance frequencies, making it a versatile system.

[0050] In some implementations, the resonator unit 106 includes a microwave resonator device that resides in a cryogenic environment (e.g., at 77 K, 4 K, or other cryogenic temperatures below 273 K), for example, in a cryostat. The microwave resonator device of the resonator unit 106 may include multiple planar transmission line resonators, each of which has a resonance frequency in a range of 2 GHz to 90 GHz or in another frequency range. In some implementations, the microwave resonator device is a split- planar transmission line resonator device, which includes a first planar transmission line resonator and a second planar transmission line resonator. The first and second planar transmission line resonators reside on respective surfaces of two separate substrates. The two substrates are oriented parallel to each other with the respective surfaces facing each other; and spaced apart from each other by a separation distance d. The transmission line resonators may be implemented as microstrip resonators, coplanar waveguide resonators, or other types of structures.

[0051] In some instances, the microwave resonator device includes multiple conductors, two ground planes disposed on surfaces of the two separate substrates. In particular, the first planar transmission line resonator resides on a first surface of a first substrate; the first ground plane resides on a second, opposite surface of the first substrate. Similarly, the second planar transmission line resonator resides on a first surface of a second substrate; the second ground plane resides on a second, opposite surface of the second substrate. In some instances, the ground planes of the microwave resonator device may be configured in another manner. For example, ground planes may be disposed on the same surface as transmission line conductors in a coplanar waveguide arrangement. In some instances, each of the multiple conductors and the ground plane are patterned on a substrate as a microstrip, a microstrip line, a coplanar waveguide, or another type of transmission line pattern. In some implementations, the multiple conductors and the ground plane include superconducting material. In some implementations, each of the first and second planar transmission line resonators includes a subset of the multiple conductors, which are formed in an array of conductive segments. In some instances, the conductive segments in the first and second planar transmission line resonators are arranged in parallel to one another with equal spacing between each neighboring pair ofconductive segments. Each conductive segment in the first and second planar transmission line resonators may be configured to resonate at the same microwave resonance frequency. Each of the conductive segments in the first and second planar transmission line resonators can be implemented, for example, as a half-wave resonator, a full-wave resonator, or a multi-half-wave resonator. Under a half-wave resonator configuration, each of the conductive segments in the first and second planar transmission line resonators may be configured to provide maximum magnetic field at the center of each conductive segment, where a sample region of the microwave resonator device resides.

[0052] In some implementations, the first planar transmission line resonator has a first intrinsic resonance frequency; and the second planar transmission line resonator has a second intrinsic resonance frequency. In some instances, the first intrinsic resonance frequency may be identical to the second intrinsic resonance frequency. In certain cases, the first and second intrinsic resonance frequencies may have a detuning, e.g., the first intrinsic resonance frequency may be offset from the second intrinsic resonance frequency.

[0053] In some instances, the first and second planar transmission line resonators may share the identical physical design (e.g., number of microstrip lines, width and length of microstrip lines, capacitive gaps for coupling the microstrip lines to terminals, etc.) and thus the same intrinsic resonance frequency. In some instances, the first and second planar transmission line resonators may have different physical designs and have distinct resonance frequencies. The first and second planar transmission line resonators can each generate microwave magnetic fields (e.g., drive magnetic fields or control field) to a sample in a sample region to constructively interfere, generating a highly uniform microwave magnetic field according to the electron spin resonance control signals received at the microwave resonator device.

[0054] In some implementations, the first and second planar transmission line resonators in the microwave resonator device may be coupled to each other, for example, in parallel through a pair of microwave baluns (e.g., the microwave baluns 502A / 502B, the power dividers and the delay lines 1104A / 1122A, 1104B / 1122B as shown in the resonator unit 500, 1100 shown in FIGS. 5, 11) to form a two-port device to communicate control signals and detection signals with the control system 114, or in another manner. The firstand second planar transmission line resonators may be connected to the microwave baluns through connectors on the microwave resonator device. In some instances, the first and second planar transmission line resonators in the microwave resonator device may be coupled through microwave power divider, hybrid or any other microwave components.

[0055] In some instances, the microwave resonator device of the resonator unit 106 may be represented by one or more of the equivalent circuit diagrams shown in FIGS. 3 and 4. In some instances, the microwave resonator device of the resonator unit 106 may be implemented as the microwave resonator device 200, 504, 600, 1102,1500, 1600, 1700, 1801, 1900, 2204 in FIGS. 2, 5, 6, 11, 15A-15B, 16, 17A-17B, 18, 19A, 22, or in another manner. In some instances, the resonator unit 106 may include signal wirings for communicating microwave signals and digital control signals, cryogenic receiver components, and internal hardware for temperature setting and stabilization. In some instances, the control system 114 (e.g., the computer and signal processing units 102 and the spectrometer 104) may also communicate electron spin resonance control signals to the microwave resonator device of the resonator unit 106 and receive electron spin resonance detection signals from the microwave resonator device of the resonator unit 106. In some implementations, the microwave resonator device may be operated to perform EPR measurements according to the operations in the example process 1300 shown in FIG. 13 or in another manner.

[0056] In some implementations, the TCU 108 monitors and stabilizes the temperature of the environment where the microwave resonator device of the resonator unit 106 resides. In some examples, the example electron spin resonance system 100 includes other circuits or components. For example, the TCU 108 may measure and stabilize temperatures of various components using closed loop feedback control. In some instances, the example electron spin resonance system 100 includes a cryostat cooled by liquid Helium or liquid Nitrogen which can be maintained at a cryogenic environment (e.g., at 77 K, 4 K, or other cryogenic temperatures below 273 K). In certain examples, a cryostat of the example electron spin resonance system 100 includes liquid cryogen-free system, e.g., dry cryostats. In some instances, a cryostat of the example electron spin resonance system 100 includes internal control hardware for temperature setting and stabilization.

[0057] In some instances, the FCU 110 can monitor, stabilize, and vary a primary magnetic field in the electron spin resonance system. The primary magnetic field is the external Bofield (the quantizing field) that is applied to the sample region and is generated by the primary magnet system 112, which can be implemented as an electromagnet, a permanent magnet, a superconducting magnet, or another type of magnet. For example, the FCU 110 may measure and stabilize a quantizing magnetic field using closed loop feedback control. The FCU 110 of the electron spin resonance system 100 may include a magnet configured to generate magnetic fields corresponding to X-band spin resonance (e.g., a field strength in the range of approximately 0 - 4000 G). In some implementations, the FCU 110 further includes a Hall probe which interfaces with the computer and signal processing units 102 to receive control signals from the computer and signal processing units 102 and apply appropriate current to the primary magnet system 112.

[0058] In some implementations, the primary magnet system 112 provides a primary magnetic field in the electron spin resonance system 100 including the sample region of the microwave resonator device in the resonator unit 106 (e.g., the sample regions 650, 850, 1250 in FIGS. 6, 8, 12). As shown in FIG. 1, the primary magnet system 112 in the electron spin resonance system 100 generates a primary magnetic field in a controlled environment of a sample region defined by the resonator unit 106. In some implementations, the primary magnet system 112 includes an electromagnet system that can be controlled by the FCU 110 by tuning the current from an electromagnet power supply. In some instances, the primary magnet system 112 may include a gradient system that generates one or more gradient fields that spatially vary over the sample region. Generally, the primary magnetic field generated by the primary magnet system 112 controls electron spins; quantizes the spin states; sets the Larmor frequency of the spin ensemble; interact with nitrogen-vacancy (NV) centers; polarize electron spins in NV centers; and may be used in other applications.

[0059] In some aspects of operation, a spin ensemble in the sample interacts with the resonator unit 106. Control of spins in the sample can be achieved, for example, by a radio frequency or microwave magnetic field generated by the resonator unit 106. The drive frequency can be tuned to the spins’ resonance frequency, which is determined by the strength of the primary magnetic field and the gyromagnetic ratio of the spins. The spinscan be a collection of particles having non-zero spins that interact magnetically with the applied fields. For example, the spin ensemble can include nuclear spins, electron spins, or a combination of nuclear and electron spins. Examples of nuclear spins include hydrogen nuclei (1H), carbon-13 nuclei (13C), and others. In some implementations, the spin ensemble is a collection of identical spin- 1 / 2 free electron spins attached to an ensemble of large molecules.

[0060] FIG. 2 is a side view of an example microwave resonator device 200. As shown in FIG. 2, the microwave resonator device 200 is a split-planar microwave resonator device which includes a first microwave resonator unit 202A and a second microwave resonator unit 202B. The first microwave resonator unit 202A includes a first planar transmission line resonator 214A and a first ground plane 212A disposed on a first substrate 216A; and the second microwave resonator unit 202B includes a second planar transmission line resonator 214B and a second ground plane 212B disposed on a second substrate 216B. In particular, the first transmission line resonator 214A is deposited on a first surface of the first substrate; and the first ground plane 212A is disposed on a second, opposite surface of the first substrate 216A. The second transmission line resonator 214B is deposited on a first surface of the second substrate 216B; and the second ground plane 212B is disposed on a second, opposite surface of the second substrate 216B.

[0061] As shown in FIG. 2, the first and second microwave resonator units 202A and 202B are spatially arranged and assembled such that the first and second substrates are oriented parallel to each other. The first and second planar transmission line resonators 214A and 214B are facing each other and spaced apart by a separation distance d. In some instances, the separation distance d can be adjusted to tune the resonance frequencies of the microwave resonator device, the coupling between the first and second planar transmission line resonators, or other parameters of the microwave resonator device. In some implementations, the separation distance is in a range of 0.5 to 2.5 mm. In some implementations, the separation distance is in another range (e.g., 0.3 to 3.0 mm, 1.0 to 2.0 mm, etc.). The example microwave resonator device 200 can include additional or different features, and the features of the example microwave resonator device 200 may be arranged in the configuration shown or in another configuration. For example, each of the first andsecond substrates 216A, 216B may include terminals through which the first and second transmission line resonators 214A, 214B can be connected to signal lines (e.g., coaxial cables) or electrical devices (e.g., connectors connected to the terminals and microwave baluns connected to the connectors). In some implementations, the terminals are capacitively coupled to the respective sets of conductors in the first and second planar transmission line resonators. In some instances, the terminals may include delay lines which are configured to introduce phase shifts (e.g., a 0-degree phase shift or a 180-degree phase shift) to the control signals and to allow a selection of different resonance modes (e.g., odd or even mode).

[0062] In some instances, each of the first and second planar transmission line resonators 214A, 214B includes one or more conductors. For example, the first planar transmission line resonator 214A may include a first set of conductors configured as an array of conductive segments (e.g., the conductive segments 626 of the first transmission line resonator 612A shown in FIG. 6); and the second transmission line resonator 214B may include a second set of conductors configured as an array of conductive segments (e.g., the conductive segments 636 of the second transmission line resonator 612B shown in FIG. 6). In the example shown, the conductors that form the first and second planar transmission line resonators 214A, 214B are patterned on the surfaces of the respective first and second substrates 216A, 216B. In general, conductors can be patterned on a substrate using standard microfabrication processes, which may include, for example, various combinations of material deposition, lithography, and material removal processes.

[0063] In some instances, the first and second planar transmission line resonators 214A, 214B are communicably connected to a control system (e.g., the control system 114 in FIG. 1) via respective feedlines to receive the magnetic resonance control signals from a spectrometer; and transmit the magnetic resonance detection signal to the spectrometer. In some instances, the respective feedlines are capacitively coupled to the respective sets of conductive segments in the respective transmission line resonators. In some instances, the first and second planar transmission line resonators 214A, 214B are connected to the control system under a two-terminal configuration, a four-terminal configuration, or in another manner.

[0064] In some instances, the example microwave resonator device 200 may be enclosed by an RF package. During operation, an EPR sample can be placed in a cavity 204 between the first and second planar transmission line resonators 214A, 214B. Microwave magnetic fields (Bl) generated by the first and second planar transmission line resonators 214A, 214B share a common sample region 220 and are arranged to constructively interfere, generating a highly uniform microwave magnetic field. In some implementations, the volume of the sample region is in a range of 0.5 to 100 microliters (pL), 50 to 200 microliters (pL), or another range that may include larger or smaller volumes. The separation distance 222 between the first and second planar transmission line resonators 214A, 214B can determine the strength and uniformity of the Bl field. In some implementations, the microwave magnetic field (Bl) in the sample region 220 has a direction (e.g., along the Y-axis) perpendicular to the extension direction of the first and second sets of conductors.

[0065] In some instances, the first and second planar transmission line resonators are coupled to each other. By operating the microwave resonator device at a single resonance mode, a first microwave magnetic field generated by the first planar transmission line resonator and a second microwave magnetic field generated by the second planar transmission line resonator constructively interfere with each other in the sample region. The constructive interference between the first and second microwave magnetic fields in the sample region generates an overall control field (e.g., magnetic drive field) in the sample region.

[0066] In some instances, the first and second planar transmission line resonators may be over-coupled, where most of the electromagnetic (EM) energy is dissipated in the external load of the microwave resonator device. In this case, the internal quality factor (Qint) is higher than the external quality factor Qext)- The coupling coefficient, defined by 9 = Q.tntlQ.ext isgreater than 1, and the coupling capacitance is high and the size of the coupling gap is small. The coupling capacitance gap is defined between the branching structure of the feedline and a corresponding transmission line resonator, e.g., 642A, 642B, 644A, 644B. In some instances, the first and second planar transmission line resonators may be under-coupled, where most of the EM energy is dissipated inside the microwaveresonator device. In this case, the internal Quality factoris lower than the external quality factor The coupling coefficient is less than 1, and the coupling capacitance is low and the size of the coupling gap is big. In certain examples, the first and second planar transmission line resonators may be critically coupled, where the EM energy is dissipated equally in both the microwave resonator device and the external impedance load. In this case, the internal quality factor Qtnt) equals the external quality factor Qext). When the first and second planar transmission line resonators are critically coupled, the drive magnetic field generated by the microwave resonator device is at its maximum value; and the coupling coefficient g) is equal to 1. In some instances, the coupling between the first and second transmission line resonators can be tuned, adjusted and otherwise controlled by adjusting the capacitive coupling (e.g., the coupling gaps 642A, 642B, 644A, 644B in the example microwave resonator device 600 shown in FIG. 6) between the feedline and the respective sets of conductive segments of the respective transmission line resonators.

[0067] In some instances, the first and second transmission line resonators 214A, 214B are configured to receive control signals with a 180-degree phase difference to support an odd resonance mode of high microwave field homogeneity. In some instances, the first and second transmission line resonators 214A, 214B are configured to receive control signals with a 0-degree phase difference to support an even resonance mode with a defined spatial microwave field gradient. In some instances, the first and second transmission line resonators 214A, 214B are configured to receive control signals to support both even and odd resonance modes in the sample region. For example, the first and second transmission line resonators 214A, 214B are configured to receive control signals with a phase difference of 90 degrees or another value that is not 0 or 180 degrees.

[0068] In some instances, the first and second transmission line resonators 214A, 214B, the first and second ground planes 212A, 212B can be fabricated on the first and second substrate 216A, 216B using superconducting materials including type 1 or type 2 superconducting materials, low- / High-Temperature Superconductors (LTS / HTS), elemental or alloy, metallic or ceramic, conventional or unconventional, non-exotic or exotic superconducting materials. For example, the first and second transmission line resonators 214A, 214B, the first and second ground planes 212A, 212B may includetitanium (Ti), aluminum (Al), tin (Sn), zinc (Zn), niobium (Nb), niobium nitride (NbN), titanium nitride (TiN), NbsSn, vanadium gallium alloy (VsGa), magnesium boride (MgB2), Yttrium barium copper oxide (YBCO), Bismuth strontium calcium copper oxide (BSCCO), and more. In the case when superconducting materials are used in the first and second planar transmission line resonators 214A, 214B, the example microwave resonator device 200 may be configured such that the static magnetic field (Bo) generated by a primary magnet system (e.g., the primary magnet system 112 in FIG. 1) are parallel to the ground planes 212A, 212B to avoid Bofield inhomogeneity introduced by inherent magnetic screening effects of the superconducting film; and the static magnetic field may be along the extension direction of the planar transmission line resonators 214A, 214B.

[0069] In some instances, the first and second planar transmission line resonators 214A, 214B may be implemented by other planar platforms, including coplanar waveguides, striplines, single microstrip lines, or other specialized designs like a Bow Tie configuration, planar loop gap resonators, lumped element resonators with straight, curved, meandered line or any configuration of inductor and capacitor, or arrays of resonators. In certain instances, depending on the specific resonator type and intended applications, the first and second ground planes 216A, 216B may be configured in another manner. In some instances, the first and second planar transmission line resonators 214A, 214B maybe identical, e.g., having the same number of conductive segments, and conductive segments having the same geometry (e.g., line, width, thickness, etc.), such that the first and second planar transmission line resonators 214A, 214B may have identical intrinsic resonance frequencies. In some implementations, conductive segments of the first planar transmission line resonators 214A are parallel to conductive segments of the second planar transmission line resonators 214B as shown in FIG. 2. In some examples, the conductive segments of the first planar transmission line resonators 214A may not be parallel to the conductive segments of the second planar transmission line resonators 214B, e.g., the conductive segments of the first planar transmission line resonators 214A may extend along the X axis and the conductive segments of the second planar transmission line resonators 214B may extend along the Y axis. In certain instances, the first and second planar transmission line resonators 214A, 214B may have distinct intrinsicresonance frequencies, e.g., the first and second planar transmission line resonators 214A, 214B may be asynchronously tuned. In some instances, coupling gaps (e.g., the coupling gaps 642A, 642B, 644A, 644B in the example microwave resonator device 600 shown in FIG. 6) for coupling the microstrip lines of the first and second planar transmission line resonators 214A, 214B to respective terminals may be the same or different. The first and second planar transmission line resonators 214A, 214B may be implemented, fabricated, and operated as respective components of the example microwave resonator device 504, 600, 1102 shown in FIGS. 5, 6, 11, or in another manner.

[0070] In some implementations, the first and second microwave resonator units 202A, 202B maybe designed, fabricated on separate substrates, tested, and assembled for a target resonance frequency and sample region. The separation distance d 222 can be set based on a target microwave field homogeneity over a target sample region. Coupling parameters (e.g., the coupling gaps between respective terminals of respective sets of conductors in the first and second planar microwave resonator devices 214A, 214B) can be tuned according to the behavior of a single mode of the two-resonator system, e.g., undercoupled, critically coupled, or over-coupled. In this configuration, an electron spin resonance (ESR) sample is physically positioned in the sample region 220.

[0071] In some instances, the microwave resonator device 200 maybe tuned and matched in a similar manner to planar resonators via inductive or capacitive coupling mechanisms and have a variable quality factor (Q) that depends on the internal Q - mostly given by the geometry and material used to fabricate the device - and the coupling strength. In some instances, the quality factor (Q) can be defined as the frequency of the resonator divided by its bandwidth. The total Q, Qtot, is related to an internal quality factor Qint and an external quality factor Qext, e.g., 1 / Qtot= 1 / Qint+ k / Qext, where k is a coupling factor. In some implementations, the internal Qintquantifies the losses intrinsic to the resonator and may be determined by under coupling the device (e.g., k ~ 0) and measuring Qtot. In some implementations, the external quality factor Qextquantifies external losses (e.g., in transmission lines, etc.) and may be determined once Qintis determined. In some instances, the Qtot, Qint, and Qextmay be determined in another manner.

[0072] In some implementations, the two first and second planar transmission line resonators 214A, 214B when assembled, exhibit electromagnetic coupling arising from a spatial overlap of their respective electric and magnetic fields: H1. H20 and E . E2#= 0. To understand the behavior of the example microwave resonator device 200 shown in FIG. 2, an equivalent circuit model that includes mutual inductance or capacitance may be used and shown in FIGS. 3 and 4. The equivalent circuit model 300, 302 in FIG. 3 are analyzed assuming a mutual inductance and the first and second planar transmission line resonators 214A, 214B are identical.

[0073] As shown in FIG. 2, the microwave resonator device 200 is enclosed and supported by a radiofrequency (RF) package 230. In some instances, the RF package 230 provides a housing, electrical connectivity, thermal management, and protection to the microwave resonator device 200. In some instances, the RF package 230 may include metals (e.g., Copper, etc.), metal alloys, ceramics, conductive coatings, or other materials. In some instances, the RF package 230 may include RF components for transmitting control or detection microwave signals (e.g., connectors or ports, amplifiers, filters, mixers, shifters, etc.). In some instances, the first and second transmission line resonator devices are mechanically supported (e.g., pined, clamped, adhered, etc.) on respective stages. In some instances, the separation distance and the relative orientation between the first and second transmission line resonator devices may be controlled by tuning the separation distance between the two stages. In some instances, the RF package 230 may be implemented as shown in FIGS. 14A-14B or in another manner. In some instances, the first and second microwave resonator devices are at least partially separated by vacuum (e.g., below atmospheric pressure, 25 to le-3 Torr, le-3 to le-9 Torr, le-9 to le-12 Torr, or in another pressure range), air, or dielectric material (e.g., rexolite or another type of polymer).

[0074] FIG. 3 includes circuit diagrams showing equivalent circuit models 300, 302 of the example microwave resonator device 200 shown in FIG. 2. The equivalent circuit model 300 represents the first and second planar transmission line resonators having a mutual capacitance. The first planar transmission line resonator 214A can be represented by a first resonator 312A; and the second planar transmission line resonator 214B can berepresented by a second resonator 312B. The first and second resonators 312A, 312B are coupled capacitively which is modeled by a capacitor 314 with a capacitance of Cm. The equivalent circuit model 302 represents the first and second planar transmission line resonators having a mutual capacitance. In this case, the first resonator 312A and the second resonator 312B are also coupled inductively which is modeled by an inductor 316, with a mutual inductance of Lmbetween the inductors of the first and second resonators 312A, 312B. As shown in FIG. 3, each of the two resonators 312A, 312B includes an RLC resonator with a combination of a resistor (R), an inductor (L), and a capacitor (C) to resonate a specific intrinsic resonance frequency. In particular, the first resonator 312A and the second resonator 312B are identical, each including an RLC resonator with a resistor having a resistance of Ro, an inductor having an inductance of Lo, and a capacitor having a capacitance of Co.

[0075] FIG. 4 includes effective circuit diagrams 400, 402, 410, 412 showing modes of operation (Odd" and "Even" modes) of an example microwave resonator device represented by the equivalent circuit models 300, 302 shown in FIG. 3. In some implementations, the first and second resonators 312A, 312B in FIG. 3 are synchronously tuned to resonate at the same resonance frequency. The circuit exhibits symmetry that permits an "Even" and "Odd" mode analysis based on the superposition theorem as shown in FIG.4. The Odd mode represented by a circuit diagram 400 in FIG. 4 corresponds to an RLC resonator with a resistor having a resistance of Ro, an inductor having an inductance of LQ, and a capacitor having a capacitance of 2Cm+ Co. Conversely, the Even mode represented by a circuit diagram 402 in FIG. 4 corresponds to an RLC resonator with a resistor having a resistance of Ro, an inductor having an inductance of Lo, and a capacitor having a capacitance of Co.

[0076] The Odd mode represented by a circuit diagram 410 in FIG. 4 corresponds to an RLC resonator with a resistor having a resistance of Ro, an inductor having an inductance of Lo— Lm, and a capacitor having a capacitance of Co. Conversely, the Even mode represented by a circuit diagram 412 in FIG. 4 corresponds to an RLC resonator with a resistor having a resistance of Ro, an inductor having an inductance of Lo+ Lm, and a capacitor having a capacitance of Co.

[0077] As a result of the mutual inductance between the two identical resonators, theindividual resonance frequencies, <D0= . - , hybridize into two distinct modes. In someV CQLO implementations, the Even mode corresponds to co-directional currents in the first and second resonators 312A, 312B with respect to one another, which can be avoided for EPR applications. In some implementations, the Odd mode corresponds to anti-directional currents in the first and second resonators 312A, 312B with respect to one another which can be tuned and selected for EPR applications. The resonance frequency of each mode for the combined electric (capacitive) and magnetic (inductive) coupling may be calculated from the circuit parameters:Even mode:Odd mode:where Loand Corepresent the inductance and capacitance associated with the respective resonators, while Lmand Cmdenote the mutual inductance and capacitance between the two resonators. The mutual inductance Lmis a geometrical quantity that depends on the separation distance d 222 between the first and second planar transmission line resonators (between circuits Ci and C2) may be defined by the spatial line integralwhere dltand dl2are differential length vector along the circuits Ci and C2. Therefore, the mutual inductance Lmdictating the resulting hybridized resonance frequencies between the two resonators depends on the separation distance d 222. In some implementations, the mutual capacitance Cmis also determined by the separation distance 222.

[0078] FIG. 5 is a block diagram showing aspects of an example resonator unit 500. As shown in FIG. 5, The example resonator unit 500 includes a first microwave balun 502A, a second microwave balun 502B, and a microwave resonator device 504. The example resonator unit 500 is configured to allow the microwave resonator device 504 to operateunder a two-port configuration; selectively operate the microwave resonator device 504 in an odd mode; and communicate with a control system to receive control signals and transfer detection signals. In some instances, the microwave resonator device 504 may be implemented as the microwave resonator device 200 shown in FIG. 2; may be represented by the equivalent circuit models shown in FIGS. 3 and 4; or in another manner. In some instances, the resonator unit 500 may be implemented as the resonator unit 106, 1100 in FIGS. 1, 11, or in another manner. The example resonator unit 500 can include additional or different features, and the features of the example resonator unit 500 may be arranged in the configuration shown or in another configuration.

[0079] In some implementations, the microwave resonator device 504 is a split-planar microwave resonator device including two planar transmission line resonators disposed on two substrates which are oriented parallel to each other. The two planar transmission line resonators are disposed on two surfaces of the respective substrates, and the two surfaces are configured facing each other with a separate distance. The two planar transmission line resonators generate microwave magnetic fields in a sample region. In other words, the two planar transmission line resonators are capacitively and inductively coupled when microwave control signals are supplied. Each planar transmission line resonator of the microwave resonator device 504 contains two physical ports; and thus is a 2-port device from the perspective of the microwave electronics used to control and readout the planar transmission line resonator. Therefore, the microwave resonator device 504 shown in FIG.5 contains four ports 512A, 512B, 514A, 514C; and is, thus, a 4-port device. The ports 512A, 512B are associated with a first planar transmission line resonator, while the ports 514A, 514B are associated with a second planar transmission line resonator.

[0080] In some implementations, the microwave baluns 502A, 502B are configured to interface the 4-port microwave resonator device 504 with a 2-port control system. The first and second microwave baluns 502A, 502B are communicably connected to the microwave resonator device 504. In particular, the first microwave balun 502A includes a first port 522 for receiving microwave control signals from a control system; and second and third ports 524A, 524B which are connected to the port 512A, 514A of the microwave resonator device, respectively, providing the microwave control signals to the two planartransmission line resonators. The second microwave balun 502B includes first and second ports 528A, 528B which are connected to the ports 512B and 514B of the microwave resonator device 504 for receiving microwave detection signals from the first and second transmission line resonators; and a third port 526 for transmitting the microwave detection signals to the control system. In some implementations, the first and second microwave baluns 502A, 502B enable the excitation of the microwave resonator device 504 in the odd mode. For example, the microwave baluns 502A, 502B may include phase shifter devices or components. In some instances, the microwave baluns 502A, 502B may not include phase shifter devices or components; and one of the first and second planar transmission line resonators in the microwave resonator device 504 includes delay lines. The first port 522 of the first microwave balun 502A is connected to a matched source and the third port 526 of the second microwave balun 502B is terminated in a matched load.

[0081] In some instances, mixed-mode scattering parameters (s-parameters) can be defined in terms of the set of 4-port single-ended s-parameters of the microwave resonator device 504:Sdd11= O.SfSii — S13— S31+ S33}Sdc1= O.Sf ^ + ^13—^31—33}Sdd12= 0.5{S12— S14— S32+ S34]Sdc12=0.5{S12+ ^14—^32—^34}Sdd21= 0.5{S21—^23—^41 + ^43} (4)Sdc21= 0.5{S21+ ^23—^41—43}Sdd22=0.5{S22— S24— S42+ S44}Sdc22= 0.5{S22+ ^24—^42—^44}Scd11— 0.5{SX1S13+ S3 x33}(5)Seen = 0.5(544 + S13+ ^31 + ^33}Scd12= 0.5{S12— S14+ S32— 5’34} cci2=0-5{5’12+ S14+ S32+ S34] cd21= 0.5{S21— S23+ S41— S43}Scc21= 0.5{S21+ S23+ S41+ S43}Scd22= 0.5{S22— S24+ S42— S44}SCC22=0.5{S22+ S24+ S42+ S44} where the subscripts ‘c’ and ‘d’ denote common-mode or differential-mode behavior, respectively. In some implementations, the design of the microwave baluns 502A, 502B allows selection of these modes corresponding to excitation of the resonance modes depicted in FIGS. 3 and 4. For example, when the microwave device 504 is operated in a pure differential mode (Sdd'), the ports 512A, 514A are differentially excited and the ports 512B, 514B differentially receive the response. In this case, the odd resonance mode can be selected. In contrast, when the microwave device 504 is operated in a common mode (See), the even resonance mode can be selected.

[0082] In some implementations, the microwave resonator device 504 is operated using a differential stimulus configuration so that the odd resonance mode can be tuned for EPR applications. In other words, under differential mode, the ports 512A, 514A and the ports 512B, 514B simultaneously experience two control signals with a 180-degree phase difference. In some instances, the microwave baluns 502A, 502B may include two phase shifter devices which are associated with the same planar transmission line resonator and configured to cause a 180-degree phase shift between phases of the control signals applied on the two planar transmission line resonators and between the phases of the microwave detection signals received from the two planar transmission line resonators. As depicted in FIG. 5, an unbalanced microwave input is directed into the first microwave balun 502A, which transforms it into balanced outputs with a 180-degree phase difference. Subsequently, these two balanced lines are connected to the ports 512A, 514A of the microwave resonator device 504 to excite the odd resonance mode. The response of themicrowave resonator device 504 is collected from the ports 512B, 514B via the second microwave balun 502B.

[0083] In some instances, the first and second microwave baluns 502A, 502B may be implemented in a variety of ways for narrowband or broadband behavior, including bulk connectorized designs, on-chip fabricated designs, and surface-mounted planar or nonplanar designs or in another manner. In some instances, the first and second microwave baluns 502A, 502B be transformer-based, transmission line-based, lumped element-based, coaxial, waveguide-based, or another type. For example, the first and second microwave baluns 502A, 502B may include Marchand baluns, Lange couplers, Guanella baluns, rat-race couplers, branch-line couplers, bifilar baluns, and others.

[0084] FIG. 6 is a perspective view of an example microwave resonator device 600. As shown in FIG. 6, the microwave resonator device 600 is a split planar microwave resonator device, including a first microwave resonator unit 602A and a second microwave resonator unit 602B which are configured facing each other and spatially separated by a separation distance (d) forming a cavity 652 between the first and second microwave resonator units 602A, 602B. In some implementations, the first microwave resonator unit 602A includes a first planar transmission line resonator 612A which includes an array of conductive segments 626 and a ground plane on a first substrate; the second microwave resonator unit 602B includes a second planar transmission line resonator 612B which includes an array of conductive segments 636 and a ground plane on a second substrate. In some implementations, the first and second planar transmission line resonators 612A, 612B are identical and synchronously tuned. In some instances, the EPR sample can be positioned in the cavity 652 in a sample region 650. The example microwave resonator device 600 can include additional or different features, and the features of the example microwave resonator device 600 may be arranged in the configuration shown or in another configuration.

[0085] The first microwave resonator unit 602A shown in FIG. 6 includes a first terminal 652A and a second terminal 652B. The first and second terminals 652A, 652B, the first transmission line resonator 612A, and the ground plane can define planar transmission line structures on the first substrate. The second microwave resonator unit602B shown in FIG. 6 includes a third terminal 652C and a fourth terminal 652D. The third and fourth terminals 652C, 652D, the second transmission line resonator 612B, and the ground plane can define planar transmission line structures on the second substrate.

[0086] In some implementations, the microwave resonator device 600 may be part of the resonator unit 106 of the example electron spin resonance system 100; and coupled with the control system 114 of the electron spin resonance system 100 for providing electron spin resonance control signals to the microwave resonator device 600 to perform multiple resonance measurements of multiple electron spin centers in the sample region 650 of the microwave resonator device 600. In some instances, the control system 114 may operate the microwave resonator device 600 to perform double resonance measurements of the electron spins in the sample region. For example, the microwave resonator device 600 may be operated to perform Double Electron-Electron Resonance (DEER) spectroscopy; Pulse Electron Double Resonance (PELDOR) spectroscopy, or other resonance spectroscopy. The microwave resonator device 600 may be operated to produce a probe frequency that creates observable coherence that evolves under pairwise coupling of the electron spins; and a pump frequency that refocuses pairwise interactions at varying times to reveal a distribution of coupling strength of the pairwise couplings.

[0087] In some implementations, the example microwave resonator device 600 can be operated according to the operations in the example process 1300 in FIG. 13 to produce a time-varying microwave field in the sample region 650 of the microwave resonator device 600. For example, the microwave resonator device 600 may produce a microwave field at a radio frequency or microwave frequency configured to manipulate electron spins in the sample region 650 between the first and second transmission line resonators 612A, 612B.

[0088] As shown in FIG. 6, the first terminal 652A includes a respective conductor disposed on the first substrate. The first terminal 652A has terminal segments 624A and a feedline 622A galvanically connected to the terminal segments 624A. The terminal segments 624A extend from the feedline 622A toward the first planar transmission line resonator 612A. The first terminal 652A includes sixteen terminal segments 624A, each extending toward a respective conductive segment 626 of the first planar transmission line resonator 612A. In some instances, the first terminal 652A can include two terminalsegments 624A, four terminal segments 624A, eight terminal segments 624A, sixteen terminal segments 624A, thirty-two terminal segments 624A, sixty-four terminal segments 624A, or in general powers of two, according to the number of the conductive segments 626 in the first planar transmission resonator 612A. In some implementations, the terminal segments 624A of the first terminal 652A have a width identical to the width of the conductive segments 626 of the first planar transmission line resonator 612A.

[0089] Similarly, the second terminal 652B includes a respective conductor disposed on the first substrate. The second terminal 652B has terminal segments 624B and a feedline 622B galvanically connected to the terminal segments 624B. The terminal segments 624B extend from the feedline 622B toward the first planar transmission line resonator 612A. The second terminal 652B includes sixteen terminal segments 624B, each extending toward a respective conductive segment 626 of the first planar transmission line resonator 612A. In some instances, the second terminal 652B can include two terminal segments 624B, four terminal segments 624B, eight terminal segments 624B, sixteen terminal segments 624B, thirty-two terminal segments 624B, sixty-four terminal segments 624B, or in general powers of two, according to the number of the conductive segments 626 in the first transmission resonator 612A. In some implementations, the terminal segments 624B of the second terminal 652B have a width identical to the width of the conductive segments 626 of the first planar transmission line resonator 612A.

[0090] In some implementations, the first and second terminals 652A, 652B include branching structures 628A, 628B galvanically connecting the respective terminal segments 624A, 624B to the respective feedlines 622A, 622B. The branching structures 628A, 628B can function as a power divider that divides and delivers the power from an input to the terminal segments 624A, 624B. In some instances, the branching structure 628A, 628B can include successive levels (or division stages). In some instances, the branching structure 628A, 628B can be configured to achieve desirable branch impedances at each division stage. For example, the branching structure 628A, 628B can be designed to match all input impedances of the branches in certain division stages to improve (e.g., increase, maximize, optimize, or otherwise improve) power transfer and reduce signal reflections. In some implementations, the individual branches in each level may have twice the impedance ofthe individual branches in the preceding level. In some implementations, the power dividers can include tapered branch sections, for example, to adjust the lines for impedance matching.

[0091] As shown schematically in FIG. 6, each of the conductive segments 626 in the first planar transmission line resonator 612A includes a respective conductor disposed on a surface of the first substrate. A first end of each of the conductive segments 626 in the first planar transmission line resonator 612A is aligned with a respective terminal segment 624A of the first terminal 652A. Each of the conductive segments 626 is elongated. Each of the conductive segments 626 is capacitively coupled to a respective one of the terminal segments 624A, while a second, opposite end of each of the conductive segments 626 is capacitively coupled to a respective one of coupling segments 624B of the second terminal 652B. In certain instances, the array of conductive segments 626 can include two conductive segments, four conductive segments, eight conductive segments, sixteen conductive segments, thirty-two conductive segments, sixty-four conductive segments, or in general powers of two.

[0092] In some implementations, each of the conductive segments 626 and the ground plane define a microstrip line resonator. In some implementations, the conductive segments 626 in the first planar transmission line resonator 612A can be identical to each other. In some examples, the conductive segments 626 are parallel to each other, with equal spacing between each neighboring pair of the conductive segments 626. Here, "parallel" is used broadly to describe structures that are exactly or substantially parallel, when considered on the structures’ largest length scales. Two structures can be considered parallel, for example, when their neighboring sides, centerlines, or other dominant structural features are parallel or include only insubstantial deviations from parallel (e.g., deviations that do not significantly impact functionality or performance of the device).

[0093] The example conductive segment 626 can be sized based on the wavelength of a desired resonance frequency. For example, the length of the conductive segment 626 (e.g., from the first end to the second opposite end) can be designed to produce a resonance mode around the specified resonance frequency of operation (e.g., a>r= 2TI ■ 10 GHz). Each conductive segment 626 can be a half-wave resonator, a full-wave resonator, or a multi-half- wave resonator. For example, if the desired resonance frequency is A, the conductive segment 626 can have a length of A / 2, A, 3A / 2, 2A, etc.

[0094] The multiple conductive segments 626 can be configured to resonate at the same microwave resonance frequency. In some instances, the conductive segment 626 can be configured to generate a microwave magnetic field with a maximum field intensity at the center of the half-wave segments of the microstrip line resonators, for example, by using a half-wave resonator for each of the conductive segment 626. In some implementations, the conductive segments 626 can be edge-coupled to each other so that the magnetic field generated by each resonator interferes with the magnetic field generated by one or more neighboring conductive segments 626. In some cases, the conductive segments 626 produce an in-plane uniform field in a direction perpendicular to the surface of the first substrate.

[0095] In the example shown in FIG. 6, a coupling gap 642A is defined between the first end of the conductive segments 626 and the respective terminal segments 624A of the first terminal 652A. Similarly, a coupling gap 642B is defined between the second end of the conductive segments 626 and the terminal segments 624B of the second terminal 652B. The coupling gaps 642A, 642B can include vacuum, dielectric material (e.g., sapphire, silicon, quartz, etc.), or a combination of them. The terminal segments 624A in the first terminal 652A and the terminal segments 624B in the second terminal 652B can serve as feedlines coupled to the array of conductive segments 626 via the coupling gaps 642A, 642B. In some instances, during operation, all of the conductive segments 626 experience an electromagnetically equivalent feedline path from a pair of a terminal segment 624A of the first terminal 652A and a respective terminal segment 624B of the second terminal 652B, and the conductive segments 626 of the first transmission line resonator 612A can resonate in-phase at their fundamental frequency. Each conductive segment 626 is configured to resonate at a first intrinsic resonance frequency, and the length of the conductive segments 626 may be an even number of half- wavelengths for the first intrinsic resonance frequency; and the length of the conductive elements 626 maybe an odd number of half- wavelengths for the first intrinsic resonance frequency.

[0096] As shown in FIG. 6, the first and second terminals 652A 652B, and the first planar transmission line resonator 612A each have a planar transmission line structure. Here "planar" is used broadly to describe structures that are substantially larger in one or both planar dimensions (length and width) than in their height dimension. In some instances, a planar structure has a height that is substantially uniform (e.g., compared to the overall length and width of the structure) over its planar extent. In some implementations, the planar transmission line structure can receive an input signal (e.g., electron spin resonance control signals through the first terminal 652A), conduct the signal across the parallel conductive segments 626 in the same direction in the first planar transmission line resonator 612A; and generate a microwave magnetic field in the sample region 650.

[0097] In some implementations, the first and second terminals 652A 652B, the first planar transmission line resonator 612A are configured as superconducting transmission line resonators. The conducting material of the first and second terminals 652A 652B, the first planar transmission line resonator 612A, and ground plane can be made of superconducting material, such as, for example, niobium, niobium titanium, niobium nitride, aluminum, yttrium barium copper oxide (aka, "YBCO"), or another appropriate material. The superconducting materials can be deposited on the substrate by standard deposition techniques. The substrate can be etched or otherwise conditioned based on standard fabrication techniques. In certain instances, the substrate can be made of dielectric material such as, for example, sapphire, silicon, quartz, or another type of nonmagnetic dielectric crystalline material.

[0098] In some instances, the second microwave resonator unit 602B may be implemented identical to the first microwave resonator unit 602A or in another manner. For example, components (e.g., terminals 652C, 652D, feedlines 632A, 632B, terminal segments 634A, 634B, conductive segments 636, branching structures 638A, 638B, and coupling gaps 644A, 644B) of the second microwave resonator unit 602B may be implemented as the respective components of the first microwave resonator unit 602A.

[0099] In some implementations, the sample region 650 of the microwave resonator device 600 is located in the cavity 652 between the conductive segments 626 of the firstplanar transmission line resonator 612A and the conductive segments 636 of the second planar transmission line resonator 612B. The sample region 650 can be a 3-dimensional sample region or another type of volume. In some instances, the microwave magnetic fields generated by the first and second planar transmission line resonators 612A, 612B form a control field in the sample region 650. In some instances, the control field may be uniform across the sample region 650 (e.g., in both amplitude and direction as shown in FIGS. 7C, 8B, 8C, 9B). For example, the sample region 650 can include planes (parallel to the surface) over which the instantaneous magnetic fields generated by the first and second planar transmission line resonator 612A, 612B are homogeneous during operation. In some instances, the sample region 650 may include samples for ESR applications or experiments, or for additional or different applications. In some implementations, the samples can be thin planar samples, for example, Langmuir-Blodgett films or self-assembled monolayer films, polymer films, biological films, etc. Some example applications of the microwave resonator device 600 can include using the Langmuir Blodgett films or self-assembled monolayer films with free radicals for quantum computing, and using the biological films to, for example, label electrons and study membrane bound proteins using ESR. In some implementations, the sample region 650 is a region of given homogeneity interacting with the sample. In some instances, the control field in the sample region 650 may have a defined spatial microwave field gradient, for example when a different single resonance mode is selected.

[0100] In some implementations, the example microwave resonator device 600 and the sample can be positioned in an external, static primary magnetic field (Bo). The primary magnetic field can be parallel to the surfaces of the first and second substrates along the X axis. The primary magnetic field can polarize the electron spins in the sample. The electron spins have one or more resonance frequencies or a distribution of resonant frequencies (or spin precession frequencies) in the primary magnetic field. The resonance frequencies are typically in the GHz range (e.g., microwave frequencies) in ESR applications. In operation, the conductive segments 626, 636 can generate a microwave magnetic field at the resonance frequencies of the electron spins to manipulate the electron spinssimultaneously perpendicular to the extension direction of the conductive segments 626, 636 (e.g., along the X or Z axis).

[0101] In some instances, for optimization of bandwidth, the quality factor of the microwave resonance modes can be controlled by varying the size of the coupling gaps 642A, 642B, 644A, 644B at the ends of each conductive segments 626, 636, provided that the internal quality factor remains significantly higher than the external quality factor. The first and second planar transmission line resonators 612A, 612B are initially designed separately to ensure they share identical and desired intrinsic resonance frequencies and quality factors. In some instances, the second transmission line resonator 612B may have a second, distinct intrinsic resonance frequency; and the first and second intrinsic resonance frequencies of the first and second transmission line resonators 612A, 612B may have a frequency detuning.

[0102] In some instances, the microwave resonator device 600 can convert the electron spin resonance control signals to a microwave magnetic field in the sample region 650. In some implementations, the microwave magnetic field can be homogeneous in a sample region 650, such that the microwave magnetic field is uniform throughout the sample region 650. This microwave magnetic field can be substantially uniform in strength and occupy a small mode volume well matched to the volume of the sample. The microwave magnetic field can be applied to one or more samples in the sample region 650, for example, for pulsed ESR or multi-resonance ESR measurements.

[0103] In the example shown in FIG. 6, the first and second planar transmission line resonators 612A, 612B each includes an array of 16 straight A / 2 microstrip lines. The first and second microwave resonator units 602A, 602B are fabricated on two separate substrates or may be fabricated on the same substrate and further separated in different dies. They are assembled face-to-face, with the extension directions of the microstrip lines on the first and second microwave resonator units 602A, 602B aligned in parallel (e.g., along the X-axis). Ground planes are patterned on the backside of respective substrates. The first and second planar transmission line resonators 612A, 612B are identical, e.g., the microstrip lines in the first and second planar transmission line resonators 612A, 612B having the same length l0of 5150 pm, the same width w of 40 pm, and the same spacing s0between neighboring microstrip lines of 100 pm. In some instances, the microwave resonator device 600 includes an RF enclosure which is configured to fully house the first and second microwave resonator units 602A, 602B and other components. During operation, the microwave magnetic field generated by each of the first and second planar transmission line resonators 612A, 612B constructively interfere at the sample region 650. In some instances, the sample region of the sample region 650 may be up to 100.0 pL or more.

[0104] In some instances, the first and second planar transmission line resonators 612A, 612B of the first and second microwave resonator units 602A, 602B may be different with different number of microstrips, different geometries, different substrate materials, and different intrinsic resonance frequencies. In some instances, the first and second microwave resonator units 602A, 602B may be assembled with a separation distance of a different value. In some instances, the microwave resonator device 600 may be operated under an odd resonance mode by receiving odd excitations that result in a constructive interference of magnetic fields generated by the first and second transmission line resonators; or under an even resonance mode by receiving even excitations that result in a destructive interference of the magnetic fields generated by the first and second transmission line resonators. The odd or even excitations may be introduced in the control signals or may be introduced by internal delay lines (e.g., the delay lines 1122A, 1122B shown in FIG. 11) or external baluns (e.g., the microwave baluns 502A, 502B in FIG. 5) or in another manner.

[0105] FIGS. 7A-7C include field overlays 700, 710, 720 showing spatial distributions of control fields generated by example microwave resonator devices at respective resonance frequencies. In other words, the spatial distribution of the control fields shown in FIGS. 7A- 7C show respective resonance mode structures of the respective microwave resonator devices. In particular, FIG. 7A shows a spatial distribution of a control field generated by a first microwave resonator device that includes a single planar transmission line resonator with 16 microstrip lines at a resonance frequency of 9.66 GHz; and FIGS. 7B and 7C show spatial distributions of control fields generated by a second microwave resonator device that includes two planar transmission line resonators each with 16 microstrip lines for theeven mode at a resonance frequency of 9.45 GHz and for the odd mode at a resonance frequency of 9.88 GHz. The planar transmission lie resonator of the first microwave resonator device is implemented as the second transmission line resonator 612B in FIG. 6. The second microwave resonator device is implemented as the microwave resonator device 600; and the two planar transmission line resonators are implemented as the transmission line resonators 612A, 612B shown in FIG. 6. The microstrip lines of the first and second microwave resonator devices have a length l0of 5150 pm, a width w of 40 pm, and a spacing s0between neighboring microstrip lines of 100 pm. The 16-strip transmission line resonators of the first and second microwave resonator devices are fabricated on 430 pm thick R-cut sapphire substrates with an anisotropic dielectric constant of (10.0078, 10.0078, 9.8643). The two planar transmission line resonators of the second microwave resonator device are separated by a separation distance d of 2 mm. The control fields shown in FIGS. 7A-7C are calculated over a sample region of 2.4 pL (2 mm x 3 mm x 0.4 mm) contained in a borosilicate sample cartridge with a dielectric constant of 4.04. The magnetic field structure and resonance mode frequencies were computed using the eigenmode solver of the HFSS module of AN SYS. As shown in FIG. 7B, a minimal value of the amplitude of the magnetic field is at the center of the sample region. As shown in FIG. 7C, a maximal value of the amplitude of the magnetic field is at the center of the sample region.

[0106] By computing the resonance frequencies associated with the respective modes at different separation distances, a coupling coefficient k between the two planar transmission line resonators in the second microwave resonator device (e.g., the microwave resonator device 600 shown in FIG. 6) can be defined by the following equation:wherein f01and f02are resonance frequencies of the respective planar transmission line resonators before coupling, and fpland fp2are two new resonance frequencies of the respective planar transmission line resonators after coupling.

[0107] In some implementations, a field homogeneity of the control field generated by the microwave resonator device can be used to describe the uniformity in the distribution of the amplitude and direction of the control field in the sample region. Inhomogeneity of the control field may cause errors in pulsed control sequences and reduce signal intensity integrated over the volume of the sample. As shown in FIG. 7A, the control field of the first microwave resonator device with a single planar transmission line resonator varies significantly over the sample region, particularly in the direction perpendicular to the substrate surface (e.g., along the Z-axis). As shown in FIGS. 7C, the second microwave resonator device with two face-to-face planar transmission line resonators can reduce the spatial variation of the microwave field in the sample region, leading to higher fidelity control sequences and enhanced signal intensity.

[0108] FIG. 7D is a plot showing resonance frequency in GHz and coupling coefficient as a function of the separation distance d in mm in the first and second microwave resonator devices shown in FIGS. 7A-7C. The resonance frequency of the first microwave resonator device with a single transmission line resonator (curve 742) does not vary with the separation distance. The resonance frequency of the second microwave resonator device with two face-to-face transmission line resonators operating at an odd resonance mode (curve 744) decreases from 10.15 GHz to 9.9 GHz when the separation distance d increases from 0.8 to 2 mm; and the resonance frequency of the second microwave resonator device operating at an even resonance mode (curve 746) increases from 9.2 GHz to ~9.48 GHz when the separation distance d increases from 0.8 to 2 mm. The coupling coefficient (curve748) decreases from 0.095 to ~0.044 when the separation distance d increases from 0.8 to 2 mm.

[0109] To compare the signal intensities of the first and second microwave resonator devices shown in FIGS. 7A-7C, the spin-cavity coupling parameter that defines the interaction strength of a single spin with the resonator mode can be defined as:wherein y = 2.8024 MHz / G is the electron gyromagnetic ratio, p0is the vacuum permeability, h is the plank constant, a>ris the resonant frequency, {Hmaxl is the maximum of the magnetic field magnitude, \H (r)| is the magnetic field magnitude at position r, and l^n is the mode volume defined as the ratio of the total average energy stored in the resonator to the maximum magnetic energy density. This quantity is a normalized representation of the magnetic field, and it closely mirrors the distribution of the magnetic field.

[0110] FIG. 8A is a perspective 800 of the second microwave resonator device in FIGS. 7B-7C. There are three lines associated with three heights 802A, 802B, 802C from the center of the sample region.

[0111] FIG. 8B includes plots 810, 820 showing the spin-cavity interaction strength in Hz as a function of distance in Y direction across the sample region in the first and second microwave resonator devices in FIGS. 7A-7C. FIGS. 8B displays the variation of g0(r) along the three lines 802A (Z=200 pm), 802B (Z=0 pm), 802C (Z=-200 pm) shown in FIG. 8A along the center of the ESR sample with a separation distance d of 0.8 mm and a sample region of 2.4 pL (3000um by 2000um by 400um) contained in a borosilicate cartridge. Curves 812, 814, 816 corresponding to the positions in the sample region defined by the three lines 802A (Z=200 pm), 802B (Z=0 pm), 802C (Z=-200 pm) show spatial uniformity of the control field in the second microwave resonator device. In particular, the maximum single spin-cavity interaction strength remains fairly constant (~0.1 Hz) when the distance along the Y-axis is in a range -1 and 1 mm. The single spin-cavity interaction strength drops at the edge of the second microwave resonator device along the Y-axis. The spin-cavity coupling in the first microwave resonator device with a single transmission line resonator is non-uniform compared to the second microwave resonator device as depicted in the plot 820. The second microwave resonator device in FIG. 8A shows significantly reduced spincavity coupling variation over the sample region.

[0112] FIG. 8C includes a plot 830 showing the spin-cavity interaction strength in Hz along the Z-axis in the sample region of the second microwave resonator device in FIG. 8A as a function of a height for different separation distances d, and a plot 840 showing the spin-cavity interaction strength in the sample region of the first microwave resonatordevice shown in FIG. 7A as a function of a height to the resonator plane of the first microwave resonator device. The spin-cavity interaction strength along the Z axis perpendicular to the resonator substrate surfaces is depicted from the surface of one resonator to the surface of the other resonator. Three separation distances include 800 pm (curve 832), 1500 pm (curve 834), and 2000 pm (curve 836). When the separation distance between the two planar transmission line resonators reduces, the sample region is reduced and the field homogeneity, where the spin-cavity interaction strength does not significantly vary, can be improved. When the separation distance between the two planar transmission line resonators increases, the sample region increases; and the field homogeneity decreases. Depending on the application, the separation distance may be designed to achieve a target homogeneity over a target sample region. As shown in FIG, 8C, the homogeneity of the second microwave resonator device with a split-planar configuration exceeds that of the first microwave resonator device with a single planar device.

[0113] In addition to increased field amplitude homogeneity, the second microwave resonator device with the split-planar transmission line resonator configuration also provides better uniformity of the direction of the control field. In the situation where the amplitude of the control field generated by a microwave resonator device is uniform, but the direction is not, the device performance becomes susceptible to signal loss due to spin diffusion or spectral diffusion. In these processes a spin state will effectively have moved in the time between excitation and detection, causing a spatially dependent phase to accumulate that leads to signal degradation when integrating the signal over the sample region.

[0114] FIGS. 9A-9B show cross-sectional view of the control fields along the YZ plane at X=0 in the first microwave resonator device 700 shown in FIG. 7A and the second microwave resonator device 710, 720 in FIG. 7B-7C. The separation distance in the second microwave resonator device is 1 mm. 1W RF excitation within a cross-section of the EPR sample is applied on the first and second microwave resonator devices. As shown in FIG. 9A, the control field of the first microwave resonator device includes a combination of vertical and horizontal components over a significant portion of the sample region. Incontrast, the control field of the second microwave resonator device in FIG. 9B is well- aligned over nearly the entire sample region.

[0115] FIG. 10A includes a plot 1000 showing single-ended scattering parameters (S- parameters) in dB as a function of frequency in GHz on the microwave resonator device 600 shown in FIG. 6. The separation distance between the first and second microwave resonator units 602A and 602B is 1 mm. Each of the first and second microwave resonator units 602A, 602B includes a planar transmission line resonator device with 16 microstrip lines patterned on respective substrates. The capacitive coupling gaps between the respective sets of terminal segments and the respective microstrip lines are 200 pm. As shown in FIG. 10A, both even and odd resonance modes are present with a 6 dB transmission loss which is a minimum value achievable for each mode, corresponding to a factor of two reduction in signal intensity and conversion efficiency (measured in G / W . When microwave baluns are used, a single resonance mode (odd or even) may be selected with no reduction in transmission. Curve 1002 shows the Sil parameter of the microwave resonator device; curve 1004 represents the S21 parameter of the microwave resonator device; curve 1006 represents the S34 parameter of the microwave resonator device; curve 1008 represents the S44 parameter of the microwave resonator device; curve 1012 represents the S32 parameter of the microwave resonator device; and curve 1010 represents the S42 parameter of the microwave resonator device.

[0116] FIG. 10B includes a plot 1020 showing mixed-mode s-parameters in dB as a function of frequency in GHz for differential (odd) and common (even) excitation and response using microwave baluns on the microwave resonator device 1100 shown in FIG. 11. Each resonance mode can be selected individually with no transmission loss. For comparison, the s-parameters for a single 16-strip microstrip line resonator are also displayed. Curve 1026 shows the S21 parameter of the microwave resonator device with a single planar transmission line resonator; and curve 1028 represents the Sil parameter of the microwave resonator device with a single planar transmission line resonator. The Quality factors of distinct modes can be different. In some implementations, a split-planar microwave resonator device with two transmission line resonator devices facing each other can provide a higher Quality factor for the odd mode than that of a singletransmission line resonator, while a lower quality factor for the even mode than that of a single transmission line resonator. In the example shown in FIG. 11, given a quality factor of 350 for a single 16-strip device, the quality factors of a split-planar microwave resonator device operating at the even and odd resonance modes are 190 and 1800, respectively.

[0117] FIG. 11 is a perspective view of an example resonator unit 1100. As shown in FIG. 11, the example resonator unit 1100, which may be implemented as the resonator unit 106 in FIG. 1, includes a microwave resonator device 1102 communicably coupled to two microwave power dividers 1104A, 1104B. In particular, the microwave resonator device 1102 includes a first microwave resonator unit 1112A and a second microwave resonator unit 1112B, each of which include a planar transmission line resonator. The two planar transmission line resonators are spatially configured such that the two planar transmission line resonators are facing each other and spaced apart by a separation distance d. In some instances, the microwave resonator device 1102 may be implemented as the microwave resonator device 600 shown in FIG. 6. A first microwave balun 1104A is connected to a first terminal 1124A of the first microwave resonator unit 1112A and a first terminal 1124C of the second microwave resonator unit 1112B; and a second microwave balun 1104B is connected to a second terminal 1124B of the first microwave resonator unit 1112A and a second terminal 1124D of the second microwave resonator unit 1112B. In some implementations, microwave power dividers 1104A, 1104B are configured to allow the 4- port microwave resonator device 1102 to interface with a 2-port control system; and allow a single resonance mode (odd or even) to be selected and supported for full power transmission.

[0118] The example microwave resonator device 1102 shown in FIG. 11 is configured for installation in a magnetic resonance system (e.g., the magnetic resonance system 100 shown in FIG. 1) that generates a principal magnetic field Bo. The principal magnetic field Bocan be a static magnetic field that polarizes a spin ensemble in the sample residing at the sample region 1130. The microwave resonator device 1102 can be oriented in the principal magnetic field Bosuch that the first and second planar transmission line resonators extend parallel to the principal magnetic field Bo.

[0119] In some aspects of operation, the sample can be positioned between the first and second microwave resonator units 1112A, 1112B in the sample region 1130. The sample can be, for example, a magnetic resonance sample that includes an ensemble of electron spins. The principal magnetic field Bocan polarize the spins in the sample. The spins have a resonance frequency (or spin precession frequency) in the principal magnetic field Bo. The resonance frequency is typically in the MHz or GHz range (radio or microwave frequencies) in magnetic resonance applications. In operation, the first and second planar transmission line resonators are fed by the microwave power dividers 1104A, 1104B and generate a microwave field at their resonance frequency. The time-varying control field can be generated in the sample region 1130 and tuned to the resonance frequency of the spins in the sample region 1130, for instance, to manipulate the spins.

[0120] In some aspects of operation, the microwave signal is fed into the microwave power dividers 1104A, 1104B at their respective inputs. The microwave power dividers 1104A, 1104B are each configured to split the microwave signal to a pair of unbalanced microwave signals in two respective branches 1126A / 1126B, 1128A / 1128B. The signals are then passed through the 180-degree delay lines 1122A, 1122B where they can be converted into a pair of balanced microwave signals.

[0121] Each of the first terminal 1124A and the second terminal 1124B of the first microwave resonator unit 1112A includes a feedline that is different from that of the first terminal 1124C and the second terminal 1124D of the second microwave resonator unit 1112D. In particular, the feedline of the first terminal 1124A includes a first delay line 1122A galvanically coupled to a first branching structure which are capacitively coupled to first ends of a first plurality of microstrip resonators of the first microwave resonator unit 1112A. The feedline of the second terminal 1124B includes a second delay line 1122B galvanically coupled to a second branching structure which are capacitively coupled to second ends of the first plurality of microstrip resonators of the first microwave resonator unit 1112A. As shown in FIG. 11, the first and second delay lines 1122A, 1122B both extend along the X axis and have two turns. In some instances, the delay lines 1122A, 1122B can have another shape. In some cases, the turns can be rounded turns (e.g., having a radius) or angled turns (e.g., at right angles, as shown), or the turns can have another shape. In somecases, the delay lines 1122A, 1122B may be extended in different directions e.g., along the Y axis. In some instances, the respective delay lines 1122A, 1122B and the power dividers 1104A, 1104B can form respective microwave baluns.

[0122] In some aspects of operation, the microwave power dividers 1104A, 1104B drive the first and second plurality of microstrip resonators through the capacitive gap at the ends of the first and second plurality of microstrip resonators between respective branching structures and the first and second plurality of microstrip resonators. The microwave power dividers 1104A, 1104B are symmetrically arranged on opposite sides of the first and second plurality of microstrip resonators. In the example shown, the symmetric two-port arrangement satisfies the impedance matching condition over a large range of the gap size which is used for quality factor adjustment. Each of the delay lines 1122A, 1122B can introduce a 180-degree phase difference in even excitations received at the respective pairs of terminals 1124A / 1124C and 1124B / 1124D. In particular, the delay line 1122A can introduce a 180-degree shift to the phase of the microwave signal that is fed into the first plurality of microstrip resonators, relative to the phase of the microwave signal that is fed into the second plurality of microstrip resonators. Similarly, the delay line 1122B can introduce a 180-degree shift to the phase of the microwave signal that is fed into the first plurality of microstrip resonators, relative to the phase of the microwave signal that is fed into the second plurality of microstrip resonators. As such, the phase shift produced by the delay line 1122A compensates for the phase shift produced by the other delay line 1122B. The same phase shift can be introduced by the delay lines 1122A, 1122B into the detection signals.

[0123] In some aspects of operation, the first and second plurality of microstrip resonators are simultaneously excited to support an odd resonance mode of high microwave field homogeneity. The first and second plurality of microstrip resonators can be excited differentially and carry the same current distributions in opposite directions. In such instances, the microwave magnetic fields generated by the first and second plurality of microstrip resonators constructively add in the sample region 1130. When operated as half-wavelength resonators, the current over the length of the first and second plurality of microstrip resonators has a sinusoidal distribution. In such instances, the microwavemagnetic field generated by the first and second plurality of microstrip resonators is at a maximum in the sample region 1130 where the sample resides. In the example shown, the direction of the magnetic field generated by the first and second plurality of microstrip resonators is oriented in the Y-direction (perpendicular to the XZ-plane). Thus, the spin ensemble in the sample experiences microwave-frequency magnetic field that is primarily oriented in the Y-direction, which is perpendicular to the principal magnetic field Bo(oriented in the X-direction).

[0124] In some aspects of operation, the first and second plurality of microstrip resonators may be simultaneously excited to support an even resonance mode of a defined spatial microwave field gradient, for example, by receiving an odd excitation at the respective pairs of terminals 1124A / 1124C and 1124B / 1124D. In this case, the delay lines 1122A, 1122B may be configured to compensate for the existing 180-degree phase difference in the phases of the control signals at the respective pairs of terminals 1124A / 1124C and 1124B / 1124D, generating a 0-degree phase difference to the microwave signals in the first and second plurality of microstrip resonators. In some instances, the respective pairs of terminals 1124A / 1124C and 1124B / 1124D include connectors or other RF components to connect to the respective microwave power dividers 1104A, 1104B.

[0125] In some instances, the example resonator device 1102 can be operated to produce a time-varying control field in the sample region 1130. For example, the resonator device 1102 may produce a control field configured to manipulate spins in the sample region 1130. In some instances, the control field is formed by coupling a first microwave magnetic field generated by the first microwave resonator unit 1112A and a second microwave magnetic field generated by the second microwave resonator unit 1112B. In some instances, the example resonator device 1102 can be operated to produce a detection signal. The detection signal can be produced by a voltage induced across the first and second plurality of microstrip resonators by precession of spins in the sample region 1130. For example, the spins can inductively couple to the resonators as the spins precess in the principal magnetic field Bo. The first and second plurality of microstrip resonators can transfer the detection signal to the feeds 1132A, 1132B of the microwave power dividers1104A, 1104B. The feeds 1132A, 1132B can transfer the detection signal to an external system (e.g., a control system), where it can be detected, recorded, and further processed.

[0126] In some instances, the microwave power dividers 1104A, 1104B may be implemented as a narrowband microwave balun which includes a coaxial cable divider with its branches connected to two transmission lines with different length, creating a 180- degree phase difference. The initial portion of the divider is a coaxial cable with a characteristic impedance of Zoi=5O £1. This cable connects to a segment of coaxial cable with a characteristic impedance of Zo2=35 £1, having a length equivalent to a quarter wavelength (X / 4) at 9.6 GHz. Subsequently, it bifurcates into two 50 £1 coaxial cables, which extend to terminals of the first and second microwave resonator units 1112A, 1112B.

[0127] FIG. 12A is a plot 1200 showing S-parameters of the microwave resonator device 1102 shown in FIG. 11 as a function of frequency in GHz. The separation distance d between the two 16-strip microstrip line resonators is 2.5 mm, and all capacitive coupling gaps are 200 pm. As shown in FIG. 12A, the microwave resonator device 1102 with microwave power dividers 1104A, 1104B demonstrates a selection of the odd resonance mode at 9.7535 GHz and suppression of the even resonance mode at 9.0755 GHz. Curve 1202 represents the Sil parameter and curve 1204 represents the S21 parameter. The residual presence of the even mode can be attributed to the tolerance of the 180-degree phase shift in the design, which can be mitigated by fine-tuning the electrical length of the delay lines 1122A, 1122B.

[0128] FIG. 12B shows current distribution over the first terminals 1124A and 1124C of first and second microwave resonator units 1112A, 1112B in the microwave resonator device 1102. The current distribution demonstrates a 180-degree phase difference between the microwave signals to the respective planar transmission line resonators of the first and second microwave resonator units 1112A, 1112B. The phase difference is introduced by the delay line 1122A of the first terminal 1124A of the first microwave resonator unit 1112A. In some instances, a slight difference in phase offset from the ideal 180 degrees may exist which may cause some residual response in the even resonance mode.

[0129] FIG. 12C shows a distribution of a control field in the sample region 1130 when the microwave device 1102 is operating under an odd resonance mode at 9.7535 GHz. As shown in FIG. 12C, a single-mode homogeneous microwave field over a relatively large EPR sample region can be achieved in the sample region 1130.

[0130] FIG. 13 is a flow chart showing aspects of an example process 1300 for operating a microwave resonator device in an EPR measurement. The example process 1300 can be used for performing an electron spin resonance process by operation of a microwave resonator device. In some implementations the microwave resonator device is a split planar microwave resonator device with two planar transmission line resonators facing each other and separated by a separation distance. In some instances, microwave fields generated by the two planar transmission line resonators in the microwave resonator device may be along planes parallel or perpendicular to each other. In some implementations, the microwave resonator device maybe implemented as the example microwave resonator devices 200, 504, 600, 1102,1500, 1600, 1700, 1801, 1900, 2204 in FIGS. 2, 5, 6, 11, 15A-15B, 16, 17A-17B, 18, 19A, 22, or another type of resonator device.

[0131] In some instances, the microwave resonator device may be configured to provide a high filling factor, high sensitivity, and high field homogeneity for 2-dimensional (2D) samples, pseudo 2D samples, or 3-dimensional (3D) samples. The operations of the example process 1300 may be performed by operation of the electron spin resonance system 100 in FIG. 1. The example process 1300, individual operations of the process 1300, or groups of operations may be iterated or performed simultaneously to achieve a desired result. In some cases, the example process 1300 may include the same, additional, fewer, or different operations performed in the same or a different order.

[0132] In some implementations, modulated pulses are used in multiple resonance measurements. The modulated pulses are applied at several independent and distinct carrier frequencies to create and measure the evolution of multi-spin correlated states over a large spectral bandwidth. In some instances, to minimize undesirable measurement artifacts generated by interference between frequency channels, pulse bandwidths may be designed to have minimal spectral overlap between channels. In certain instances, frequency channels may be implemented in a magnetic resonance spectrometer either as amultiplexed signal transmitted through a single high-bandwidth hardware channel, or as a set of signals with distinct carrier frequencies transmitted through separate hardware channels. In some instances, a combination of the two approaches in a single system may be used. In some implementations, one or more of the operation frequencies are generally assigned as an observer frequency for measuring and demodulating detectable spin coherence. In some instances, the corresponding carrier frequencies may be demodulated by operation of a detection system. The mode structure of the microwave resonator device is used to transmit multiple resonance pulses to a spin system and detect the resulting spin signal which may have at least one of two characteristics: a single resonance mode with sufficient bandwidth to transmit and detect signals at all carrier frequencies simultaneously; or multiple resonance modes that each correspond to one or more carrier frequencies to be used in the pulse sequence.

[0133] At 1302, a sample is positioned at a sample region of the microwave resonator device. In some instances, a sample containing an ensemble of electron spins can be placed in a static, external magnetic field, and the external magnetic field can (at least partially) polarize the ensemble and define a resonance frequency of the electron spins. The sample can be positioned in a sample region of the microwave resonator device (e.g., the sample region 220, 650, 1130, 1520, 1650, 1750, 1850, 1950 in the cavity defined by the separated first and second planar transmission line resonators). In some instances, the geometrical parameters and material properties of the microwave resonator device can be designed according to the electron spin systems to be measured. For example, a sample may be a biological sample (e.g., a blood sample, a urine sample, a saliva sample, a sweat sample, or another type of biological sample). In some implementations, the samples can be thin planar samples, for example, Langmuir-Blodgett films or self-assembled monolayer films, polymer films, biological films, etc. In some instances, a sample may be preprocessed, e.g., attaching molecules containing paramagnetic centers as spin labels to specific sites on the biomolecule of interest.

[0134] In some implementations, multiple resonance measurements are used in pulsed EPR to examine the nature of multi-spin coupling networks in samples containing multiple unpaired electron spins. In contrast to single resonance measurements, microwave pulsesare applied in a sequence at multiple frequencies across the spin resonance spectrum to create correlated multi-spin states whose evolution under the coupling network is then monitored. The most common class of multiple resonance measurements are double resonance (DEER or PELDOR) measurements that examine pairwise interactions of electron spins. A series of pulses at two or more distinct frequencies are applied to the microwave resonator device. The multiple frequencies include a 'probe' frequency that creates observable coherence that evolves under pairwise couplings and is detected; and a pump frequency that that serves to refocus pairwise couplings at varying times to reveal a distribution of coupling strengths of the pairwise couplings.

[0135] At 1304, two or more frequency channels are defined as a set of modulated pulses with distinct carrier frequencies. In some implementations, the carrier frequency can be in the microwave frequency, e.g., in a range of 2 to 90 GHz. In some instances, the carrier frequencies of the pulsed microwave signal are determined according to one of the multiple microwave resonance modes of the resonator device. For example, if the microwave resonator device has multiple resonance frequencies in a range of 9-10 GHz, the carrier frequency of the pulsed microwave signal may be in the same range. A set of pulses with distinct carrier frequencies can be modulated; and modulated pulses define respective frequency channels.

[0136] At 1306, the frequency channels are assigned to one or more control hardware channels. The control system 114 can generate a hardware control sequence corresponding to the modulated pulses; and corresponding hardware control signals of the modulated pulses are determined according to the frequency and bandwidth of hardware channels in the computer and signal processing unit 102, e.g., DAC (digital to analog converter) channels, ADC (analog to digital converter) channels, DIO (digital input / output) channels, transmitter and receiver of the spectrometer 104, and possibly other control hardware channels. For example, a respective control hardware channel needs to have a sufficient bandwidth to cover a respective pulse bandwidth. Corresponding hardware control signals for controlling output of respective control hardware channels can be generated, by operation of the control system 114.

[0137] At 1308, the frequency channels are assigned to one or more resonance modes of the microwave resonator device. In some instances, the resonance modes need to have sufficient bandwidths to cover the pulse bandwidths of the pulses in the pulse sequence.

[0138] In some instances, the pulsed microwave signal is generated externally (e.g., external to the microwave resonator device) and provided to the microwave resonator device through one or more leads on the microwave resonator device. For example, the pulsed microwave signal can be generated by external electronics that are connected to the terminals of the microwave resonator device by operation of the control systemll4 of the electron spin resonance system 100 in FIG. 1. As an example, the pulsed microwave signal can be received at a first pair of terminals 512A / 514A, 652A / 652C, 1124A / 1124C and further delivered to the microwave resonator devices 504, 600, 1102 shown in FIGS. 5, 6, 11.

[0139] The pulsed microwave signal is provided to the two planar transmission line resonators of the microwave resonator device. In some implementations, a phase difference of 180 degrees between the pulsed microwave signals received at the two planar transmission line resonators is introduced. In some instances, a phase difference can be introduced using a delay line (e.g., the delay line 1122A of the microwave resonator device 1102 in FIG. 11) as part of the terminal of the microwave resonator device, a phase shifter in a microwave balun or an electrical cable (e.g., coaxial cable) connected to the terminals, or in another manner. When each of the two planar transmission line resonators includes multiple microstrip line resonators, the pulsed microwave signal can be delivered in-phase to each of the multiple microstrip line resonators of the same planar transmission line resonator. In this case, all of the multiple microstrip line resonators in the same planar transmission line resonator can simultaneously receive the same signal with a common phase at each location on the conductive segments. As such, the phase of the pulsed microwave signal on each conductive segment in the same planar transmission line resonator can be substantially identical at each instant in time; and the phases of the pulsed microwave signals on the two planar transmission line resonators can be offset by 180 degrees at each instant in time. In some implementations, the phase difference allows a selection of the odd mode and operation of the microwave resonator device under the oddmode; or a selection of the even mode if desired to obtain a microwave field gradient. In some instances, the microwave resonator device may not include a delay line or connected to a phase shifter; and in some examples, the microwave resonator device may include a delay line or connected to a phase shifter for introducing a phase difference of a different value.

[0140] In some implementations, communicating the pulsed microwave signal from the first pair of terminals to a second pair of terminals (e.g., the terminals 512B / 514B, 652B / 652D, 1124B / 1124D as shown in FIGS. 5, 6, 11) across the two planar transmission line resonators can create a single resonance mode in a cavity confined between the two planar transmission line resonators. The two planar transmission line resonators are configured to generate microwave magnetic fields (e.g., drive magnetic fields) in a sample region within the cavity to allow exchange of magnetic field energy at the resonance frequency according to the pulsed microwave signal received. In some instances, the two planar transmission line resonators may have the same resonance frequency with or without a small amount of detuning, the different microwave resonance modes and frequency separates may be introduced to the sample region by tuning the design parameters of the coupling transmission line resonator and the coupling gaps. In some instances, the two planar transmission line resonators may have different resonance frequencies.

[0141] For example, the two planar transmission line resonators of the microwave resonator device can convert the pulsed microwave signal to a microwave magnetic field in the sample region. The microwave magnetic field is generated over the sample region of the microwave resonator device (e.g., between the two planar transmission line resonators). In some implementations, the microwave magnetic field can be in-plane homogeneous in a sample region (e.g., a planar sample region), such that the microwave magnetic field is uniform in planes crossing the sample region. This microwave magnetic field can be substantially uniform in strength and occupies a small mode volume well matched to the volume of the sample. The generated microwave magnetic field can be applied to one or more samples in the sample region, for example, for pulsed ESR.

[0142] In some instances, the microwave magnetic field at multiple distinct carrier frequencies can be used to manipulate the electron spins in the sample region. The resonance frequencies of the magnetic field produced by the microwave resonator device can be designed, tuned, or otherwise controlled according to the resonance frequencies of the electron spins in the sample, and the design parameters of the microwave resonator device (e.g., width of coupling gaps, electrical length of conductors, delay length, etc.). In some implementations, the duration and power of the microwave magnetic field can be specified to rotate the electron spins by a particular angle. In some instances, there may be electron spins that have different resonance frequencies in a given sample, and the multiple frequencies of the magnetic field can be tuned to simultaneously detect EPR signals from different types of paramagnetic centers or from different orientations of the same type of paramagnetic center in a sample. In this case, the pulsed microwave signal communicated to the microwave resonator device may include a third resonance frequency component, which can be used to generate a microwave magnetic field at the third, distinct resonance frequency to interact with the different types of paramagnetic centers or the same type of paramagnetic center with different orientations.

[0143] At 1310, at least one of the defined frequency channels is designated as an observe frequency. In some instances, the magnetic resonance detection signal, e.g., electron spin signals, from all resonance modes maybe received and detected simultaneously. In some implementations, the magnetic resonance detection signal at the observe frequency from the microwave resonator device can be demodulated by operation of the spectrometer 104. In some instances, during the multiple resonance measurement, the demodulated magnetic resonance detection signals from all resonance modes may be processed in parallel. The demodulated magnetic resonance detection signal can be processed for measurement, for pulse transient control and correction, or for other purposes.

[0144] FIGS. 14A-14B are schematic diagrams showing an example resonator unit 1400. As shown in FIG. 14A-14B, the example resonator unit 1400 includes a microwave resonator device enclosed in a RF package 1402. In particular, the microwave resonator device includes a first microwave resonator unit 1412 and a second microwave resonatorunit 1422, each of which include a planar transmission line resonator. The two planar transmission line resonators are spatially configured such that the two planar transmission line resonators are oriented in parallel with each other and facing each other and are spaced apart by a separation distance d. In some instances, the microwave resonator device may be implemented as the microwave resonator device 600, 1102 shown in FIGS. 6, 12 or in another manner.

[0145] As shown in FIG. 14, the first microwave resonator unit 1412 is mechanically clamped on a first stage 1416 by a first pair of clamps 1414; and the second microwave resonator unit 1422 is mechanically clamped on a second stage 1426 by a second pair of clamps 1424. The first microwave resonator unit 1412 is also electrically grounded to the first stage 1416 through a first ground plane; and the second microwave resonator unit 1422 may be electrically grounded to the second stage 1426 through a second ground plane. In some instances, the first and second microwave resonator units 1412, 1422 may be in thermal contact with the first and second stages 1416, 1426. The orientation of the first and second microwave resonator units 1412, 1422 and the separation distance d can be adjusted by the physical dimensions of the first and second stages 1416, 1426, the clamps 1414, 1424, and other components of the RF package 1402. The separation of the first and second microwave resonator units 1412, 1422 defines a cavity and a sample region where a sample can be placed. In some instances, the RF package 1402 may include RF connectors, mechanical fasteners, metal plates, windows, alignment pins, etc.

[0146] FIGS. 15A-15C include a side view, perspective view, and top view of an example microwave resonator device 1500. As shown in FIGS. 15A-15C, the microwave resonator device 1500 is a split-planar microwave resonator device which includes a first microwave resonator unit 1502A and a second microwave resonator unit 1502B. The first microwave resonator unit 1502A includes a first planar transmission line resonator 1514A and a first ground plane 1512A disposed on a first substrate 1516A; and the second microwave resonator unit 1502B includes a second planar transmission line resonator 1514B and a second ground plane 1512B disposed on a second substrate 1516B. In particular, the first transmission line resonator 1514A is deposited on a first surface of the first substrate 1516A; and the first ground plane 1512A is disposed on a second, opposite surface of thefirst substrate 1516A. The second transmission line resonator 1514B is deposited on a first surface of the second substrate 1516B; and the second ground plane 1512B is disposed on a second, opposite surface of the second substrate 1516B. In some instances, the microwave resonator device 1500 may be operated according to the operations in the example process 1300 or in another manner.

[0147] In some instances, the microwave resonator device 1500 can provide sensitivity enhancement of planar devices due to small mode volume and high filling factor. The device performance for relatively large samples (~ 1 pL to 100 pL) is the same as for a single planar resonator, with identical requirements of sample placement and limitations on microwave field homogeneity. In some instances, the microwave resonator device 1500 can be operated and optimized for relatively small samples (< 1 pL) or thin-film samples.

[0148] As shown in FIGS. 15A-15B, the first and second microwave resonator units 1502A and 1502B are spatially arranged and assembled such that the first and second substrates 1516A, 1516B are oriented parallel to each other. Two planar substrates can be considered parallel, for example, when they are exactly parallel or substantially parallel, which may include deviations that do not significantly impact functionality or performance of the microwave resonator units. The first and second planar transmission line resonators 1514A and 1514B are facing each other and spaced apart by a separation distance 1522 (d). In some implementations, the separation distance 1522 is in a range of 0.5-3 mm. The example microwave resonator device 1500 can include additional or different features, and the features of the example microwave resonator device 1500 may be arranged in the configuration shown or in another configuration. For example, each of the first and second substrates 1516A, 1516B may include terminals, delay lines, coupling networks, or other components, through which the first and second transmission line resonators 1514A, 1514B can be connected to signal lines (e.g., coaxial cables) or electrical devices (e.g., connectors connected to transmitter / receiver circuitry 1822A / 1822B, quadrature hybrids 2202A, 2202B, or other microwave devices). In some implementations, the terminals are capacitively coupled to the respective sets of conductors in the first and second planar transmission line resonators 1514A, 1514B.

[0149] In some implementations, the example microwave resonator device 1500 shown in FIG. 15A-15C is a crossed split-planar microwave resonator device. As shown in FIGS. 15B-15C, the first planar transmission line resonator 1514A is a Y-resonator which includes conductors extending along the Y-axis. During operation for example when control signals are applied to the first planar transmission line resonator 1514A, the first planar transmission line resonator 1514A can generate a first microwave magnetic field along the Z axis in the sample region, e.g., Biz. The second planar transmission line resonator 1514B is a Z-resonator which includes conductors extending along the Z-axis perpendicular to the Y axis. During operation for example when the control signals are applied to the second planar transmission line resonator 1514B, the second planar transmission line resonator 1514B can generate a second microwave magnetic field along the Y axis perpendicular to the Z axis in the sample region, e.g., Bly. The generated microwave magnetic fields, e.g., Blz and Bly, are spatially orthogonal.

[0150] In some implementations, the first and second planar transmission line resonators 1514A, 1514B share a common sample region 1520, e.g., the first microwave magnetic field along the Z axis, Blz, generated by the Y-resonator and the second microwave magnetic field along the Y axis, Bly, generated by the Z-resonator coexist in the sample region 1520. An EPR sample residing in the sample region 1520 between the first and second microwave resonator units 1502A, 1502B, during the operation of the microwave resonator device 1500, can simultaneously experience Bl fields generated by the Y- and Z-resonators. In some instances, a static external magnetic field Bois oriented at a 45-degree angle from both the Blyand Blzorientations, bisecting them. In some instances, the orientation of the static magnetic field Bomay be configured according to the conductive materials used in the first and second microwave resonator units 1502A, 1502B or according to another design parameter. For example, when normal metal materials are used in the first and second microwave resonator units 1502A, 1502B, the microwave resonator device 1500 can be configured such that the static magnetic field Bocan be oriented along the X axis. When superconducting materials are used in the first and second microwave resonator units 1502A, 1502B, the microwave resonator device 1500 can be configured such that the static magnetic field (Bo) can be parallel to the ground planes (e.g.,along the YZ plane) to avoid Bofield inhomogeneity introduced by inherent magnetic screening effects of the superconducting film. In some instances, aligning the static magnetic field (Bo) as close to parallel with the long dimensions of both of the first and second planar transmission line resonators 1514A, 1514B can reduce the induced losses due to vortex motion. As shown in FIG. 15C, the static magnetic field Bois oriented along the YZ plane having a direction that forms a 45-degree angle relative to the Y or Z axis can reduce or otherwise minimize vortex losses for both of the first and second microwave resonator units 1502A, 1502B.

[0151] In some implementations, the first and second planar transmission line resonators 1514A, 1514B are arranged to generate magnetic fields that are decoupled from one another. The magnetic fields generated by the first and second planar transmission line resonators 1514A, 1514B are orthogonal, e.g.,=0; and the electric fields generated by the first and second planar transmission line resonators 1514A, 1514B are orthogonal, e.g., E1. E2= 0. In some implementations, this is achieved by orienting the extension directions of the conductors of the first and second planar transmission line resonators 1514A, 1514B perpendicular to one another. In some instances, the strength and uniformity of the B field in the sample region associated with each of the first and second planar transmission line resonators 1514A, 1514B are determined by the separation distance 1522 and the placement of the EPR sample within the sample region 1520 in the cavity 1504. The uniformity of the B field over all space is independent of the separation distance 1522 since the first and second planar transmission line resonators 1514A, 1514B operate independently.

[0152] In some instances, each of the first and second planar transmission line resonators 1514A, 1514B includes one or more conductors. For example, the first planar transmission line resonator 1514A may include a first set of conductors configured as an array of conductive segments (e.g., the conductive segments 1626 of the first transmission line resonator 1612A shown in FIG. 16); and the second transmission line resonator 1514B may include a second set of conductors configured as an array of conductive segments (e.g., the conductive segments 1636 of the second transmission line resonator 1612B shown in FIG. 16). In the example shown, the conductors that form the first and second planartransmission line resonators 1514A, 1514B are patterned on the surfaces of the respective first and second substrates 1516A, 1516B. In general, conductors can be patterned on a substrate using standard microfabrication processes, which may include, for example, various combinations of material deposition, lithography, and material removal processes.

[0153] In some instances, the first and second planar transmission line resonators 1514A, 1514B can be communicab ly connected to a control system (e.g., the control system 114 in FIG. 1) via respective feedlines to receive magnetic resonance control signals from a spectrometer; and transmit magnetic resonance detection signal to the spectrometer. In some instances, the respective feedlines are capacitively coupled to the respective sets of conductive segments in the respective transmission line resonators. In some instances, the terminals and feedlines may be configured as the respective components shown in FIGS. 17A-17B, 18, 19A, 22. In some instances, the first and second planar transmission line resonators 1514A, 1514B are connected to the control system under a two-terminal configuration, a four-terminal configuration, or in another manner. In some instances, the example microwave resonator device 1500 may be enclosed by an RF package.

[0154] In some instances, the first and second planar transmission line resonators 1514A, 1514B may be over-coupled, where most of the electromagnetic (EM) energy is dissipated in the external load of the microwave resonator device 1500. In this case, the internal quality factor (Qint) is higher than the external quality factor {Qext}. The coupling coefficient, defined by g =is greater than 1, and the coupling capacitance is high; and the size of the coupling gap is small. The coupling capacitance gap is defined between the branching structure of the feedline and a corresponding transmission line resonator, e.g., 1742A, 1742B, 1744A, 1744B as shown in FIG. 17A. In some instances, the first and second planar transmission line resonators 1514A, 1514B may be under-coupled, where most of the EM energy is dissipated inside the microwave resonator device 1500. In this case, the internal Quality factor (Qint) is lower than the external quality factor Qext. The coupling coefficient is less than 1, and the coupling capacitance is low; and the size of the coupling gap is big. In certain examples, the first and second planar transmission line resonators 1514A, 1414B may be critically coupled, where the EM energy is dissipated equally in both the microwave resonator device 1500 and the external impedance load. Inthis case, the internal quality factor Qtnt) equals the external quality factor (Qext - When the first and second planar transmission line resonators 1514A, 1514B are critically coupled, the drive magnetic field generated by the microwave resonator device 1500 is at its maximum value; and the coupling coefficient g) is equal to 1. In some instances, the coupling between the first and second planar transmission line resonators 1514A, 1514B can be tuned, adjusted and otherwise controlled by adjusting the capacitive coupling (e.g., the coupling gaps 1742A, 1742B, 1744A, 1744B in the example microwave resonator device 1700 shown in FIG. 17A) between the feedline and the respective sets of conductive segments of the respective transmission line resonators.

[0155] In some instances, parameters of control signals, e.g., phase, frequency, etc., communicated to the first and second planar transmission line resonators 1514A, 1514B may be independently designed and tuned.

[0156] In some instances, the first and second planar transmission line resonators 1514A, 1514B, the first and second ground planes 1512A, 1512B can be fabricated on the first and second substrates 1516A, 1516B using superconducting materials including type 1 or type 2 superconducting materials, low- / High-Temperature Superconductors (LTS / HTS), elemental or alloy, metallic or ceramic, conventional or unconventional, nonexotic or exotic superconducting materials. In some instances, the first and second planar transmission line resonators 1514A, 1514B, and the first and second ground planes 1512A, 1512B may be implemented as the respective components of the example microwave resonator device 200 shown in FIG. 2 with a different arrangement in extending orientations.

[0157] In some instances, the first and second planar transmission line resonators 1514A, 1514B may be implemented as coplanar waveguides, striplines, single microstrip lines, lumped element resonators with straight, curved, meandered line or any configuration of inductor and capacitor, arrays of resonators, or in another manner. In certain instances, depending on the specific resonator type and intended applications, the first and second ground planes 1516A, 1516B may be configured in another manner. In some instances, the first and second planar transmission line resonators 1514A, 1514B may be identical, e.g., having the same number of conductive segments, and conductivesegments having the same geometry (e.g., number of conductive segments, length, width, thickness, spacing, etc.), such that the first and second planar transmission line resonators 1514A, 1514B may have identical intrinsic resonance frequencies. In some implementations, conductive segments of the first planar transmission line resonators 1514A are oriented perpendicular to conductive segments of the second planar transmission line resonators 1514B as shown in FIGS. 15A-15B. In certain instances, the first and second planar transmission line resonators 1514A, 1514B may have distinct intrinsic resonance frequencies, e.g., the first and second planar transmission line resonators 1514A, 1514B may be asynchronously tuned. In some instances, coupling gaps (e.g., the coupling gaps 1742A, 1742B, 1744A, 1744B in the example microwave resonator device 1700 shown in FIG. 17A) for coupling microstrip line resonators of the first and second planar transmission line resonators 1514A, 1514B to respective terminals may be the same or different. The first and second planar transmission line resonators 1514A, 1514B may be implemented, fabricated, and operated as respective components of the example microwave resonator device 1600, 1700, 1801, 1900, 2204 shown in FIGS. 16, 17A-17B, 18, 19A, 22, or in another manner.

[0158] In some implementations, the first and second microwave resonator units 1502A, 1502B may be designed, fabricated on separate substrates, tested, and assembled for a target resonance frequency and sample region. The separation distance 1522 can be set based on a target microwave field homogeneity over a target sample region. Coupling parameters (e.g., the coupling gaps between respective terminals of respective sets of conductors in the first and second planar microwave resonator devices 1514A, 1514B) can be tuned according to the behavior of a single mode of the two-resonator system, e.g., under-coupled, critically coupled, or over-coupled. In this configuration, an electron spin resonance (ESR) sample is physically positioned in the sample region 1520.

[0159] In some instances, the microwave resonator device 1500 may be tuned and matched in a similar manner to single planar resonators via inductive or capacitive coupling mechanisms and have a variable quality factor (Q) that depends on the internal Q - mostly given by the geometry and material used to fabricate the device - and the coupling strength.

[0160] In some instances, when the first and second microwave resonator units 1502A, 1502B of the microwave resonator device 1500 are implemented as a pair of a transmission microwave resonator unit and a detection microwave resonator unit (e.g., as the example shown in FIG. 18), the microwave resonator device can 1500 can provide increased dynamic range by providing high isolation of transmission and detection circuitry.

[0161] In some instances, the first and second microwave resonator units 1502A, 1502B may be designed independently and differently. For example, the two microwave resonator units may have different quality factors (Q), which enables performing CW measurements at high Q and pulsed measurements at low Q with the same microwave resonator device. The microwave resonator device with two different microwave resonator units can enable applications of pulsing on the microwave resonator unit with a low Q for a high control bandwidth and detecting on the detection microwave resonator unit with a high Q for high sensitivity or vice-versa.

[0162] In some instances, the first and second microwave resonator units 1502A, 1502B may include different materials. For example, the first microwave resonator unit 1502A may include normal metal to operate at all temperatures; and the second microwave resonator unit 1502B may include superconducting material to minimize internal losses. For another example, the first and second microwave resonator units 1502A, 1502B may be made of different superconducting material, with different kinetic inductance response.

[0163] In some instances, the first and second microwave resonator units 1502A, 1502B may have different coupling (e.g., under coupled, over coupled, or critical coupled). Bandwidth and sensitivity of each microwave resonator unit may be independently adjusted. In some instances, the two microwave resonator units 1502A, 1502B can be tuned to different frequencies. In this case, coupling and quality factor may be optimized independently for double-resonance measurements. In some instances, the first and second microwave resonator units 1502A, 1502B can be tuned to different frequency bands. For example, one resonator may be designed to operate at X-band while the other operates at Q-band. This provides multifrequency EPR capability to the microwave resonator device1500. In some instances, the first and second microwave resonator units 1502A, 1502B can be designed to work collectively to generate a single-mode resonance with circular polarization. Such configuration can offer a V2 increase in sensitivity and signal-to-noise ratio (SNR), and a factor of 2 increase in control efficiency.

[0164] In certain examples, the first and second planar transmission line resonators 1514A, 1514B can be implemented by a variety of 2D designs, including lumped elements (interdigital capacitors and meandered line inductors), coplanar waveguides, striplines, single microstrip lines, or other specialized designs like arrays of inductors and resonators, including multi-strip microstrip line setups. In some implementations, the general design principles include designing two planar resonators on separate substrates for a target resonance frequency, coupling factor, sample region, spin-cavity coupling, and quality factor. These parameters may be optimized by varying geometric features of each resonator independently, such as resonator size or the dimensions of capacitive or inductive coupling elements; determining the separation required to obtain a desired microwave field homogeneity and strength for each resonator interacting independently with the ESR sample; designing a coupling network to route microwave signals to and from each resonator either independently (as a 4-port device) or collectively (as a 2-port device), depending on application.

[0165] As shown in FIG. 15A, the microwave resonator device 1500 is enclosed and supported by a radiofrequency (RF) package 1530. In some instances, the RF package 1530 provides a housing, an electrical connectivity, thermal management, and protection to the microwave resonator device 1500. In some instances, the RF package 1530 may include metals (e.g., Copper, etc.), metal alloys, ceramics, conductive coatings, or other materials. In some instances, the first and second microwave resonator units 1502A, 1502B are mechanically supported by the RF package 1530 and the ground plane 1512A, 1512B can be electrically grounded to the RF packagel530. In some instances, the RF package 1530 may be implemented as the RF package 230 in FIG. 2.

[0166] FIG. 16 is a perspective view of an example microwave resonator device 1600 with an ESR sample placed in a sample region. As shown in FIG. 16, the microwave resonator device 1600 is a crossed split planar microwave resonator device, including afirst microwave resonator unit 1602A and a second microwave resonator unit 1602B which are configured facing each other and spatially separated by a separation distance (d) forming a cavity 1652 between the first and second microwave resonator units 1602A, 1602B. A sample cartridge 1654 can fit between the first and second microwave resonator units 1602A, 1602B in the cavity 1652. In some implementations, the first microwave resonator unit 1602A includes a first planar transmission line resonator 1612A which includes an array of conductive segments 1626 and a ground plane on a first substrate; and the second microwave resonator unit 1602B includes a second planar transmission line resonator 1612B which includes an array of conductive segments 1636 and a ground plane on a second substrate. In some implementations, the first and second planar transmission line resonators 1612A, 1612B are identical. As shown in FIG. 16, the first and second planar transmission line resonators 1612A, 1612B extend along the YZ plane and in directions perpendicular to each other. In some instances, the first and second planar transmission line resonators 1612A, 1612B are configured as the first and second planar transmission line resonators 1514A, 1514B in the example microwave resonator unit 1500 shown in FIGS. 15A-15B. In some instances, the EPR sample can be positioned on the cartridge 1654 and posited in a sample region 1650. The example microwave resonator device 1600 can include additional or different features, and the features of the example microwave resonator device 1600 may be arranged in the configuration shown or in another configuration. In some instances, the microwave resonator device 1600 may be operated according to the operations in the example process 1300 or in another manner.

[0167] In some implementations, the microwave resonator device 1600 may be part of the resonator unit 106 of the example electron spin resonance system 100; and coupled with the control system 114 of the electron spin resonance system 100 for providing electron spin resonance control signals to the microwave resonator device 600 to perform multiple resonance measurements of multiple electron spin centers in the sample region 1650 of the microwave resonator device 1600. In some instances, the control system 114 may operate the microwave resonator device 1600 to perform double resonance measurements of the electron spins in the sample region. For example, the microwave resonator device 1600 may be operated to perform Double Electron-Electron Resonance(DEER) spectroscopy; Pulse Electron Double Resonance (PELDOR) spectroscopy, or other resonance spectroscopy. The microwave resonator device 1600 may be operated to produce a probe frequency that creates observable coherence that evolves under pairwise coupling of the electron spins; and a pump frequency that refocuses pairwise interactions at varying times to reveal a distribution of coupling strength of the pairwise couplings.

[0168] In some implementations, the example microwave resonator device 1600 can be operated according to the operations in the example process 1300 in FIG. 13 to produce a time-varying microwave field in the sample region 1650 of the microwave resonator device 1600. For example, the microwave resonator device 1600 may produce a microwave field at a radio frequency or microwave frequency configured to manipulate electron spins in the sample region 1650 between the first and second planar transmission line resonators 1612A, 1612B.

[0169] As shown schematically in FIG. 16, each of the conductive segments 1626 in the first planar transmission line resonator 1612A includes a respective conductor disposed on a surface of the first substrate. Each of the conductive segments 1626 is elongated along the Y axis. In certain instances, the array of conductive segments 1626 can include two conductive segments, four conductive segments, eight conductive segments, sixteen conductive segments, thirty-two conductive segments, sixty-four conductive segments, or in general powers of two.

[0170] In some implementations, each of the conductive segments 1626 and the ground plane define a microstrip line resonator. In some implementations, the conductive segments 1626 in the first planar transmission line resonator 1612A can be identical to each other. In some examples, the conductive segments 1626 are parallel to each other, with equal spacing between each neighboring pair of the conductive segments 1626. Here, "parallel" is used broadly to describe structures that are exactly or substantially parallel, when considered on the structures’ largest length scales. Two structures can be considered parallel, for example, when their neighboring sides, centerlines, or other dominant structural features are parallel or include only insubstantial deviations from parallel.

[0171] The example conductive segment 1626 can be sized based on the wavelength of a desired resonance frequency. For example, the length of the conductive segment 1626 (e.g., from the first end to the second opposite end) can be designed to produce a resonance mode around the specified resonance frequency of operation (e.g., a>r= 2TI ■ 10 GHz). Each conductive segment 1626 can be a half-wave resonator, a full-wave resonator, or a multi- half- wave resonator. For example, if the desired resonance frequency is A, the conductive segment 1626 can have a length of A / 2, A, 3A / 2, 2A, etc.

[0172] The multiple conductive segments 1626 can be configured to resonate at the same microwave resonance frequency. In some instances, the conductive segment 1626 can be configured to generate a microwave magnetic field with a maximum field intensity at the center of the half-wave segments of the microstrip line resonators, for example, by using a half-wave resonator for each of the conductive segment 1626. In some implementations, the conductive segments 1626 can be edge-coupled to each other so that the magnetic field generated by each resonator interferes with the magnetic field generated by one or more neighboring conductive segments 1626. In some cases, the conductive segments 1626 produce an in-plane uniform field in a direction perpendicular to the surface of the first substrate.

[0173] In some implementations, the first planar transmission line resonator 1612A is configured as a superconducting transmission line resonator. The conducting material of the first planar transmission line resonator 1612A, and ground plane can be made of superconducting material, such as, for example, niobium, niobium titanium, niobium nitride, aluminum, yttrium barium copper oxide (aka, "YBCO"), or another appropriate material. The superconducting materials can be deposited on the substrate by standard deposition techniques. The substrate can be etched or otherwise conditioned based on standard fabrication techniques. In certain instances, the substrate can be made of dielectric material such as, for example, sapphire, silicon, quartz, magnesium oxide (MgO), lanthanum aluminate (LaAlOs), or another type of non-magnetic dielectric crystalline material.

[0174] In some instances, the second microwave resonator unit 1602B may be implemented identical to the first microwave resonator unit 1602A or in another manner.In some implementations, each of the conductive segments 1636 in the second planar transmission line resonator 1612B includes a respective conductor disposed on a surface of the first substrate. Each of the conductive segments 1636 is elongated along the Z axis.

[0175] In some implementations, the sample region 1650 of the microwave resonator device 1600 is located in the cavity 1652 between the conductive segments 1626 of the first planar transmission line resonator 1612A and the conductive segments 1636 of the second planar transmission line resonator 1612B. The sample region 1650 can be a 2- dimensional sample region (a planar sample region), a pseudo planar sample region, a 3- dimensional sample region, or another type of volume. In a 2-dimensional (planar) sample region, one spatial dimension (e.g., thickness) of the sample region is insubstantial (e.g., at least an order of magnitude smaller) than the other two dimensions of the sample region (e.g., length and width). In a 3-dimensional sample region, all three spatial dimensions are substantially similar in size (e.g., same or similar orders of magnitude). In some instances, the microwave magnetic fields generated by the first and second planar transmission line resonators 1612A, 1612B form a control field in the sample region 1650. In some instances, the control field may be uniform across the sample region 1650 (e.g., in both amplitude and direction). For example, the sample region 1650 can include planes (parallel to the surface) over which the instantaneous magnetic fields generated by the first and second planar transmission line resonator 1612A, 1612B are homogeneous during operation. In some instances, the sample region 650 may include samples for ESR applications or experiments, or for additional or different applications. In some implementations, the samples can be thin planar samples, for example, Langmuir-Blodgett films or self-assembled monolayer films, polymer films, biological films, etc. Some example applications of the microwave resonator device 1600 can include using the Langmuir Blodgett films or self-assembled monolayer films with free radicals for quantum computing, and using the biological films to, for example, label electrons and study membrane bound proteins using ESR. In some implementations, the sample region 1650 is a region of given homogeneity interacting with the sample.

[0176] In some implementations, the example microwave resonator device 600 and the sample can be positioned in an external, static primary magnetic field (Bo). The primarymagnetic field can be parallel to the surfaces of the first and second substrates along the YZ plane in a direction perpendicular to the X axis. For example, the static primary magnetic field may be in a direction that forms a 45-degree angle with the Y and Z axis. The primary magnetic field can polarize the electron spins in the sample. The electron spins can have one or more resonance frequencies or a distribution of resonant frequencies (or spin precession frequencies) in the primary magnetic field. The resonance frequencies are typically in the GHz range (e.g., microwave frequencies) in ESR applications. In operation, the conductive segments 1626, 1636 can generate a microwave magnetic field at the resonance frequencies of the electron spins to manipulate the electron spins simultaneously perpendicular to the extension direction of the conductive segments 1626, 1636 (e.g., along the Z and Y axis, respectively).

[0177] The first and second planar transmission line resonators 1612A, 1612B are initially designed separately to ensure they share identical and desired intrinsic resonance frequencies and quality factors. In some instances, the second transmission line resonator 1612B may have a second, distinct intrinsic resonance frequency; and the first and second intrinsic resonance frequencies of the first and second transmission line resonators 1612A, 1612B may have a frequency detuning.

[0178] In some instances, the microwave resonator device 1600 can convert the electron spin resonance control signals to a microwave magnetic field in the sample region 1650. In some implementations, the microwave magnetic field can be homogeneous in a sample region 1650, such that the microwave magnetic field is uniform throughout the sample region 1650. This microwave magnetic field can be substantially uniform in strength and occupy a small mode volume well matched to the volume of the sample. The microwave magnetic field can be applied to one or more samples in the sample region 1650, for example, for pulsed ESR or multi-resonance ESR measurements.

[0179] In some instances, the microwave resonator device 1600 includes an RF enclosure which is configured to fully house the first and second microwave resonator units 1602A, 1602B and other components. During operation, the microwave magnetic field generated by each of the first and second planar transmission line resonators 1612A,1612B are independent and decoupled from each other in the sample region. In some instances, the volume of the sample region 1650 may be up to 100.0 pL or more.

[0180] In some instances, the first and second planar transmission line resonators 1612A, 1612B of the first and second microwave resonator units 1602A, 1602B may be different with different number of microstrips, different geometries, different substrate materials, and different intrinsic resonance frequencies. In some instances, the first and second microwave resonator units 1602A, 1602B may be assembled with a separation distance of a different value. In some instances, the microwave resonator device 1600 may be operated under two distinct resonance modes simultaneously.

[0181] FIGS. 17A-17B are perspective views of an example microwave resonator device 1700 including feedlines for excitation and readout. As shown in FIG. 17, the example microwave resonator device 1700 is a crossed split planar microwave resonator device, including a first microwave resonator unit 1702A and a second microwave resonator unit 1702B which are configured facing each other and spatially separated by a separation distance (d) forming a cavity 1752 between the first and second microwave resonator units 1702A, 1702B. In some implementations, the first microwave resonator unit 1702A includes a first planar transmission line resonator 1712A which includes an array of conductive segments 1726 and a ground plane on a first substrate; the second microwave resonator unit 1702B includes a second planar transmission line resonator 1712B which includes an array of conductive segments 1736 and a ground plane on a second substrate. In some implementations, the first and second planar transmission line resonators 1712A, 1712B are identical. In some instances, the EPR sample can be positioned on a sample cartridge 1754 in the cavity 1752 at a sample region 1750. The example microwave resonator device 1700 can include additional or different features, and the features of the example microwave resonator device 1700 may be arranged in the configuration shown or in another configuration. In some instances, the microwave resonator device 1700 may be operated according to the operations in the example process 1300 or in another manner.

[0182] In some implementations, the microwave resonator device 1700 may be part of the resonator unit 106 of the example electron spin resonance system 100; and coupled with the control system 114 of the electron spin resonance system 100 for providingelectron spin resonance control signals to the microwave resonator device 1700 to perform multiple resonance measurements of multiple electron spin centers in the sample region 1750 of the microwave resonator device 1700. In some instances, the control system 114 may operate the microwave resonator device 1700 to perform double resonance measurements of the electron spins in the sample region. For example, the microwave resonator device 1700 may be operated to perform Double Electron-Electron Resonance (DEER) spectroscopy; Pulse Electron Double Resonance (PELDOR) spectroscopy, or other resonance spectroscopy. The microwave resonator device 1700 may be operated to produce a probe frequency that creates observable coherence that evolves under pairwise coupling of the electron spins; and a pump frequency that refocuses pairwise interactions at varying times to reveal a distribution of coupling strength of the pairwise couplings.

[0183] The first microwave resonator unit 1702A shown in FIGS. 17A-17B includes a first terminal 1752A and a second terminal 1752B. The first and second terminals 1752A, 1752B, the first planar transmission line resonator 1712A, and the ground plane can define planar transmission line structures on the first substrate. The second microwave resonator unit 1702B shown in FIGS. 17A-17B includes a third terminal 1752C and a fourth terminal 1752D. The third and fourth terminals 1752C, 1752D, the second planar transmission line resonator 1712B, and the ground plane can define planar transmission line structures on the second substrate.

[0184] As shown in FIGS. 17A-17B, the first terminal 1752A includes a respective conductor disposed on the first substrate. The first terminal 1752A has terminal segments 1724A and a feedline 1722A galvanically connected to the terminal segments 1724A. The terminal segments 1724A extend from the feedline 1722A toward the first planar transmission line resonator 1712A. The first terminal 1752A includes sixteen terminal segments 1724A, each extending toward a respective conductive segment 1726 of the first planar transmission line resonator 1712A. In some instances, the first terminal 1752A can include two terminal segments 1724A, four terminal segments 1724A, eight terminal segments 1724A, sixteen terminal segments 1724A, thirty-two terminal segments 1724A, sixty-four terminal segments 1724A, or in general powers of two, according to the number of the conductive segments 1726 in the first planar transmission resonator 1712A. In someimplementations, the terminal segments 1724A of the first terminal 1752A have a width identical to the width of the conductive segments 1726 of the first planar transmission line resonator 1712A.

[0185] Similarly, the second terminal 1752B includes a respective conductor disposed on the first substrate. The second terminal 1752B has terminal segments 1724B and a feedline 1722B galvanically connected to the terminal segments 1724B. The terminal segments 1724B extend from the feedline 1722B toward the first planar transmission line resonator 1712A. The second terminal 1752B includes sixteen terminal segments 1724B, each extending toward a respective conductive segment 1726 of the first planar transmission line resonator 1712A. In some instances, the second terminal 1752B can include two terminal segments 1724B, four terminal segments 1724B, eight terminal segments 1724B, sixteen terminal segments 1724B, thirty-two terminal segments 1724B, sixty-four terminal segments 1724B, or in general powers of two, according to the number of the conductive segments 1726 in the first transmission resonator 1712A. In some implementations, the terminal segments 1724B of the second terminal 1752B have a width identical to the width of the conductive segments 1726 of the first planar transmission line resonator 1712A.

[0186] In some implementations, the first and second terminals 1752A, 1752B include branching structures 1728A, 728B galvanically connecting the respective terminal segments 1724A, 1724B to the respective feedlines 1722A, 1722B. The branching structures 1728A, 1728B can function as a power divider that divides and delivers the power from an input to the terminal segments 1724A, 724B. In some instances, the branching structures 1728A, 1728B can include successive levels (or division stages). In some instances, the branching structure 1728A, 1728B can be configured to achieve desirable branch impedances at each division stage. For example, the branching structure 1728A, 1728B can be designed to match all input impedances of the branches in certain division stages to improve (e.g., increase, maximize, optimize, or otherwise improve) power transfer and reduce signal reflections. In some implementations, the individual branches in each level may have twice the impedance of the individual branches in thepreceding level. In some implementations, the power dividers can include tapered branch sections, for example, to adjust the lines for impedance matching.

[0187] As shown schematically in FIGS. 17A-17B, each of the conductive segments 1726 in the first planar transmission line resonator 1712A includes a respective conductor disposed on a surface of the first substrate. A first end of each of the conductive segments 1726 in the first planar transmission line resonator 1712A is aligned with a respective terminal segment 1724A of the first terminal 1752A. Each of the conductive segments 1726 is elongated. Each of the conductive segments 1726 is capacitively coupled to a respective one of the terminal segments 1724A, while a second, opposite end of each of the conductive segments 1726 is capacitively coupled to a respective one of coupling segments 1724B of the second terminal 1752B. In certain instances, the array of conductive segments 1726 can include two conductive segments, four conductive segments, eight conductive segments, sixteen conductive segments, thirty-two conductive segments, sixty-four conductive segments, or in general powers of two.

[0188] In some implementations, each of the conductive segments 1726 and the ground plane define a microstrip line resonator. In some implementations, the conductive segments 1726 in the first planar transmission line resonator 1712A can be identical to each other. In some examples, the conductive segments 1726 are parallel to each other, with equal spacing between each neighboring pair of the conductive segments 1726. Here, "parallel" is used broadly to describe structures that are exactly or substantially parallel, when considered on the structures’ largest length scales. Two structures can be considered parallel, for example, when their neighboring sides, centerlines, or other dominant structural features are parallel or include only insubstantial deviations from parallel.

[0189] The example conductive segments 1726 can be sized based on the wavelength of a desired resonance frequency. The multiple conductive segments 1726 can be configured to resonate at the same microwave resonance frequency. For example, the length of the conductive segment 1726 (e.g., from the first end to the second opposite end) can be designed to produce a resonance mode around the specified resonance frequency of operation (e.g., a>r= 2TI ■ 10 GHz). Each conductive segment 1726 can be a half-wave resonator, a full-wave resonator, or a multi-half-wave resonator. For example, if the desiredresonance frequency is A, the conductive segment 1726 can have a length of A / 2, A, 3A / 2, 2A, etc. The conductive segments 1726 may be configured as the conductive segments 1626 in FIG. 16.

[0190] In some instances, the conductive segment 1726 can be configured to generate a microwave magnetic field with a maximum field intensity at the center of the half-wave segments of the microstrip line resonators, for example, by using a half-wave resonator for each of the conductive segment 1726. In some implementations, the conductive segments 1726 can be edge-coupled to each other so that the magnetic field generated by each resonator interferes with the magnetic field generated by one or more neighboring conductive segments 1726. In some cases, the conductive segments 1726 produce an inplane uniform field in a direction perpendicular to the surface of the first substrate.

[0191] In the example shown in FIGS. 17A-17B, a coupling gap 1742A is defined between the first end of the conductive segments 1726 and the respective terminal segments 1724A of the first terminal 1752A. Similarly, a coupling gap 1742B is defined between the second end of the conductive segments 1726 and the terminal segments 1724B of the second terminal 1752B. The coupling gaps 1742A, 1742B can include vacuum, dielectric material (e.g., sapphire, silicon, quartz, etc.), or a combination of them. The terminal segments 1724A in the first terminal 1752A and the terminal segments 1724B in the second terminal 1752B can serve as feedlines coupled to the array of conductive segments 1726 via the coupling gaps 1742A, 1742B. In some instances, during operation, all of the conductive segments 1726 experience an electromagnetically equivalent feedline path from a pair of a terminal segment 1724A of the first terminal 1752A and a respective terminal segment 1724B of the second terminal 1752B, and the conductive segments 1726 of the first transmission line resonator 1712A can resonate in-phase at their fundamental frequency. Each conductive segment 1726 is configured to resonate at a first intrinsic resonance frequency, and the length of the conductive segments 1726 may be an even number of half- wavelengths for the first intrinsic resonance frequency; and the length of the conductive elements 1726 may be an odd number of half- wavelengths for the first intrinsic resonance frequency.

[0192] As shown in FIGS. 17A-17B, the first and second terminals 1752A, 1752B, and the first planar transmission line resonator 1712A each have a planar transmission line structure. Here "planar" is used broadly to describe structures that are substantially larger in one or both planar dimensions (length and width) than in their height dimension. In some instances, a planar structure has a height that is substantially uniform (e.g., compared to the overall length and width of the structure) over its planar extent. In some implementations, the planar transmission line structure can receive an input signal (e.g., electron spin resonance control signals through the first terminal 1752A), conduct the signal across the parallel conductive segments 1726 in the same direction in the first planar transmission line resonator 1712A; and generate a microwave magnetic field in the sample region 1750.

[0193] In some implementations, the first and second terminals 1752A, 1752B, the first planar transmission line resonator 1712A are configured as superconducting transmission line resonators. The conducting material of the first and second terminals 1752A, 1752B, the first planar transmission line resonator 1712A, and ground plane can be made of superconducting material, such as, for example, niobium, niobium titanium, niobium nitride, aluminum, yttrium barium copper oxide (YBCO), or another appropriate material. The superconducting materials can be deposited on the substrate by standard deposition techniques. The substrate can be etched or otherwise conditioned based on standard fabrication techniques. In certain instances, the substrate can be made of dielectric material such as, for example, sapphire, silicon, quartz, magnesium oxide (MgO), lanthanum aluminate (LaAlOs), or another type of non-magnetic dielectric crystalline material.

[0194] In some instances, the second microwave resonator unit 1702B may be implemented identical to the first microwave resonator unit 1702A or in another manner. For example, components (e.g., terminals 1752C, 1752D, feedlines 1732A, 1732B, terminal segments 1734A, 1734B, conductive segments 1736, branching structures 1738A, 1738B, and coupling gaps 1744A, 1744B) of the second microwave resonator unit 1702B may be implemented as the respective components of the first microwave resonator unit 1702A. In some instances, the first and second microwave resonator units 1702A, 1702B may be configured as the first and second microwave resonator units 1602A, 1602B in FIG. 16. Asshown in FIGS. 17A-17B, the first transmission line resonator 1712A is oriented along the Z direction; and the second transmission line resonator 1712B is oriented along the Y direction. In some implementations, the first transmission line resonator 1712A is a Z resonator of the crossed split-planar microwave resonator device 1700; and the second transmission line resonator 1712B is a Y resonator of the crossed split-planar microwave resonator device 1700.

[0195] In some implementations, the crossed split-planar resonator device 1700 depicted in FIG. 17A-17B is a 4-port device. The first and second planar transmission line resonator 1712A, 1712B may be excited independently by receiving control signals on respective terminals. In some instances, ports that are connected to the respective terminals may be arranged on the same side or different sides of the microwave resonator device 1700. For example, as shown in FIG. 17A, three ports that are connected to the terminals 1752B, 1752C, 1752D may reside on one side of the microwave resonator device 1700 and one port connected to the terminal 1752A may reside on a different side of the microwave resonator device 1700. For another example, as shown in FIG. 17B, two ports connected to the terminals 1752A, 1752B of the first planar transmission line resonator 1712A reside on a first side of the microwave resonator device 1700; and two ports connected to the terminals 1752C, 1752D of the second planar transmission line resonator 1712B reside on a second different side of the microwave resonator device 1700.

[0196] As shown in FIGS. 17A-17B, the 16-strip transmission line resonators of the first and second microwave resonator devices 1702A, 1702B are fabricated on 430 pm thick R- cut sapphire substrates with an anisotropic dielectric constant of (10.0078, 10.0078, 9.8643). The two planar transmission line resonators 1712A, 1712B of the first and second microwave resonator devices 1702A, 1702B are separated by a separation distance d of 3 mm. The sample region is a 2 mm x 2 mm cavity embedded in a 4 mm wide borosilicate cartridge 1754. The capacitive coupling gaps 1742A, 1742B, 1744A, 1744B between the terminal segments and respective conductive segments of the first and second planar transmission line resonators 1712A, 1712B are 200 pm. In the example shown in FIGS. 17A-17B, the first and second planar transmission line resonators 1712A, 1712B each includes an array of 16 straight X / 2 microstrip lines. The first and second planartransmission line resonators 1712A, 1712B are identical, e.g., the microstrip lines in the first and second planar transmission line resonators 1712A, 1712B having the same length l0of 5150 pm, the same width w of 40 pm, and the same spacing s0between neighboring microstrip lines of 100 pm. In some instances, the sample region of the sample region 1750 may be up to 100.0 pL or more.

[0197] In some implementations, the example microwave resonator device 1700 and the sample can be positioned in an external, static primary magnetic field (Bo). The primary magnetic field can be parallel to the surfaces of the first and second substrates along the Y- Z plane. The primary magnetic field Bocan polarize the electron spins in the sample region 1750. The electron spins have one or more resonance frequencies or a distribution of resonant frequencies (or spin precession frequencies) in the primary magnetic field Bo. The resonance frequencies are typically in the GHz range (e.g., microwave frequencies) in ESR applications. In operation, the conductive segments 1726, 1736 can generate microwave magnetic fields at the resonance frequencies of the electron spins to manipulate the electron spins simultaneously. The microwave magnetic fields are perpendicular to the extension direction of the respective conductive segments 1726, 1736 (e.g., along the XY or XZ plane).

[0198] In some instances, the first and second planar transmission line resonators 1712A, 1712B can be customized to meet specific application requirements, offering choices between identical resonators with the same resonant frequency or variations in dimensions, resonance frequencies, spin-cavity coupling, gaps, quality factors, materials, substrates, the number of strips, and more. This configuration allows the establishment of separate circuitry for transmission and detection, increasing dynamic range through high isolation of the spectrometer transmission and detection circuits, and allowing continuous monitoring of the spin signal through the detection resonator while control signals are applied to the transmission resonator (zero-deadtime measurement).

[0199] In some implementations, the EPR sample is positioned in the sample region 1700 between the microwave resonator device 1700 at the midpoint of each and interacts independently with the microwave magnetic fields generated by the first and second planar transmission line resonators 1712A, 1712B. The dimensions of the EPR sample andthe separation distance can be selected according to a target field homogeneity profile for a given application, including high uniformity or a designed gradient. The spatial uniformity of each planar transmission line resonator is the same as for a single planar resonator. For example, when the first and second planar transmission line resonators 1712A, 1712B have identical geometric parameters for general EPR applications with high field homogeneity, the sample can ideally be square in both the Z and Y dimensions. In cases where the sample cavity is rectangular, adjustments to the width and separation distance may be made to accommodate the sample geometry.

[0200] In some instances, the first and second planar transmission line resonators 1712A, 1712B of the first and second microwave resonator units 1702A, 1702B may be different with different number of microstrips, different geometries, different substrate materials, and different intrinsic resonance frequencies. In some instances, the first and second microwave resonator units 1702A, 1702B may be assembled with a separation distance of a different value. In some instances, the microwave resonator device 1700 may be operated under two distinct resonance modes.

[0201] In some implementations, the electric field generated by each of the first and second planar transmission line resonators 1712A, 1712B is maximal at the gap locations, while the magnetic field is maximal at the center of the resonators. As shown in FIG. 17A, the gaps between the first and second planar transmission line resonators 1712A, 1712B are sufficiently spaced apart so that the electric fields of these two resonators 1712A, 1712B do not overlap and respective magnetic fields do overlap. The magnetic field associated with the Z-resonator (e.g., the first planar transmission line resonator 1712B) is transverse to the Z-direction and can be represented as H1= Hxlx + Hyly, with Hylbeing significantly larger than HX1in the central region of the sample. For the Y-resonator (e.g., the second planar transmission line resonator 1712A), the magnetic field is given by H2= Hx2x + HZ2Z, where Hz2is significantly larger than Hx2in the central region of the sample region. The coupling between the two resonators 1712A, 1712B is determined by the dot product of the magnetic fields, denoted as H1. H2= HxlHx2, which varies spatially depending on the separation between the two resonators 1712A, 1712B. When the separation distance is greater than 2 mm and within a sample region located symmetricallybetween the centers of the two resonators, the field overlap becomes very small, leading to complete decoupling of the two resonance modes. In some instances, smaller separations may result in less isolation between the two resonance modes, with a tolerance dictated by the target application and spectrometer hardware.

[0202] FIG. 17C is a plot showing scattering parameters (S-parameters) in dB as a function of frequency in GHz of the microwave resonator device shown in FIG. 17B. As shown in FIG. 17C, the first and second planar transmission line resonators 1712A, 1712B resonate at approximately 9.57 GHz with complete decoupling. Consequently, each of the first and second planar transmission line resonators 1712A, 1712B can be individually addressed without mutual interference. Curve 1762 shows the Sil parameter of the microwave resonator device; curve 1764 represents the S21 parameter of the microwave resonator device; curve 1766 represents the S34 parameter of the microwave resonator device; and curve 1768 represents the S44 parameter of the microwave resonator device.

[0203] FIG. 18 is a schematic diagram of an example resonator unit 1800 connected to a microwave transceiver. As shown in FIG. 18, the resonator unit 1800 includes a microwave resonator device 1801 which is a crossed split-planar microwave resonator device. The microwave resonator device 1801 includes a first microwave resonator unit 1802A and a second microwave resonator unit 1802B which are configured facing each other and spatially separated by a separation distance (d) forming a cavity 1852 between the first and second microwave resonator units 1802A, 1802B. In some implementations, the first microwave resonator unit 1802A includes a first planar transmission line resonator 1812A which includes an array of conductive segments 1826 and a ground plane on a first substrate; the second microwave resonator unit 1702B includes a second planar transmission line resonator 1812B which includes an array of conductive segments 1836 and a ground plane on a second substrate. In some implementations, the first and second planar transmission line resonators 1812A, 1812B are identical. In some instances, the EPR sample can be positioned on a sample cartridge 1854 in the cavity 1852 at a sample region 1850. In some instances, the example crossed split planar microwave resonator device 1801 may be implemented as the microwave resonator device 1700 shown in FIG. 17B. The example microwave resonator device 1801 can include additional or different features, andthe features of the example microwave resonator device 1801 may be arranged in the configuration shown or in another configuration. In some instances, the microwave resonator device 1801 may be operated according to the operations in the example process 1300 or in another manner.

[0204] As shown in FIG. 18, the second planar transmission line resonator 1812B is communicably coupled to a transmitter circuit 1822A at respective terminals 1852C, 1852D configured to receive signals from the transmitter circuit 1822, which maybe part of the spectrometer 104 of the control system 114 shown in FIG. 1; and the first planar transmission line resonator 1812A is communicably coupled to a receiver circuit 1822B at respective terminals 1852A, 1852D configured to transmit signals to the receiver circuit 1822B which may be the spectrometer 104 of the control system 114 shown in FIG. 1. The Y-resonator (e.g., the second planar transmission line resonator 1802B) is linked to the spectrometer transmitter (Tx) circuitry 1822A, responsible for exciting the EPR sample residing in the sample region 1850 by receiving electron spin resonance control signals from the transmitter circuit. The Z-resonator (e.g., the first planar transmission line resonator 1802A) receives the EPR detection signal from the sample and can further provide electron spin resonance detection signals to the spectrometer receiver (Rx) circuitry 1822B.

[0205] In some instances, the crossed split-planar microwave resonator device 1801 can improve or maximize isolation of spectrometer transmitter and receiver circuitry; can reduce the requirement for numerous microwave components in the spectrometer, especially those needed to separate the transmitter (Tx) and receiver (Rx) paths; and can simplify the spectrometer's design, resulting in a reduction in overall complexity.

[0206] In some instances, the Blzand Blymicrowave magnetic fields generated by the second and first planar transmission line resonators 1812B, 1812A, respectively, may not be completely perpendicular to the main quantizing static magnetic field Bo. In this case, the microwave field component parallel with the static magnetic field Boinduces a timedependent perturbation of the spin Larmor frequency. In general, the strength of the static magnetic field Bois several orders of magnitude greater than the strength of themicrowave magnetic field Blyand Blzgenerated by the first and second planar transmission line resonators 1812A, 1812B, permitting the time-dependence to be removed through a perturbative approximation used to derive Bloch-Siegert shifts.

[0207] In some implementations, the first and second microwave resonator units 1802A, 1802B include superconducting materials. The losses arising from the disruption of Cooper pairs and the movement of vortices depend on the orientation of the static magnetic fields Boapplied to the microwave resonator device 1801. In some instances, such losses may be noticeable compared to the case when Bois aligned with the long dimension of the resonators. However, these challenges can be mitigated by optimizing the superconducting film thickness and using superconducting materials with advantageous properties. For example, high-temperature superconductors like YBCO or type-2 superconductors like Nb with periodically trapped flux centers or holes, can be used.

[0208] FIG. 19A is a top view of an example microwave resonator device 1900. As shown in FIG. 19A, the microwave resonator device 1900 is a crossed split-planar microwave resonator device, including a first microwave resonator unit and a second microwave resonator unit which are configured facing each other and spatially separated by a separation distance (d) between the first and second microwave resonator units. In some implementations, the first microwave resonator unit includes a first planar transmission line resonator 1912A which includes an array of conductive segments 1926 and a ground plane on a first substrate; the second microwave resonator unit includes a second planar transmission line resonator 1912B which includes an array of conductive segments 1936 and a ground plane on a second substrate. In some instances, the EPR sample can be positioned on a sample cartridge 1954 in the cavity at a sample region 1950. The example microwave resonator device 1900 can include additional or different features, and the features of the example microwave resonator device 1900 may be arranged in the configuration shown or in another configuration. In some instances, the microwave resonator device 1900 may be operated according to the operations in the example process 1300 or in another manner.

[0209] In some implementations, the microwave resonator device 1900 may be part of the resonator unit 106 of the example electron spin resonance system 100; and coupledwith the control system 114 of the electron spin resonance system 100 for providing electron spin resonance control signals to the microwave resonator device 1900 to perform multiple resonance measurements of multiple electron spin centers in the sample region 1950 of the microwave resonator device 1900. In some instances, the control system 114 may operate the microwave resonator device 1900 to perform double resonance measurements of the electron spins in the sample region. For example, the microwave resonator device 1900 may be operated to perform Double Electron-Electron Resonance (DEER) spectroscopy; Pulse Electron Double Resonance (PELDOR) spectroscopy, or other resonance spectroscopy. The microwave resonator device 1900 may be operated to produce a probe frequency that creates observable coherence that evolves under pairwise coupling of the electron spins; and a pump frequency that refocuses pairwise interactions at varying times to reveal a distribution of coupling strength of the pairwise couplings.

[0210] The first microwave resonator unit includes a first terminal 1952 A and a second terminal 1952B. The first and second terminals 1952A, 1952B, the first transmission line resonator 1912A, and the ground plane can define planar transmission line structures on the first substrate. The second microwave resonator unit includes a third terminal 1952C and a fourth terminal 1952D. The third and fourth terminals 1952C, 1952D, the second transmission line resonator 1912B, and the ground plane can define planar transmission line structures on the second substrate.

[0211] As shown in FIG. 19A, the first terminal 1952A has terminal segments 1924A and a feedline 1922A galvanically connected to the terminal segments 1924A. The terminal segments 1924A extend from the feedline 1922A toward the first planar transmission line resonator 1912A. The second terminal 1952B has terminal segments 1924B and a feedline 1922B galvanically connected to the terminal segments 1924B. The terminal segments 1924B extend from the feedline 1922B toward the first planar transmission line resonator 1912A. Each of the first and second terminals 1952A, 1952B includes sixteen terminal segments 1924A, 1924B, each extending toward a respective conductive segment 1926 of the first planar transmission line resonator 1912A. In some implementations, the first and second terminals 1952A, 1952B include branching structures 1928A, 1928B galvanically connecting the respective terminal segments 1924A, 1924B to the respective feedlines1922A, 1922B. A first end of each of the conductive segments 1926 is capacitively coupled to a respective one of the terminal segments 1924A of the first terminal 1952A via a coupling gap 1942A, while a second, opposite end of each of the conductive segments 1926 is capacitively coupled to a respective one of coupling segments 1924B of the second terminal 1952B via a coupling gap 1942B. In some instances, the first planar transmission line resonator 1912A may be designed, fabricated and operated as the first planar transmission line resonator 1612A, 1712A, 1812A in FIGS. 16-18 or in another manner.

[0212] As shown in FIG. 19A, the third terminal 1952C has terminal segments 1934A and a feedline 1932A galvanically connected to the terminal segments 1934A. The terminal segments 1934A extend from the feedline 1932A toward the second planar transmission line resonator 1912B. The fourth terminal 1952D has terminal segments 1934B and a feedline 1932B galvanically connected to the terminal segments 1934B. Each of the third and fourth terminals 1952C, 1952D includes sixteen terminal segments 1934A, 1934B, each extending toward a respective conductive segment 1936 of the second planar transmission line resonator 1912B. The terminal segments 1934A, 1934B extend from the respective feedline 1932A, 1932B toward the second planar transmission line resonator 1912B. In some implementations, the third and fourth terminals 1952C, 1952D include branching structures 1938A, 1938B galvanically connecting the respective terminal segments 1934A, 1934B to the respective feedlines 1932A, 1932B. A first end of each of the conductive segments 1936 is capacitively coupled to a respective one of the terminal segments 1934A of the third terminal 1952C via a coupling gap 1944A, while a second, opposite end of each of the conductive segments 1936 is capacitively coupled to a respective one of coupling segments 1934B of the fourth terminal 1952D via a coupling gap 1944B. In some instances, the second planar transmission line resonator 1912B may be designed, fabricated and operated as the second planar transmission line resonator 1612B, 1712B, 1812B in FIGS. 16-18 or in another manner.

[0213] When two resonators of the same frequency are used with different coupling gaps, the quality factors and coupling factors of the two resonators can be different. This arrangement is useful for transmitting and detecting signals with different bandwidths and efficiencies. For example, a low Q resonator could be used to maximize control bandwidthof a transmission signal while a high Q resonator could be used to maximize detection sensitivity and SNR over a narrow bandwidth. Another example is using a low Q resonator to perform high bandwidth pulsed EPR measurements while using a high Q resonator to perform high sensitivity CW EPR measurements. Additionally, the two resonators can be made from different materials to enable operation at varying temperature ranges and with different kinetic inductance behavior.

[0214] In some implementations, the size of the coupling gaps is different from the size of the coupling gaps 1944A, 1944B. As shown in FIG. 19A, the conductive segments 1926 of the first planar transmission line resonator 1912A has a length of 5150 pm and a dimension of the coupling gaps 1942A, 1942B of 350 pm, whereas the conductive segments 1936 of the second planar transmission line resonator 1912B has a length of 5150 pm and a dimension of the coupling gaps 1944A, 1944B of 200 pm. In some instances, the first and second planar transmission line resonators 1912A, 1912B maybe designed to have resonance frequencies in different frequency bands (e.g., X-band and Q-band). In some instances, the first and second planar transmission line resonators 1912A, 1912B may be designed to have small detuning for double-resonance measurements (e.g., < 1 GHz detuning).

[0215] FIG. 19B is a plot showing scattering parameters (S-parameters) in dB as a function of frequency in GHz of the microwave resonator device shown in FIG. 19A. The first and second planar transmission line resonators 1912A, 1912B include superconducting material. The surface impedance of each superconducting resonator is assumed to be 2xl0’4£1. s21 is measured between the terminals 1952C and 1952D of the second planar transmission line resonator 1912B (Y-resonator); and s43 is measured between the terminals 1952A and 1952B of the first planar transmission line resonator 1912A (Z-resonator). The Y-resonator exhibits a Q-factor of 280 with an insertion loss (IL) of -0.39 dB, while the Z-resonator exhibits a Q-factor of 800 with an IL of -1.15 dB. Curve 1952 shows the S21 parameter of the microwave resonator device; and curve 1954 represents the S43 parameter of the microwave resonator device.

[0216] FIGS. 20A-20B include plots showing distributions of control fields of the microwave resonator device 1900 shown in FIG. 19A. The microwave resonator device1900 has a separation distance of 1 mm. 1W RF excitation within a cross-section of the EPR sample is applied on the first and second planar transmission line resonators 1912A, 1912B. The magnetic field vectors were computed using the eigenmode solver of the HFSS module of AN SYS.

[0217] Plot 2000 shows a perspective view of magnetic field vectors of the control field in the sample region 1950 generated by the second planar transmission line resonator 1912B. The length of the conductive segments 1936 of the second planar transmission line resonator 1912B (e.g., the Y resonator) are 5150 pm, resulting in resonance at 9.6828 GHz. Plot 2020 shows a side view of the magnetic field vectors of the control field in the sample region 1950 in the XZ plane at Y=0 generated by the second planar transmission line resonator 1912B. Plot 2030 shows a perspective view of magnetic field vectors of the control field in the sample region 1950 generated by the first planar transmission line resonator 1912A. The length of the conductive segments 1926 of the first planar transmission line resonator 1912A (e.g., the Z resonator) are 5200 pm, resulting in resonance at 9.5069 GHz. Plot 2050 shows a side view of the magnetic field vectors of the control field in the sample region 1950 in the XY plane at Z=0 generated by the first planar transmission line resonator 1912A.

[0218] As shown in FIGS. 20A-20B, the microwave magnetic field generated by the higher Q resonator (Z-resonator, the first planar transmission line resonator 1912A) is larger than the field generated by the lower Q resonator (Y-resonator, the second planar transmission line resonator 1912B). Because the first and second planar transmission line resonators 1912A, 1912B are uncoupled, the field distributions of the microwave magnetic field are identical to respective ones obtained with respective single planar devices (e.g., only the first planar transmission line resonator 1912A or only the second planar transmission line resonator 1912B).

[0219] FIGS. 21A-21B include plots of S-parameters in dB as a function of frequency in GHz of two microwave resonator devices. In some instances, each of the two microwave resonator devices may be implemented as the microwave resonator device 1500, 1600, 1700, 1900 shown in FIGS. 15A-15B, 16, 17A-17B, 19A; or in another manner. Each of the two microwave resonator devices is a crossed split-planar resonator device with tworesonance modes. The two resonance modes are distinct and uncoupled. Each of the two microwave resonator devices includes first and second planar transmission line resonators which are asynchronously tuned (e.g., different resonance frequencies). Each microwave resonator unit of the microwave resonator device includes a planar transmission line resonator with 16-strip half-wavelength resonators. The respective sets of 16-strip halfwavelength resonators of the planar transmission line resonator are oriented in directions that are orthogonal to each other. The first planar transmission line resonator is a Y resonator generating a first microwave field in a first direction in the sample region; and the second planar transmission line resonator is a Z-resonator generating a second microwave field in a second direction orthogonal to the first direction in the sample region.

[0220] The microwave resonator device with response plotted in FIG. 21A, include first and second planar transmission line resonators. The microstrip lines of the first planar transmission line resonator have a length l0of 5150 pm, a width w of 40 pm, and a spacing s0between neighboring microstrip lines of 100 pm. The microstrip lines of the second planar transmission line resonator have a length l0of 5750 pm, a width w of 40 pm, and a spacing s0between neighboring microstrip lines of 100 pm. The 16-strip transmission line resonators of the first and second planar transmission line resonators are fabricated on 430 pm thick R-cut sapphire substrates with an anisotropic dielectric constant of (10.0078, 10.0078, 9.8643). The two planar transmission line resonators of the microwave resonator device are separated by a separation distance d of 3 mm. The coupling gap between the terminal segments and conductive segments is 350 pm. The first microwave resonator can be operated to generate a first control field having a first resonance mode at about 8.83 GHz; and the second planar transmission line resonator can be operated to generate a second control field having a second independent resonance mode at about 9.59 GHz, giving two independent resonance modes detuned by 960 MHz. Curve 2102 shows the S21 parameter of the microwave resonator device; curve 2104 represents the Sil parameter of the microwave resonator device; curve 2106 represents the S43 parameter of the microwave resonator device; and curve 2108 represents the S44 parameter of the microwave resonator device.

[0221] The microwave resonator device with response plotted in FIG. 2 IB, include first and second planar transmission line resonators. The microstrip lines of the first planar transmission line resonator have a length l0of 5150 pm, a width w of 40 pm, and a spacing s0between neighboring microstrip lines of 100 pm. The microstrip lines of the second planar transmission line resonator have a length l0of 5200 pm, a width w of 40 pm, and a spacing s0between neighboring microstrip lines of 100 pm. The 16-strip transmission line resonators of the first and second microwave resonator devices are fabricated on 430 pm thick R-cut sapphire substrates with an anisotropic dielectric constant of (10.0078, 10.0078, 9.8643). The two planar transmission line resonators of the second microwave resonator device are separated by a separation distance d of 3 mm. The coupling gap between the terminal segments and conductive segments is 350 pm. The second microwave resonator device has a first resonance mode at about 9.52 GHz and a second independent resonance mode at about 9.62 GHz, giving two independent resonance modes detuned by 110 MHz. Curve 2122 shows the S21 parameter of the microwave resonator device; curve 2124 represents the Sil parameter of the microwave resonator device; curve 2126 represents the S43 parameter of the microwave resonator device; and curve 2128 represents the S44 parameter of the microwave resonator device.

[0222] In some instances, the frequency difference between the two independent resonance modes (e.g., the detuning) can be adjusted by varying the length of the planar transmission line resonators or other geometrical parameters. In some instances, two planar transmission line resonators with different resonance frequencies can be useful for performing multifrequency EPR measurements (e.g., X-band and Q-band using the same device) or double-resonance (DEER) measurements. The coupling and quality factor may be optimized independently for each resonance frequency.

[0223] FIG. 22 is a block diagram showing aspects of an example resonator unit 2200. As shown in FIG. 22, The example resonator unit 2200 includes a first quadrature hybrid 2202A, a second quadrature hybrid 2202B, and a microwave resonator device 2204. The example resonator unit 2200 is configured to allow the microwave resonator device 2204 to operate under a two-port configuration; obtain circular polarization; and communicate with a control system to receive control signals and transfer detection signals. The first andsecond quadrature hybrids 2202A, 2202B are configured to introduce phase shift to microwave input signals between ports 2224A and 2224B and to microwave output signals between 2228A and 2228B. In some instances, the microwave resonator device 2204 may be implemented as the microwave resonator device 1500, 1600, 1700, 1900 shown in FIGS. 15A-15B, 16, 17A-17B, 19A; or in another manner. The example resonator unit 2200 can include additional or different features, and the features of the example resonator unit 2200 may be arranged in the configuration shown or in another configuration. In some instances, the resonator unit 2200 may be operated according to the operations in the example process 1300 or in another manner.

[0224] In some implementations, the microwave resonator device 2204 is a crossed split-planar microwave resonator device including two planar transmission line resonators disposed on two substrates that are oriented parallel to each other. The two planar transmission line resonators are disposed on two surfaces of the respective substrates, and the two surfaces are facing each other with a separation distance between them. The two planar transmission line resonators generate microwave magnetic fields which are perpendicular to each other in a sample region. Each planar transmission line resonator of the microwave resonator device 2204 contains two physical ports; and thus is a 2-port device from the perspective of the microwave electronics used to control and readout the planar transmission line resonator. Therefore, the microwave resonator device 2204 shown in FIG. 22 contains four ports 2212A, 2212B, 2214A, 2214B; and is, thus, a 4-port device. The ports 2212A, 2212B are associated with the first planar transmission line resonator of the microwave resonator device 2204, while the ports 2214A, 214B are associated with the second planar transmission line resonator of the microwave resonator device 2204.

[0225] In some implementations, the first and second quadrature hybrids 2202A, 2202B are configured to interface the 4-port microwave resonator device 2204 with a 2- port control system. The first and second quadrature hybrids 2202A, 2202B are communicably connected to the microwave resonator device 2204. In particular, the first quadrature hybrid 2202A includes a first port 2222 for receiving microwave control signals from a control system (e.g., the spectrometer 104 of the control system 114 in FIG.1); and second and third ports 2224A, 2224B which are connected to the port 2212A, 2214A of the microwave resonator device 2204, respectively, providing the microwave input signals to the two planar transmission line resonators with a controlled phase difference. The first quadrature hybrid 2202A includes a fourth port 2232 is terminated with a 50-ohm impedance. The second quadrature hybrid 2202B includes first and second ports 2228A, 2228B which are connected to the ports 2212B and 2214B of the microwave resonator device 2204 for receiving microwave detection signals from the first and second transmission line resonators; a third port 2226 for transmitting the microwave detection signals to the control system; and a fourth port 2234 which is terminated with a 50-ohm impedance. In some implementations, the first and second quadrature hybrids 2202A, 2202B enable the excitation of the microwave resonator device 2204 and the formation of a single resonance mode with a circular polarization in the microwave resonator device 2204. In some instances, the first planar transmission line resonator of the microwave resonator device 2204 is a Z resonator generating a magnetic field in the Y direction during operation; and the second planar transmission line resonator of the microwave resonator device 2204 is a Y-resonator generating a magnetic field in the Z direction during operation. The microwave output signals (e.g., microwave detection signals) from the first and second planar transmission line resonators follow a reverse path compared to the microwave control signals. In other words, a second phase difference is introduced to the microwave output signals received from the first and second planar transmission line resonators by the second quadrature hybrid 2202B. For example, when a first phase difference of 90 degrees is introduced by the first quadrature hybrid 2202A, a second phase difference of -90 degrees can be introduced by the second quadrature hybrid 2202B. In some instances, the first and second phase difference values are opposite in their signs and have the same absolute value. In some instances, the first and second quadrature hybrids 2202A, 2202B can be operated to introduce other phase difference values to the microwave control signals received from the control system and microwave output signals from the microwave resonator device. In some instances, each of the first and second quadrature hybrids 2202A, 2202B may be a quadrature hybrid, which can be realized using either connectorized components or built-in devices like Branch-line or Lange couplers.For example, each branch may have a transmission line with a distinct length, which is configured to operate as a delay line to effectively introduce a phase shift to the signals.

[0226] In some implementations, introducing a phase shift (e.g., a 90-degree phase shift or a 270-degree phase shift) of the microwave input signals sent to each resonator enables the generation of a single resonance mode with circular polarization. In some implementations, in circular polarization, the electrical field of the electromagnetic wave linearly oscillates in two perpendicular directions in-phase, such that the electrical field vector effectively rotates in a circular motion along the plane which is defined by the two perpendicular directions. In some instances, circular polarization can provide a reduction of excitation power (up to 50% reduction) and enhancement of signal-to-noise ratio (V2) in magnetic resonance applications.

[0227] In some implementations, the microwave resonator device 2204 is operated using a differential stimulus configuration. Under the differential mode, the ports 2212A, 2214A and the ports 2212B, 2214B simultaneously experience two control signals with a certain phase difference. In some instances, the first and second quadrature hybrids 2202A, 2202B may include two phase shifter devices which are associated with the same planar transmission line resonator and configured to cause a phase shift between phases of the microwave control signals applied on the two planar transmission line resonators and between the phases of the microwave detection signals received from the two planar transmission line resonators. As depicted in FIG. 22, an unbalanced microwave input is directed into the first quadrature hybrid 2202A, which transforms it into outputs with a phase difference of 90 degrees. Subsequently, these two lines are connected to the ports 2212A, 2214A of the microwave resonator device 2204 to obtain circular polarization. The response of the microwave resonator device 2204 is collected from the ports 2212B, 2214B via the second quadrature hybrid 2202B.

[0228] In some instances, each of the first and second quadrature hybrids 2202A, 2202B may include a quadrature hybrid which may be implemented in a variety of ways for narrowband or broadband behavior, including bulk connectorized designs, on-chip fabricated designs, and surface-mounted planar or nonplanar designs or in another manner. In some instances, a quadrature hybrid may be a branch-line hybrid, a 90-degreehybrid ring, a Wilkinson power divider with 90-degree phase shift, a short slot hybrid, a Lange coupler a coupled line hybrid, or another type.

[0229] FIGS. 23A-23D are simulation results showing circularly polarized magnetic field vectors in a sample region of the example microwave resonator device 2204 in FIG. 22 at various phase differences. The microwave resonator device includes two identically tuned microwave resonator units. Each microwave resonator unit includes a planar transmission line resonator with 16-strip half-wavelength resonators. The microstrip lines of the first and second microwave resonator devices have a length l0of 5150 pm, a width w of 40 pm, and a spacing s0between neighboring microstrip lines of 100 pm. The 16-strip transmission line resonators of the first and second microwave resonator devices are fabricated on 430 pm thick R-cut sapphire substrates with an anisotropic dielectric constant of (10.0078, 10.0078, 9.8643). The two planar transmission line resonators of the microwave resonator device are separated by a separation distance d of 2 mm. The coupling gap between the terminal segments and conductive segments is 200 pm. The control fields shown in FIGS. 23A-23D are calculated using the HFSS module of AN SYS over a sample region contained in a borosilicate sample cartridge with a dielectric constant of 4.04. The microwave resonator device is a crossed split-planar microwave resonator device, which may be implemented as the example resonator device 1500, 1600, 1700 as shown in FIGS. 15A-15B, 16, and 17A-17B, or in another manner. The power of the microwave input signals to the example microwave resonator device during the simulation is fixed at 1 W. A first microwave input signal to the first planar transmission line resonator at port 2212A and a second microwave input signal to the second planar transmission line resonator at port 2212B have the same frequency. The resulting magnetic field vectors over a segment of the EPR sample are examined at different rotation angles demonstrating a circular rotation at varying phase angles. Port 2212A corresponding to the input of the Y- resonator, and port 2212B, corresponding to the input of the Z-resonator, are utilized to supply two microwave inputs.

[0230] In a general aspect of what is described above, a split-planar microwave resonator device for electron spin resonance is presented.

[0231] In a first example, a microwave resonator device for electron spin resonance includes a first substrate and a second substrate. The first substrate includes a first surface and the second substrate includes a second surface. The second surface is oriented parallel to the first substrate with the second surface facing the first surface; and the second surface is spaced apart from the first surface by a separation distance. The microwave resonator device includes a first ground plane disposed on the first substrate; a second ground plane disposed on the second substrate; a first transmission line resonator patterned on the first surface of the first substrate and configured to produce a first microwave field in a sample region between the first and second surfaces; and a second transmission line resonator patterned on the second surface of the second substrate and configured to produce a second microwave field in the sample region between the first and second surfaces.

[0232] Implementations of the first example may include one or more of the following features. The first transmission line resonator and the second transmission line resonator are made of superconducting material. The first transmission line resonator has a first quality factor; and the second transmission line resonator has a second, distinct quality factor. The first substrate includes a third surface opposite the first surface. The first ground plane is disposed on the third surface. The first transmission line resonator includes a first microstrip resonator on the first surface. The second substrate includes a fourth surface opposite the second surface. The second ground plane is disposed on the fourth surface. The second transmission line resonator includes a second microstrip resonator on the second surface. The first transmission line resonator includes a first plurality of microstrip resonators on the first surface, and the second transmission line resonator comprises a second plurality of microstrip resonators on the second surface.

[0233] Implementations of the first example may include one or more of the following features. The first transmission line resonator includes a first set of terminal segments capacitively coupled to first ends of the first plurality of microstrip resonators through a first coupling gap and a second set of terminal segments capacitively coupled to second, opposite ends of the first plurality of microstrip resonators through a second coupling gap. The second transmission line resonator includes a third set of terminal segments capacitively coupled to first ends of the second plurality of microstrip resonators through athird coupling gap and a fourth set of terminal segments capacitively coupled to second, opposites end of the second plurality of microstrip resonators through a fourth coupling gap. The first and second coupling gaps have a first value, and the third and fourth coupling gaps have a second different value. The first transmission line resonator includes a first delay line galvanically connected to the first set of terminal segments via a first branching structure; and a second delay line galvanically connected to the second set of terminal segments via a second branching structure.

[0234] Implementations of the first example may include one or more of the following features. The first transmission line resonator includes a first feedline galvanically coupled to the first set of terminal segments via a first branching structure and a second feedline galvanically coupled to the second set of terminal segments via a second branching structure. The second transmission line resonator includes a third feedline galvanically coupled to the third set of terminal segments via a third branching structure and a fourth feedline galvanically coupled to the fourth set of terminal segments via a fourth branching structure.

[0235] Implementations of the first example may include one or more of the following features. The first and second transmission line resonators are configured to support a single resonance mode in the sample region. The single resonance mode is an even resonance mode or an odd resonance mode. The first and second transmission line resonators are configured to receive control signals with a 180-degree phase difference to support a single resonance mode of high microwave field homogeneity. The first and second transmission line resonators are configured to receive control signals with a 0- degree phase difference to support a single resonance mode with a defined spatial microwave field gradient. The first and second transmission line resonators are configured to support even and odd resonance modes in the sample region.

[0236] Implementations of the first example may include one or more of the following features. The first transmission line resonator includes a first terminal and a second terminal. The second transmission line resonator includes a third terminal and a fourth terminal. The first terminal and the third terminal include connectors configured to connect to a first microwave power divider. The second terminal and the fourth terminalinclude connectors configured to connect to a second microwave power divider. The separation distance is in the range of 0.5 mm to 2.5 mm. The first and second surfaces are separated by at least one of air, vacuum, or dielectric material. The first and second substrates are mechanically supported in a radiofrequency (RF) package.

[0237] Implementations of the first example may include one or more of the following features. The first transmission line resonator is configured to produce the first microwave field in a first direction in the sample region; and the second transmission line resonator is configured to produce the second microwave field in a second direction that is orthogonal to the first direction in the sample region. The first and second transmission line resonators are configured to support a single resonance mode in the sample region. The single resonance mode has a circular polarization. The first transmission line resonator includes a first plurality of parallel conductors patterned on the first surface and oriented in a first direction; and the second transmission line resonator includes a second plurality of parallel conductors patterned on the second surface and oriented in a second direction that is orthogonal to the first direction. The first transmission line resonator is configured to support a first resonance mode; and the second transmission line resonator is configured to support a second mode that is independent of the first mode. The first transmission line resonator is configured to receive electron spin resonance control signals from a transmitter circuit; and the second transmission line resonator is configured to provide electron spin resonance detection signals to a receiver circuit. The first planar transmission line resonator has a first resonance frequency, the second planar transmission line resonator has a second, distinct resonance frequency, and the first and second resonance frequencies are in different frequency bands. The second resonance frequency is detuned from the first resonance frequency by less than 1 GHz.

[0238] In a second example, an electron spin resonance (ESR) system includes the microwave resonator device of the first example, and a control system configured to operate the microwave resonator device to perform magnetic resonance measurements of electron spins in the sample region.

[0239] Implementations of the second example may include one or more of the following features. The control system is configured to operate the microwave resonatordevice to perform double resonance measurements of the electron spins in the sample region. The control system is configured to operate the microwave resonator device to produce, in the sample region, a probe frequency that creates observable coherence that evolves under pairwise couplings of the electron spins; and a pump frequency that refocuses pairwise interactions at varying times to reveal a distribution of coupling strengths of the pairwise couplings. The control system is configured to operate the microwave resonator device to perform Double Electron-Electron Resonance (DEER) or Pulse Electron Double Resonance (PELDOR) spectroscopy.

[0240] Implementations of the second example may include one or more of the following features. The control system includes a computer and signal processing unit, and a spectrometer. The ESR system includes a primary magnet system that generates a primary magnetic field in the sample region.

[0241] Implementations of the second example may include one or more of the following features. The control system includes a transmitter circuit that provides electron spin resonance control signals to the first transmission line resonator; and a receiver circuit that receives electron spin resonance detection signals from the second transmission line resonator.

[0242] In a third example, an ESR method includes positioning a sample in the sample region of the microwave resonator device of the first example; and by operation of the microwave resonator device, applying a control field to the sample in the sample region. The method includes operating the microwave resonator device to obtain spin signals from the sample.

[0243] Implementations of the third example may include one or more of the following features. The microwave resonator device is configured to support a single resonance mode in the sample region, and applying the control field comprises operating the microwave resonator device at the single resonance mode.

[0244] In a fourth example, an ESR method includes positioning a sample in a sample region of a split-planar microwave resonator device, the sample region residing between a first transmission line resonator disposed on a first substrate of the split-planar microwaveresonator device; and a second transmission line resonator disposed on a second substrate of the split-planar microwave resonator device; and by operation of the split-planar microwave resonator device, applying one or more control fields to the sample in the sample region.

[0245] Implementations of the fourth example may include one or more of the following features. The sample includes a sample region in the range of 0.5 to 100.0 microliters (pL), or larger. The sample comprises a two-dimensional sample and the sample region is a planar sample region. The first and second transmission line resonators are coupled to each other. Applying the one or more control fields includes applying a control field with a single resonance mode to the sample by operation of the first and second transmission line resonators. The single resonance mode is generated by constructive interference between a first microwave magnetic field generated by the first transmission line resonator and a second microwave magnetic field generated by the second transmission line resonator. The first and second transmission line resonators are under-coupled. The first and second transmission line resonators are over-coupled. The first and second transmission line resonators are critically coupled. The single resonance mode has a circular polarization. Applying the one or more control fields to the sample includes by operation of the first transmission line resonator, producing a first microwave field in a first direction in the sample region; and by operation of the second transmission line resonator, producing a second microwave field in a second direction that is orthogonal to the first direction in the sample region. Applying the one or more control fields includes applying a control field with a single resonance mode to the sample by operation of the first and second transmission line resonators; and the single resonance mode has a circular polarization.

[0246] Implementations of the fourth example may include one or more of the following features. The first transmission line resonator includes a first plurality of parallel conductors patterned on the first surface and oriented in a first direction; and the second transmission line resonator includes a second plurality of parallel conductors patterned on the second surface and oriented in a second direction that is orthogonal to the first direction. Applying the one or more control fields to the sample includes operating the first and second transmission line resonators independently of each other. Applying the one ormore control fields to the sample includes operating the first transmission line resonator to apply a first control field having a first resonance mode; and operating the second transmission line resonator to apply a second control field having a second resonance mode that is independent of the first resonance mode. The method further includes at the first transmission line resonator, receiving electron spin resonance control signals from a transmitter circuit; and providing electron spin resonance detection signals from the second transmission line resonator to a receiver circuit. The ESR method includes operating the split planar microwave resonator device to obtain spin signals from the sample in the sample region. The first transmission line resonator and the second transmission line resonator are superconducting transmission line resonators.

[0247] While this specification contains many details, these should not be understood as limitations on the scope of what may be claimed, but rather as descriptions of features specific to particular examples. Certain features that are described in this specification or shown in the drawings in the context of separate implementations can also be combined. Conversely, various features that are described or shown in the context of a single implementation can also be implemented in multiple embodiments separately or in any suitable sub-combination.

[0248] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single product or packaged into multiple products.

[0249] A number of examples have been described. Nevertheless, it will be understood that various modifications can be made. Accordingly, other examples are within the scope of the following claims.

Claims

CLAIMSWhat is claimed is:

1. A microwave resonator device for electron spin resonance, the microwave resonator device comprising: a first substrate comprising a first surface; a second substrate comprising a second surface facing the first surface, the second surface being spaced apart from the first surface by a separation distance; a first ground plane disposed on the first substrate; a second ground plane disposed on the second substrate; a first transmission line resonator patterned on the first surface of the first substrate and configured to produce a first microwave field in a sample region between the first and second surfaces; and a second transmission line resonator patterned on the second surface of the second substrate and configured to produce a second microwave field in the sample region between the first and second surfaces.

2. The microwave resonator device of claim 1, wherein: the first substrate comprises a third surface opposite the first surface, the first ground plane is disposed on the third surface, and the first transmission line resonator comprises a first microstrip resonator on the first surface, and the second substrate comprises a fourth surface opposite the second surface, the second ground plane is disposed on the fourth surface, and the second transmission line resonator comprises a second microstrip resonator on the second surface.

3. The microwave resonator device of claim 2, wherein: the first transmission line resonator comprises a first plurality of microstrip resonators on the first surface, and the second transmission line resonator comprises a second plurality of microstrip resonators on the second surface.

4. The microwave resonator device of claim 3, wherein: the first transmission line resonator comprises a first set of terminal segmentscapacitively coupled to first ends of the first plurality of microstrip resonators through a first coupling gap and a second set of terminal segments capacitively coupled to second, opposite ends of the first plurality of microstrip resonators through a second coupling gap, and the second transmission line resonator comprises a third set of terminal segments capacitively coupled to first ends of the second plurality of microstrip resonators through a third coupling gap and a fourth set of terminal segments capacitively coupled to second, opposites end of the second plurality of microstrip resonators through a fourth coupling gap-5. The microwave resonator device of claim 4, wherein the first transmission line resonator comprises: a first delay line galvanically connected to the first set of terminal segments via a first branching structure; and a second delay line galvanically connected to the second set of terminal segments via a second branching structure.

6. The microwave resonator device of claim 4, wherein: the first transmission line resonator comprises a first feedline galvanically connected to the first set of terminal segments via a first branching structure and a second feedline galvanically connected to the second set of terminal segments via a second branching structure; and the second transmission line resonator comprises a third feedline galvanically connected to the third set of terminal segments via a third branching structure and a fourth feedline galvanically connected to the fourth set of terminal segments via a fourth branching structure.

7. The microwave resonator device of claim 1, wherein the first and second transmission line resonators are configured to support a single resonance mode in the sample region.

8. The microwave resonator device of claim 7, wherein the single resonance mode is an even resonance mode or an odd resonance mode.

9. The microwave resonator device of claim 7, wherein the first and second transmission line resonators are configured to receive control signals with a 180-degree phase difference to support a single resonance mode of high microwave field homogeneity.

10. The microwave resonator device of claim 7, wherein the first and second transmission line resonators are configured to receive control signals with a 0-degree phase difference to support a single resonance mode with a defined spatial microwave field gradient.

11. The microwave resonator device of claim 1, wherein: the first transmission line resonator is configured to produce the first microwave field in a first direction in the sample region; and the second transmission line resonator is configured to produce the second microwave field in a second direction that is orthogonal to the first direction in the sample region.

12. The microwave resonator device of claim 11, wherein the first and second transmission line resonators are configured to support a single resonance mode in the sample region, and the single resonance mode has a circular polarization.

13. The microwave resonator device of claim 1, wherein the first planar transmission line resonator has a first resonance frequency, the second planar transmission line resonator has a second, distinct resonance frequency, and the first and second resonance frequencies are in distinct frequency bands.

14. The microwave resonator device of claim 13, wherein the second resonance frequency is detuned from the first resonance frequency by less than 1 GHz.

15. The microwave resonator device of any one of claims 1 through 14, wherein the first and second transmission line resonators are configured to support even and odd resonance modes in the sample region.

16. The microwave resonator device of any one of claims 1 through 14, wherein the first transmission line resonator comprises a first terminal and a second terminal, the second transmission line resonator comprises a third terminal and a fourth terminal, the firstterminal and the third terminal comprise connectors configured to connect to a first microwave balun or power divider, and the second terminal and the fourth terminal comprise connectors configured to connect to a second microwave balun or power divider.

17. The microwave resonator device of any one of claims 1 through 14, wherein the separation distance is in the range of 0.5 mm to 2.5 mm.

18. The microwave resonator device of any one of claims 1 through 14, wherein the first and second surfaces are separated by at least one of air, vacuum, or dielectric material.

19. The microwave resonator device of any one of claims 1 through 14, wherein the first and second substrates are mechanically supported in a radiofrequency package.

20. The microwave resonator device of any one of claims 1 through 14, wherein: the first transmission line resonator comprises a first plurality of parallel conductors patterned on the first surface and oriented in a first direction; and the second transmission line resonator comprises a second plurality of parallel conductors patterned on the second surface and oriented in a second direction that is orthogonal to the first direction.

21. The microwave resonator device of any one of claims 1 through 14, wherein: the first transmission line resonator is configured to support a first resonance mode; and the second transmission line resonator is configured to support a second mode that is independent of the first mode.

22. The microwave resonator device of any one of claims 1 through 14, wherein: the first transmission line resonator is configured to receive electron spin resonance control signals from a transmitter circuit; and the second transmission line resonator is configured to provide electron spin resonance detection signals to a receiver circuit.

23. The microwave resonator device of any one of claims 1 through 14, wherein: the first transmission line resonator and the second transmission line resonator are made of superconducting material.

24. The microwave resonator device of any one of claims 1 through 14, wherein: the first transmission line resonator has a first quality factor; and the second transmission line resonator has a second, distinct quality factor.

25. An electron spin resonance (ESR) system comprising: the microwave resonator device of any one of claims 1 through 14; and a control system configured to operate the microwave resonator device to perform magnetic resonance measurements of electron spins in the sample region.

26. The ESR system of claim 25, wherein the control system is configured to operate the microwave resonator device to perform double resonance measurements of the electron spins in the sample region.

27. The ESR system of claim 26, wherein the control system is configured to operate the microwave resonator device to produce, in the sample region: a probe frequency that creates observable coherence that evolves under pairwise couplings of the electron spins; and a pump frequency that refocuses pairwise interactions at varying times to reveal a distribution of coupling strengths of the pairwise couplings.

28. The ESR system of claim 26, wherein the control system is configured to operate the microwave resonator device to perform Double Electron-Electron Resonance (DEER) or Pulse Electron Double Resonance (PELDOR) spectroscopy.

29. The ESR system of claim 25, wherein the control system comprises a computer and signal processing unit, and a spectrometer.

30. The ESR system of claim 29, comprising a primary magnet system that generates a primary magnetic field in the sample region.

31. The ESR system of claim 25, wherein the control system comprises: a transmitter circuit that provides electron spin resonance control signals to the first transmission line resonator; and a receiver circuit that receives electron spin resonance detection signals from the second transmission line resonator.

32. An electron spin resonance method comprising: positioning a sample in a sample region of a microwave resonator device, the microwave resonator device comprising: a first substrate comprising a first surface; a second substrate comprising a second surface facing the first surface, the second surface being spaced apart from the first surface by a separation distance; a first ground plane disposed on the first substrate; a second ground plane disposed on the second substrate; a first transmission line resonator patterned on the first surface of the first substrate and configured to produce a first microwave field in the sample region between the first and second surfaces; and a second transmission line resonator patterned on the second surface of the second substrate and configured to produce a second microwave field in the sample region between the first and second surfaces; and by operation of the microwave resonator device, applying a control field to the sample in the sample region.

33. The method of claim 32, wherein the first and second transmission line resonators are configured to support a single resonance mode in the sample region, and applying the control field comprises operating the microwave resonator device at the single resonance mode.

34. The method of claim 32, comprising operating the microwave resonator device to obtain spin signals from the sample.

35. An electron spin resonance method comprising: positioning a sample in a sample region of a split-planar microwave resonator device, the sample region residing between: a first transmission line resonator disposed on a first substrate of the split- planar microwave resonator device; and a second transmission line resonator disposed on a second substrate of the split-planar microwave resonator device; andby operation of the split-planar microwave resonator device, applying one or more control fields to the sample in the sample region.

36. The method of claim 35, wherein the first and second transmission line resonators are coupled to each other, and applying the one or more control fields comprises applying a control field with a single resonance mode to the sample by operation of the first and second transmission line resonators.

37. The method of claim 36, wherein the single resonance mode is generated by constructive interference between a first microwave magnetic field generated by the first transmission line resonator and a second microwave magnetic field generated by the second transmission line resonator.

38. The method of claim 36, wherein the first and second transmission line resonators are under-coupled.

39. The method of claim 36, wherein the first and second transmission line resonators are over-coupled.

40. The method of claim 36, wherein the first and second transmission line resonators are critically coupled.

41. The method of claim 35, wherein applying the one or more control fields to the sample comprises: by operation of the first transmission line resonator, producing a first microwave field in a first direction in the sample region; and by operation of the second transmission line resonator, producing a second microwave field in a second direction that is orthogonal to the first direction in the sample region.

42. The method of claim 41, wherein applying the one or more control fields comprises applying a control field with a single resonance mode to the sample by operation of the first and second transmission line resonators and the single resonance mode has a circular polarization.

43. The method of any one of claims 35 through 42, wherein: the first transmission line resonator comprises a first plurality of parallel conductors patterned on the first surface and oriented in a first direction; and the second transmission line resonator comprises a second plurality of parallel conductors patterned on the second surface and oriented in a second direction that is orthogonal to the first direction.

44. The method of any one of claims 35 through 42, wherein applying the one or more control fields to the sample comprises operating the first and second transmission line resonators independently of each other.

45. The method of any one of claims 35 through 42, wherein applying the one or more control fields to the sample comprises: operating the first transmission line resonator to apply a first control field having a first resonance mode; and operating the second transmission line resonator to apply a second control field having a second resonance mode that is independent of the first resonance mode.

46. The method of any one of claims 35 through 42, comprising: at the first transmission line resonator, receiving electron spin resonance control signals from a transmitter circuit; and providing electron spin resonance detection signals from the second transmission line resonator to a receiver circuit.

47. The method of any one of claims 35 through 42, wherein the sample comprises a sample volume in the range of 0.5 to 100.0 microliters (pL).

48. The method of any one of claims 35 through 42, wherein the sample comprises a two-dimensional sample and the sample region is a planar sample region.

49. The method of any one of claims 35 through 42, wherein the first transmission line resonator and the second transmission line resonator are superconducting transmission line resonators.

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