Microwave resonator array for magnetic resonance

Abstract

In a general aspect, a resonator system for electron spin resonance is described. In some aspects, a resonator system includes a first transmission line resonator, a second transmission line resonator, and first and second feedlines. The first transmission line resonator is patterned on a substrate and configured to produce a first microwave field in a first sample region. The second transmission line resonator is patterned on the substrate and configured to produce a second microwave field in a second, distinct sample region. The first and second feedlines are patterned on the substrate. The first and second transmission line resonators are connected in parallel between the first and second feedlines.

Description

Microwave Resonator Array for Magnetic ResonanceCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 678,789, filed August 2, 2024, entitled "Microwave Resonator Array for Magnetic Resonance." The above-referenced priority document is incorporated herein by reference in its entirety.BACKGROUND

[0002] The following description relates to a microwave resonator array for magnetic resonance.

[0003] 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. ESR systems are used to study various types of samples and phenomena.DESCRIPTION OF DRAWINGS

[0004] FIG. 1 is a block diagram showing aspects of an example electron spin resonance(ESR) system.

[0005] FIG. 2 is a circuit diagram showing an equivalent circuit model of an example microwave resonator device.

[0006] FIG. 3A is a schematic diagram demonstrating the concept of an example microwave resonator device.

[0007] FIG. 3B includes a plot showing S-parameters (S21 and Sil) in dB as a function of frequency in Gigahertz (GHz) in the example microwave resonator device shown in FIG. 3A.

[0008] FIG. 3C includes plots showing current in Amperes (A) as a function of frequency in GHz in respective resonators of the example microwave resonator device shown in FIG. 3A.

[0009] FIGS. 4A-4B are top view and perspective view showing aspects of an example microwave resonator device.

[0010] FIG. 5A includes a plot showing S-parameters (Sil and S21) in dB as a function of frequency in GHz in the example microwave resonator device shown in FIGS. 4A-4B.

[0011] FIGS. 5B-5C include plots showing a spatial distribution of a microwave magnetic field in the microwave resonator device shown in FIGS. 4A-4B.

[0012] FIG. 6 includes a plot showing S-parameters (S21) in dB as a function of frequency in GHz for different lengths of transmission line segments between resonators in the example microwave resonator device shown in FIGS. 4A-4B.

[0013] FIG. 7A is a perspective view showing aspects of an example microwave resonator device.

[0014] FIG. 7B includes a plot showing S-parameters (Sil and S21) in dB as a function of frequency in GHz in the example microwave resonator device shown in FIG. 7A.

[0015] FIG. 8A is a circuit diagram showing an equivalent circuit model of an example microwave resonator device.

[0016] FIG. 8B includes a plot showing S-parameters (Sil and S21) in dB as a function of frequency in GHz in the example microwave resonator device shown in FIG. 8A.

[0017] FIG. 8C includes plots showing current in Amperes (A) as a function of frequency in GHz in respective microwave resonators of the example microwave resonator device shown in FIG. 8A.

[0018] FIGS. 9A-9B are top view and perspective view showing aspects of an example microwave resonator device.

[0019] FIG. 9C includes a plot showing S-parameters (Sil and S21) in dB as a function of frequency in GHz in the example microwave resonator device shown in FIGS. 9A-9B.

[0020] FIGS. 9D-9G include plots showing spin-cavity coupling in Hz for a single spin and different resonance frequencies as a function of distance from the surface of each of the planar transmission line resonators of the example microwave resonator device shown in FIG. 9A-9B.

[0021] FIG. 10 is a flow chart showing aspects of an example process for operating an example microwave resonator device.

[0022] FIG. 11 is a flow chart showing aspects of an example process for operating an example microwave resonator device.

[0023] FIG. 12 is a perspective view showing aspects of an example microwave resonator device.

[0024] FIG. 13 is a perspective view showing aspects of an example microwave resonator device.

[0025] FIG. 14 is a schematic diagram showing aspects of an example electron spin resonance (ESR) system.DETAILED DESCRIPTION

[0026] In some aspects of what is described here, a microwave resonator device for electron spin resonance includes a microwave resonator array. The microwave resonator array includes multiple microwave resonators that are each associated with a distinct sample region. Thus, a microwave resonator array may have multiple sample regions that can be used to measure multiple distinct samples (e.g., simultaneously) or a single sample (e.g., sequentially). Accordingly, the microwave resonator devices described here can be used to improve throughput, allowing a higher number of measurements to be obtained in a given time period. In some cases, the microwave resonators in an array have distinct characteristics and operating parameters, which can be used to obtain a diverse array of measurements, for example, using a different type of resonator for each sample region.

[0027] In some aspects of what is described, the microwave resonators in a microwave resonator array can be connected in parallel, between common feedlines. In operation, each microwave resonator in the microwave resonator array can generate a drive field at amicrowave resonance frequency to manipulate the electron spins in its respective sample region. In some examples, the microwave resonator device includes an array of transmission line resonators that are independently addressable and compatible with multi-sample cartridges for performing multiple electron spin resonance measurements either simultaneously or sequentially. The array of transmission line resonators may include conductors and a ground plane, which can be patterned on the same substrate (e.g., on one side of a substrate, or on both sides of a substrate). The transmission line resonators may be arranged in a one-dimensional or two-dimensional array. Generally, the resonators can be arranged in a variety of regular or irregular geometric arrangements, for example, in a linear array, a square array, a rectangular array, a hexagonal array, an irregular array, etc. In some instances, the transmission line resonators may have unique non-overlapping resonance frequencies, allowing individual sample addressing. In some cases, the techniques and system described here can be deployed in connection with continuous wave (CW) magnetic resonance (e.g., using CW electron paramagnetic resonance spectroscopy methodology), pulsed magnetic resonance (e.g., using pulsed electron paramagnetic resonance spectroscopy methodology), or a combination of these.

[0028] In some instances, the transmission line resonators in the microwave resonator array may have different quality factor (Q) values and coupling, enabling optimal measurements of different types for different applications. In some instances, the quality factor (Q) of a resonator can be defined as the frequency of the resonator divided by its bandwidth. The total Q, Qtot, is related to an internal quality factor Qintand an external quality factor Qext, e.g., 1 / Qtot=+ ^- / Qext- In some implementations, the internalQintquantifies the losses intrinsic to the resonator and may be determined by under coupling the device (e.g., k ~ 0, where the ratio k = Qint / Qext isacoupling factor) 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.

[0029] In some examples, one or more transmission line resonators in the array may be configured to have a high quality factor (Q) value and be critically coupled for CWmeasurements; one or more transmission line resonators in the array may be configured to have a high Q value and be under-coupled for high-cooperativity spin-cavity physics measurements; one or more transmission line resonators in the array may be configured to have a low Q value (~100) and to be over-coupled for high-bandwidth pulsed measurements; one or more transmission line resonators in the array may be configured to have a low to moderate Q value (~100-1000) and to be critically coupled for low- bandwidth measurements such as double resonance (DEER) measurements; and one or more transmission line resonators in the array may be configured to have a moderate Q value (<1000) for pulsed measurements including single frequency distance measurements, such as DQC (Double Quantum Coherence) and SIFTER (single frequency technique for refocusing). In some instances, one or more transmission line resonators in the array may be configured in another manner for other applications.

[0030] In some instances, the transmission line resonators in the microwave resonator array may be made of different materials, enabling measurements to be tailored or optimized for a variety of applications. For example, one or more transmission line resonators in the array may be made of non-superconducting material (e.g., normal metal) permitting room-temperature measurements; one or more transmission line resonators in the array may be made of high-temperature superconducting (HTS) material for measurements up to 100 K; and one or more transmission line resonators in the array may be made of low-temperature superconducting material for measurements below 10 K.

[0031] In some instances, the transmission line resonators in the microwave resonator array may be independently designed to operate at different frequency bands. For example, one or more transmission line resonators in the array may be configured to operate at X- band; and one or more transmission line resonators in the array may be configured to operate at Q-band. In some instances, the transmission line resonators in the microwave resonator array may be independently designed to operate at different frequencies in the same frequency band.

[0032] In some instances, 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 arrays of planar transmission line resonators patterned onsurfaces of two distinct 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 this case, the split-planar microwave resonator device includes multiple pairs of planar transmission line resonators, each including a first planar transmission line resonator from a first array and a second planar transmission line resonator from a second, distinct array. In some instances, the two planar transmission line resonators in a pair are directly facing each other and separated by a separation distance. In some implementations, microwave fields produced by one or both of the two planar transmission line resonators in a pair form a drive magnetic field in a common spatial volume in a sample region of the respective pair. In some instances, the drive magnetic field generated by a pair of transmission line resonators may be at multiple microwave resonance frequencies.

[0033] In some instances, when the microwave resonator device includes one or more arrays of transmission line resonators, a pair of two transmission line resonators from distinct arrays may be coupled to each other. For example, a pair of 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 instances, two transmission line resonators in a pair may be uncoupled from each other. For example, the transmission line resonators in a pair 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.

[0034] In some cases, the 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 spin resonance 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 andfunction 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.

[0035] In some implementations, the systems and techniques described here can provide a number of advantages. For example, the systems and techniques presented may allow multiple samples to be measured simultaneously or sequentially at a rate faster than the thermal relaxation time (7^), and may significantly improve measurement efficiency and enhance the throughput of magnetic resonance measurements by eliminating the need for sample replacement or movement between measurements. Multiple microwave resonators can be designed for specific applications to be used in the same device. In this case, samples can be moved between transmission line resonators for different types of measurements without requiring sample replacement or change of microwave resonator devices. In some cases, a combination of these and potentially other advantages and improvements may be obtained.

[0036] 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.

[0037] 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) 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 orcomponents 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 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 processing units 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.

[0038] 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-sensitivedetection; etc. In some instances, the computer and signal processing units 102 maybe 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 be controlled by software to execute a pre-configured program stored in a memory unit of the computer and signal processing units 102.

[0039] 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.

[0040] 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 signals (2-4 GHz), C-band signals (4-8 GHz), X-band signals (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 toprovide 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.

[0041] 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 in an elevated temperature, e.g., room temperature, outside of a cryogenic environment. In some instances, some components of the spectrometer 104 may operate at 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.

[0042] 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 signalinputs 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.

[0043] In some instances, the spectrometer 104 may be configured to process S-band signals (2-4 GHz), C-band signals (4-8 GHz), X-band signals (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, the spectrometer 104 may include a single stage of up-conversion or downconversion 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.

[0044] 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.

[0045] 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 furtherprocessed 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.

[0046] In some implementations, the resonator unit 106 includes a microwave resonator array 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. In some instances, the resonator unit 106 includes a microwave resonator array that resides in a roomtemperature environment. The microwave resonator array may include multiple planar transmission line resonators. In some implementations, the multiple planar transmission line resonators are coupled to each other in parallel sharing common feedlines. The multiple planar transmission line resonators may be arranged in a one-dimensional array (e.g., FIGS. 9A-9B) or a two-dimensional array (e.g., FIGS. 12-13). Each transmission line resonator in the array may generate a microwave magnetic field (e.g., a drive magnetic field) at a respective frequency in a respective sample region according to the electron spin resonance control signals received to allow exchange of magnetic field energy with a sample at the respective sample region. In other words, the multiple transmission line resonators are configured on the substrate to produce microwave fields in nonoverlapping, independent and distinct sample regions that allow measurement of multiple samples residing at multiple sample regions simultaneously or sequentially.

[0047] In some instances, the microwave resonator array includes multiple conductors and a ground plane disposed on a common substrate. In some implementations, the multiple conductors and the ground plane include superconducting or non- superconducting material. In some instances, a transmission line resonator in the array is patterned on the substrate as a single microstrip line, multiple microstrip lines, a coplanar waveguide, or another type of transmission line pattern. In some implementations, each transmission line resonator includes a subset of the multiple conductors, which are formedin an array of conductive segments. In some instances, the conductive segments in each transmission line resonator are arranged in parallel to one another with equal spacing between each neighboring pair of conductive segments. Each conductive segment in a transmission line resonator may be configured to resonate at the same microwave resonance frequency. Each of the conductive segments in a transmission line resonator can be implemented, for example, as a half-wave resonator, a full-wave resonator, or a multi- half-wave resonator. Each of the conductive segments in a transmission line resonator of the array may be configured to provide maximum magnetic field at the center of each conductive segment, where a respective sample region of the microwave resonator device resides. In some implementations, the multiple transmission line resonators of the array may be configured differently from one another. For example, each transmission line resonator in the array may have one or more different properties, e.g., intrinsic resonance frequency, quality factor, or coupling. In some instances, a subset of transmission line resonators in the array may be identical to one another. For example, transmission line resonators in a subset may have the same intrinsic resonance frequencies, the same quality factor, or the same coupling. For example, transmission line resonators from different subsets may have different properties. In some instances, the microwave resonator device of the resonator unit 106 may be represented by one or more equivalent circuit diagrams of the type shown in FIGS. 2, 3A, and 8A. In some instances, the microwave resonator device of the resonator unit 106 may be implemented as one or more microwave resonator arrays of the type shown in FIGS. 4A-4B, 7A, 9A-9B, or in another manner.

[0048] 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.

[0049] 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 temperature (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.

[0050] 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.

[0051] In some implementations, the primary magnet system 112 provides a primary magnetic field in the electron spin resonance system 100 including the sample regions 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 the sample regions defined by the resonator unit 106. In some implementations, the primary magnet system 112 includes an electromagnet system thatcan 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. In some instances, the primary magnetic system 112 can provide a primary magnetic field in the electron spin resonance system 100 with a controlled spatial variation according to the locations of the microwave resonators or sample regions, and resonance frequencies of the microwave resonators. In some instances, the spatial variation of the primary magnetic field may be configured and determined in another manner in order to tune the respective drive frequencies at the respective microwave resonators of the array.

[0052] In some aspects of operation, a spin ensemble in one or more samples interacts with the resonator unit 106. Control of spins in the samples 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 spins can be a collection of particles having non-zero spin 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 f1!!), 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.

[0053] FIG. 2 is a is a schematic diagram of an example microwave resonator device 200. In some instances, the microwave resonator device 200 may be used in an electron spin resonance system for performing ESR spectroscopy of multiple samples. In some implementations, the microwave resonator device 200 is configured to produce multiple magnetic fields at radio or microwave frequencies configured to manipulate electron spins in multiple sample regions of the microwave resonator device 200. The examplemicrowave resonator device 200 may include an array of N microwave resonators, where N is an integer equal to or greater than 2 (A > 2). Specifically, as shown in FIG. 2, the example microwave resonator device 200 includes a first microwave resonator 202A, a second microwave resonator 202B, a third microwave resonator 202C, and a fourth microwave resonator 202D which are coupled in parallel between input and output ports 206A, 206B via common feedlines 210. The microwave resonators 202A / 202B / 202C / 202D are excited by control signals received (e.g., from a spectrometer) at the input port 206A, and spin measurements generate response signals that are delivered to the output port 206B. In some instances, the microwave resonator device 200 may be implemented in the resonator unit 106 of the example ESR system 100 in FIG. 1. In some instances, each microwave resonator 202A / 202B / 202C / 202D can be controlled and measured independently, for example, by adjusting the operation frequency of the spectrometer. In some implementations, the feedlines 210 are configured to communicate magnetic resonance control signals from a transceiver (e.g., in the control system 114 of the example ESR system 100 shown in FIG. 1) to the microwave resonators 202A, 202B, 202C, 202D in parallel, and the feedlines 210 are also configured to communicate magnetic resonance response signals to the transceiver from the microwave resonators 202A, 202B, 202C, 202D in parallel.

[0054] In some instances, the microwave resonators 202A,202B, 202C, 202D may be implemented as planar transmission line resonators, 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 another 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 microwave resonators 202A, 202B, ..., 202C, 202D are arranged as a onedimensional array of planar transmission line resonators on a surface of a substrate, e.g., a single row; or a two-dimensional array, e.g., multiple rows and columns of planar transmission line resonators on a surface of a substrate. 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.

[0055] In some instances, the conductors, ground planes, feedlines, coupling elements of the microwave resonators 202A / 202B / 202C / 202D can be fabricated on the substrate 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 microwave resonators 202A / 202B / 202C / 202D may be made of titanium (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 microwave resonators 202A / 202B / 202C / 202D, 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 to reduce or 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 microwave resonators 202A / 202B / 202C / 202D. In some instances, the microwave resonators 202A / 202B / 202C / 202D may be made of copper, silver, gold, or other non- superconducting material. In some instances, the microwave resonators 202A / 202B / 202C / 202D may be made of materials (e.g., Al) that are superconductive at certain temperatures but not the temperature of operation of the resonator device. In some instances, the microwave resonators 202A / 202B / 202C / 202D may all be made of the same material or distinct materials. In general, conductors can be patterned (e.g., fabricated or formed) on a substrate using standard microfabrication processes, which may include, for example, various combinations of material deposition, lithography, and material removal processes.

[0056] In the example shown, each of the microwave resonators202A / 202B / 202C / 202D includes an RLC resonator with a combination of a resistor (R), an inductor (L), and a capacitor (C) to resonate at a specific intrinsic resonance frequency. Forexample, each of the microwave resonators 202A / 202B / 202C / 202D may be implemented as the planar transmission line resonator 412A, 412B, 712A, 712B, 712C, 912A, 912B, 912C, 912D as shown in FIGS. 4A-4B, 7A, 9A-9B or in another manner. The intrinsic resonance frequency of a planar transmission line resonator can be determined by the physical dimensions of the device (e.g., by the dimensions of the conductive segments). For example, the intrinsic resonance frequency of the planar transmission line resonator 412A can be determined by the length of the conductive segments 422.

[0057] In some implementations, each of the microwave resonators 202A / 202B / 202C / 202D is connected to the common feedlines 210 via a respective pair of coupling elements 208, which provides impedance matching and field confinement.Specifically, in the example shown in FIG. 2, the first microwave resonator 202A is coupled to the common feedlines 210 via coupling elements 208-1A and 208-1B; the second microwave resonator 202B is coupled to the common feedlines 210 via coupling elements 208-2A and 208-2B; the third microwave resonator 202C is coupled to the common feedlines 210 via coupling elements 208-3A and 208-3B; and the fourth microwave resonator 202D is coupled to the common feedlines 210 via coupling elements 208-4A and 208-4B. In some instances, the coupling element 208 can be any structure modeled as a reactive circuit element, such as a capacitor, inductor, or a combination of the two. In some instances, the coupling elements 208 may be implemented by the coupling gaps and terminals shown in FIGS. 4A-4B, 7A, 9A-9B or in another manner. The microwave resonators 202A / 202B / 202C / 202D may be capacitively coupled to the feedlines 210 through respective coupling elements 208-1A / 208-1B, 208-2A / 208-2B, 208-3A / 208-3B, 208-4A / 208-4B. In some instances, the capacitances of the respective coupling elements 208-1A / 208-1B, 208-2A / 208-2B, 208-3A / 208-3B, 208-4A / 208-4B can be different.

[0058] In some instances, a microwave resonator may be over-coupled, under-coupled, or critically coupled. When over-coupled, 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 g =is greater than 1. When the coupling element is a capacitive coupling element, the coupling capacitance is high; and the size of the couplinggap is small. When under-coupled, most of the EM energy is dissipated inside the microwave resonator device. In this case, the internal Quality factor (Qint) is lower than the external quality factor {Qext}. The coupling coefficient is less than 1, e.g., g < 1. When the coupling element is a capacitive coupling element, the coupling capacitance is low; and the size of the coupling gap is big. When critically coupled, 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), e.g., g = 1. When a microwave resonator is critically coupled, the drive magnetic field generated by the microwave resonator at the corresponding sample region is at its maximum value. In some instances, the coupling of a microwave resonator can be tuned, adjusted and otherwise controlled by adjusting the coupling elements.

[0059] The N microwave resonators 202 are electrically coupled to the common feedlines 210 via the respective coupling elements 208 at respective nodes 212. As shown in FIG. 2, the first microwave resonator 202A is electrically connected to the common feedlines 210 at nodes 212-1A, 212-1B; the second microwave resonator 202B is electrically connected to the common feedlines 210 at nodes 212-2A, 212-2B; the third microwave resonator 202C is electrically connected to the common feedlines 210 at nodes 212-3A, 212-3B; and the fourth microwave resonator 202D is electrically connected to the common feedlines 210 at nodes 212-4A, 212-4B. As shown in FIG. 2, the nodes divide the feedlines 210 into multiple segments 204. Two immediately neighboring nodes 212 on the same feedline 210 are separated by an electrical length 0 (in degrees) of the segment. As shown in FIG. 2, the first and second microwave resonators 202A, 202B are separated by segments 204-1A, 204-1B; and the third and fourth microwave resonators 202C, 202D are separated by segments 204-2A, 204-2B. In some implementations, to ensure the correct impedance, the electrical length 0 of the segments 204- 1A, 204-1B, 204-2A, 204-2B is chosen to be 180 degrees (or a multiple integer of 180 degrees), as the impedance of the load remains unchanged after each 180-degree segment of a transmission line.

[0060] In some instances, each microwave resonator 202 is configured to produce a microwave field in a respective sample region associated with a distinct ESR sample 214 to allow for independent addressability. Additionally, each microwave resonator 202 can bedesigned to have unique properties, such as resonance frequency, quality factor (Q), coupling, or other properties, to allow optimal performance for different types of measurements. As shown in FIG. 2, different ESR samples 214A, 214B, 214C, 214D reside in respective sample regions of the microwave resonators 202A, 202B, 202C, 202D. All samples can be placed in a sample holder with designated locations matched to the topology of the microwave resonator array. When the sample holder is positioned for operation of the resonator device 200, each ESR sample is positioned precisely above its corresponding resonator. This ensures that each sample interacts only with the microwave field generated by its respective microwave resonator. Specifically, a first sample 214A resides in a corresponding sample region of the first microwave resonator 202A; a second sample 214B resides in a corresponding sample region of the second microwave resonator 202B; a third sample 214C resides in a corresponding sample region of the third microwave resonator 202C; and a fourth sample 214D resides in a corresponding sample region of the fourth microwave resonator 202D. The multiple samples 214A, 214B, 214C,214D may be measured simultaneously or sequentially by operation of the microwave resonator device 200. In some instances, a sample may be transferred, for example by operation of a sample transferring mechanism, from one microwave resonator 202 to another to allow a sequential measurement using different microwave resonators optimized for different measurement types at different times.

[0061] In some instances, the microwave resonators 202A, 202B, 202C, 202D may have different resonance frequencies fltf2, ..., fN. During operation, when a microwave control signal at frequency ft (i=l, 2, ..., A) is communicated to the input port 206A, the microwave resonator 202 operating at the corresponding resonance frequency ft matching that of the microwave control signal can respond to the microwave control signal and allow the microwave control signal to pass to the output terminal 206B, while the other microwave resonators remain inactive and open-circuited. In such implementations, the electrical length 6 should be far from 90 degrees, as an open-circuit load becomes a short-circuit after a 90-degree segment of transmission line, which would degrade the circuit's performance. In some instances, a subset of the microwave resonators 202 may be designed to have identical resonance frequencies, such that the microwave resonators inthe subset resonate at the same resonance frequency. In this case, the microwave resonators 202 in the subset can resonate simultaneously when a microwave control signal is applied with a frequency matching the resonance frequencies of the microwave resonators. In some instances, a corresponding drop in the field conversion factor may occur due to energy being distributed across multiple microwave resonators of the subset.

[0062] In some instances, the microwave resonators 202A / 202B / 202C / 202D may have distinct intrinsic resonance frequencies, e.g., the first and second microwave resonators 202A, 202B may be configured to resonate at different resonance frequencies. In certain instances, the first and second microwave resonators 202A, 202B may have identical intrinsic resonance frequencies, e.g., the first and second microwave resonators 202A, 202B maybe configured to resonate at the same resonance frequency. The microwave resonators 202A / 202B / 202C / 202D are taken to be positioned at a sufficient distance to ensure substantially no overlap between their fields. Thus, coupling between the microwave resonators in the array can occur through the common feedline 210.

[0063] In some instances, the sample regions 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 selfassembled monolayer films, polymer films, biological films, single molecule magnets (SMMs), etc. Some example applications of the microwave resonator device 200 can include using the Langmuir-Blodgett films with free radicals for quantum computing, and using the biological films to, for example, label electrons and study membrane bound proteins using ESR.

[0064] When a sample (with its microwave resonator) is selected for study, the static magnetic field Bois adjusted according to the Larmor equation f = y Boto achieve the magnetic resonance condition, where f is the resonance frequency of the corresponding microwave resonator and y=2.8024 MHz / Gauss is the gyromagnetic ratio for a free electron spin.

[0065] FIG. 3A is a circuit diagram showing an equivalent circuit model of an example microwave resonator device 300. In some instances, the microwave resonator device 300may be used in an electron spin resonance system for performing ESR spectroscopy of multiple samples. The example microwave resonator device 300 includes an array of two microwave resonators 302A, 302B coupled in parallel between two nodes 312A, 312B. The microwave resonator 302A is coupled to the two nodes 312A, 312B through two capacitive coupling elements 308-1A and 308-1B; and the microwave resonator 302B is coupled to the two nodes 312A, 312B through two capacitive coupling elements 308-2A and 308-2B. The microwave resonators 302A, 302B are transmission line resonators with two different intrinsic resonance frequencies of 9.8 GHz and 9.6Hz. The two microwave resonators 302A, 302B are separated by an electrical length of 6 causing a phase difference of 180 degrees between signals transmitted to the two microwave resonators 302A, 302B and between signals received from the two microwave resonators 302A, 302B. The node 312A is a source terminal connected to an excitation source 306; and the node 312B is a load terminal connected to a load.

[0066] FIG. 3B includes a plot 320 showing S-parameters (S21 and Sil) in dB as a function of frequency in GHz in the example microwave resonator device 300 shown in FIG. 3A. Results shown in FIG. 3B are derived from circuit analysis of the circuit in FIG. 3A. The capacitance values of the coupling capacitors 308-1A / 308-1B and 308-2A / 308-2B are both equal to 8.2 fF. Curve 322 represents Sil; and curve 324 represents S21. As shown in FIG. 3B, the resonance frequencies of the microwave resonators 302A, 302B in the microwave resonator device 300 changes from their intrinsic values of 9.6 GHz and 9.8 GHz to 9.307 GHz and 9.494 GHz, respectively.

[0067] FIG. 3C includes plots 330, 332 showing current in amps as a function of frequency in GHz in respective microwave resonators 302A, 302B of the example microwave resonator device 300 shown in FIG. 3A. To calculate the magnitude of the current at the center of each microwave resonator 302A / 302B, where the current is maximum, the source and load impedance are chosen to be Rs= RL= 50 £1, and the peak-to- peak voltage of the source is Vs= 0.7 V, which is equivalent to 1 dBm input power available from the source. As shown in FIG. 3C, the microwave resonator 302A only resonates at the frequency of 9.307 GHz, while the microwave resonator 302B has no current at this frequency. Similarly, the microwave resonator 302B only resonates at 9.494 GHz, while themicrowave resonator 302A has no current at this frequency. This result demonstrates the frequency selectivity of the array of the microwave resonators, where only one microwave resonator generates the microwave field (electrical current in the circuit analysis) to address an ESR sample in the corresponding sample region. When one microwave resonator is selectively activated at a given excitation frequency, the other remains inactive.

[0068] FIGS. 4A-4B are top-view and perspective-view schematic diagrams showing aspects of an example microwave resonator device 400. As shown in FIGS. 4A-4B, the microwave resonator device 400 includes a microwave resonator array, including a first microwave resonator unit 402A and a second microwave resonator unit 402B connected in parallel between two transmission lines 410A, 410B connected to two respective ports 406A, 406B. The first and second microwave resonator units 402A, 402B are patterned on the same surface of a substrate and configured to produce microwave drive fields in distinct sample regions. In some implementations, the first microwave resonator unit 402A includes a first planar transmission line resonator 412A which includes an array of conductive segments 422 and a ground plane on a substrate 442; the second microwave resonator unit 402B includes a second planar transmission line resonator 412B which includes an array of conductive segments 432 and a ground plane on the same substrate. In some instances, the first and second planar transmission line resonators 412A, 412B may be identical and have the same resonance frequency. In some instances, distinct EPR samples can be positioned in respective sample regions of the first and second microwave resonator units 402A, 402B. In some instances, an EPR sample can be transferred between the sample regions of the first and second microwave resonator units 402A, 402B. The example microwave resonator device 400 can include additional or different features, and the features of the example microwave resonator device 400 may be arranged in the configuration shown or in another configuration.

[0069] The first microwave resonator unit 402A shown in FIGS. 4A-4B includes a first terminal 428A and a second terminal 428B. The first and second terminals 428A, 428B, the first transmission line resonator 412A, and the ground plane can define planar transmission line structures at a first area 408A of on a surface of the substrate 442. Thesecond microwave resonator unit 402B shown in FIGS. 4A-4B includes a third terminal 438A and a fourth terminal 438B. The third and fourth terminals 438A, 438B, the second transmission line resonator 412B, and the ground plane can define planar transmission line structures in a second distinct area 408B on the same surface of the substrate 442.

[0070] In some implementations, the microwave resonator device 400 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 400 to perform multiple resonance measurements of multiple electron spin centers in the different sample regions of the microwave resonator device 400 at the same time. In some instances, the control system 114 may operate the microwave resonator device 400 to perform double resonance measurements of the electron spins in the sample region. For example, the microwave resonator device 400 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 400 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.

[0071] In some implementations, the example microwave resonator device 400 can be operated according to the operations in the example process 1000 in FIG. 10 to produce a time-varying microwave field in the two sample regions of the microwave resonator device 400. For example, the microwave resonator device 400 may produce two distinct microwave fields at a radio frequency or microwave frequency configured to manipulate electron spins in the distinct sample regions defined by the respective transmission line resonators 412A, 412B.

[0072] As shown in FIGS. 4A-4B, the first terminal 428A includes conductor material disposed on the substrate 442. The first terminal 428A has a set of terminal segments 426A and a feedline 430A galvanically connected to the set of terminal segments 426A. The terminal segments 426A extend from the feedline 430A toward the first planartransmission line resonator 412A. The first terminal 428A includes sixteen terminal segments 426A, each extending toward a respective conductive segment 422 of the first planar transmission line resonator 412A. In some instances, the first terminal 428A can include two terminal segments 426A, four terminal segments 426A, eight terminal segments 426A, sixteen terminal segments 426A, thirty-two terminal segments 426A, sixty-four terminal segments 426A, or in general powers of two, according to the number of the conductive segments 422 in the first planar transmission resonator 412A. In some implementations, the set of terminal segments 426A of the first terminal 428A have a width identical to the width of the conductive segments 422 of the first planar transmission line resonator 412A.

[0073] Similarly, the second terminal 428B includes a conductor material disposed on the first substrate. The second terminal 428B has a set of terminal segments 426B and a feedline 430B galvanically connected to the set of terminal segments 426B. The terminal segments 426B extend from the feedline 430B toward the first planar transmission line resonator 412A. The second terminal 428B includes sixteen terminal segments 426B, each extending toward a respective conductive segment 422 of the first planar transmission line resonator 412A. In some instances, the second terminal 428B can include two terminal segments 426B, four terminal segments 426B, eight terminal segments 426B, sixteen terminal segments 426B, thirty-two terminal segments 426B, sixty-four terminal segments 426B, or in general powers of two, according to the number of the conductive segments 422 in the first transmission resonator 412A. In some implementations, the set of terminal segments 426B of the second terminal 428B have a width identical to the width of the conductive segments 422 of the first planar transmission line resonator 412A.

[0074] In some implementations, the first and second terminals 428A, 428B include branching structures 427A, 427B galvanically connecting the respective terminal segments 426A, 426B to the respective feedlines 430A, 430B. The branching structures 427A, 427B can function as a power divider that divides and delivers the power from an input to the terminal segments 426A, 426B. In some instances, the branching structure 427A, 427B can include successive levels (or division stages). In some instances, the branching structure 427A, 427B can be configured to achieve desirable branch impedances at each divisionstage. For example, the branching structure 427A, 427B 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 the preceding level. In some implementations, the power dividers can include tapered branch sections, for example, to adjust the lines for impedance matching.

[0075] As shown schematically in FIGS. 4A-4B, each of the conductive segments 422 in the first planar transmission line resonator 412A includes a respective conductor disposed on the surface of the substrate 442. A first end of each of the conductive segments 422 in the first planar transmission line resonator 412A is aligned with a respective terminal segment 426A of the first terminal 428A. Each of the conductive segments 422 is elongated. Each of the conductive segments 422 is capacitively coupled to a respective one of the terminal segments 426A, while a second, opposite end of each of the conductive segments 422 is capacitively coupled to a respective one of coupling segments 426B of the second terminal 428B. In certain instances, the array of conductive segments 422 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.

[0076] In some implementations, each of the conductive segments 422 and the ground plane define a microstrip line resonator. In some implementations, the conductive segments 422 in the first planar transmission line resonator 412A can be identical to each other. In some examples, the conductive segments 422 are parallel to each other, with equal spacing between each neighboring pair of the conductive segments 422. 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.

[0077] The example conductive segments 422 can be sized based on the wavelength of a desired resonance frequency. For example, the length of the conductive segment 422 (e.g., from the first end to the second opposite end) can be designed to produce a resonancemode around the specified resonance frequency of operation (e.g., a>r= 2TI ■ 10 GHz). Each conductive segment 422 can be a half-wave resonator, a full-wave resonator, or a multi- half- wave resonator. For example, if the desired resonance frequency is , the conductive segment 422 can have a length of A / 2, A, 3A / 2, 2A, etc. In other words, the desired resonance frequency corresponds to the length of the conductive segments 422.

[0078] The multiple conductive segments 422 can be configured to resonate at the same microwave resonance frequency. In some instances, the conductive segment 422 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 422. In some implementations, the conductive segments 422 can be edge-coupled to each other so that the magnetic field generated by each resonator interferes with the microwave magnetic field generated by one or more neighboring conductive segments 422. In some cases, the conductive segments 422 produce an in-plane uniform field in a direction perpendicular to the surface of the substrate 442.

[0079] In the example shown in FIGS. 4A-4B, a coupling gap 424A is defined between the first end of the conductive segments 422 and the respective terminal segments 426A of the first terminal 428A. Similarly, a coupling gap 424B is defined between the second end of the conductive segments 422 and the terminal segments 426B of the second terminal 428B. The coupling gaps 424A, 424B can include vacuum, dielectric material (e.g., sapphire, silicon, quartz, etc.), or a combination of them. The terminal segments 426A in the first terminal 428A and the terminal segments 426B in the second terminal 428B can serve as feed lines coupled to the array of conductive segments 422 via the coupling gaps 424A, 424B. In some instances, during operation, all of the conductive segments 422 experience an electromagnetically equivalent feed line path from a pair of a terminal segment 426A of the first terminal 428A and a respective terminal segment 426B of the second terminal 428B, and the conductive segments 422 of the first transmission line resonator 412A can resonate in-phase at their fundamental frequency. Each conductive segment 422 is configured to resonate at a first intrinsic resonance frequency, and the length of the conductive segments 422 may be an even number of half- wavelengths for the first intrinsicresonance frequency; and the length of the conductive elements 422 may be an odd number of half- wavelengths for the first intrinsic resonance frequency.

[0080] As shown in FIGS. 4A-4B, the first and second terminals 428A, 428B, and the first planar transmission line resonator 412A 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 428A), conduct the signal across the parallel conductive segments 422 in the same direction in the first planar transmission line resonator 412A; and generate a microwave magnetic field in the sample region.

[0081] In some implementations, the first and second terminals 428A, 428B, the first planar transmission line resonator 412A are configured as superconducting transmission line resonators. The conducting material of the first and second terminals 428A, 428B, the first planar transmission line resonator 412A, 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.

[0082] In some instances, the second microwave resonator unit 402B may be implemented identical to the first microwave resonator unit 402A or in another manner. For example, components (e.g., terminals 438A, 438B, feedlines 440A, 440B, terminal segments 436A, 436B, conductive segments 432, branching structures 437A, 437B, and coupling gaps 434A, 434B) of the second microwave resonator unit 402B may be implemented as the respective components of the first microwave resonator unit 402A.

[0083] In some implementations, sample regions of the microwave resonator device 400 are located above the conductive segments 422 of the first planar transmission line resonator 412A and the conductive segments 432 of the second planar transmission line resonator 412B. Each of the sample regions can be a 3-dimensional sample region or another type of volume. In some instances, the micro wave magnetic fields generated by the first and second planar transmission line resonators 412A, 412B form respective control fields in the sample regions. In some instances, each control field may be uniform across a respective sample region (e.g., in both amplitude and direction as shown in FIGS. 5B-5C). For example, the sample regions can include planes (parallel to the surface) over which the instantaneous magnetic fields generated by the first and second planar transmission line resonator 412A, 412B are homogeneous during operation. In some instances, the sample regions 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 400 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 regions are regions of given homogeneity interacting with the samples.

[0084] In some implementations, the example microwave resonator device 400 and the sample can be positioned in an external, static primary magnetic field (Bo). The primary magnetic field Bocan be parallel to the surface of the substrate 442 along the Y axis. The primary magnetic field Bocan 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 Bo. The resonance frequencies are typically in the GHz range (e.g., microwave frequencies) in ESR applications. In operation, the conductive segments 422, 432 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 422, 432 (e.g., along the X or Z axis).

[0085] 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 424A, 424B, 434A, 434B at the ends of each conductive segments 422, 432, provided that the internal quality factor remains significantly higher than the external quality factor. The first and second planar transmission line resonators 412A, 412B 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 412B may have a second, distinct intrinsic resonance frequency; and the first and second intrinsic resonance frequencies of the first and second transmission line resonators 412A, 412B may have a frequency detuning.

[0086] In some instances, the microwave resonator device 400 can convert the electron spin resonance control signals to microwave magnetic fields in the sample regions. In some implementations, the microwave magnetic fields can be homogeneous in the sample regions, such that the microwave magnetic fields are uniform throughout the respective sample regions. This microwave magnetic fields can be substantially uniform in strength and occupy a small mode volume well matched to the volume of the samples. The microwave magnetic fields can be applied to the samples in the sample regions, for example, for pulsed ESR or multi-resonance ESR measurements.

[0087] In the example shown in FIGS. 4A-4B, the first and second planar transmission line resonators 412A, 412B each includes an array of 16 straight X / 2 microstrip lines. The first and second microwave resonator units 402A, 402B are fabricated on the same surface of the substrate 442. Extension directions of the microstrip lines on the first and second microwave resonator units 402A, 402B are aligned in parallel (e.g., along the X-axis). Ground planes are patterned on the opposite surface of the substrate 442. In some instances, the first and second planar transmission line resonators 412A, 412B of the first and second microwave resonator units 402A, 402B may be different with different coupling gaps, different number of microstrips, different geometries, different substrate materials, and different intrinsic resonance frequencies. For example, the first planar transmission line resonator 412A may define a first resonance frequency in a first frequency band (e.g., X-band 8-12 GHz); and the second planar transmission line resonator412B may define a second, distinct resonance frequency in a second, distinct frequency band (e.g., Q-band 33-50 GHz). In some instances, the first and second resonance frequencies defined by the first and second planar transmission line resonators 412A, 412B may have different values within the same frequency band. For another example, the first planar transmission line resonator 412A may have a first quality factor; and the second planar transmission line resonator 412B may have a second distinct quality factor. In some instances, the microwave resonator device 400 includes an RF package which is configured to fully house the first and second microwave resonator units 402A, 402B and other components. In some instances, the RF package may include RF connectors, mechanical fasteners, metal plates, windows, alignment pins, etc. During operation, the microwave magnetic fields generated by each of the first and second planar transmission line resonators 412A, 412B are spatially separated from one another. In some instances, the sample regions may be up to 100.0 pL or more.

[0088] In some instances, the first and second planar transmission line resonators 412A, 412B may be over-coupled, under-coupled, or critically coupled. In some instances, the coupling of the first and second planar transmission line resonators 412A, 412B to the respective terminals 428A / 428B, 438A / 438B can be tuned, adjusted and otherwise controlled by adjusting the capacitive coupling (e.g., the coupling gaps 424A, 424B, 434A, 434B in the example microwave resonator device 400 shown in FIGS. 4A-4B) between the terminal segments 426A / 426B, 436A,436B and the respective sets of conductive segments 422, 432 of the respective planar transmission line resonators 412A, 412B.

[0089] FIG. 5A includes a plot 500 showing S-parameters (Sil and S21) in dB as a function of frequency in GHz in the example microwave resonator device 400 shown in FIGS. 4A-4B. The plot 500 shows a comparison of Sil and S21 as a function of frequency in two example microwave resonator devices, each of which includes a single microwave resonator unit. FIG. 5A presents the full-wave simulation results of the microwave resonator device 400 depicted in FIGS. 4A-4B. Curves 502 (Sil)) and 504 (S21) are obtained on the example microwave resonator device 400; curve 506 (S21) is obtained on an example microwave resonator device including only the first microwave resonator unit402A; and curve 508 (S21) is obtained on a microwave resonator device including only the second microwave resonator unit 402B.

[0090] In the simulations represented in FIGS. 5A-5C, each of the first and second planar transmission line resonators 402A, 402B of the microwave resonator device 400 includes a 16-strip microstrip A / 2-resonator. The microstrip lines of the first planar transmission line resonator 402A have a length l0of 5200 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 402B have a length l0of 5100 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 coupling gap between the terminal segments and conductive segments of the first planar transmission line resonator 402A is 250 pm; and the coupling gap between the terminal segments and conductive segments of the second planar transmission line resonator 402B is 350 pm. The electrical length of transmission line (TL) segments between the first and second microwave resonator units 402A, 402B is designed to be 180 degrees at the middle of the two resonance frequencies which is around 6 mm at 9.6 GHz.

[0091] The metal component of the microwave resonator device 400 used in this simulation is made of high-temperature YBCO films with a thickness of 300 nm, deposited on both the top and bottom faces of a sapphire substrate. A 50 Ohm feedline, 400 pm in width, originates from the input node 406A and excites the first and second planar transmission line resonators 402A, 402B, with the return path located on the opposite side. The chip dimensions are 24 mm x 15 mm.

[0092] As seen in FIG. 5A, the example microwave resonator device 500 has two resonances at frequencies of 9.494 GHz and 9.713 GHz, corresponding to the first and second planar transmission line resonators 412A, 412B respectively. The Q factors for the first and second planar transmission line resonators 412A, 412B are 527 and 511, respectively. The external Q factor associated with each planar transmission line resonator depends on the electrical length between the two planar transmission line resonators412A, 412B, as it changes the output impedance seen from the ends of each resonator planar transmission line resonator.

[0093] The Q factor of the microwave resonator device with a single microwave resonator unit identical to the first microwave resonator unit 402A is 330; and the Q factor of the microwave resoantor device with a single microwave resonator unit identical to the second microwave resoantor unit 402B is 690. This demonstrates that the Q factor of the array can be affected by the electrical coupling of the two planar transmission line resonators through the TL segments 404A, 404B.

[0094] At each resonance frequency identified in the S-parameter results shown in FIG. 5A only the corresponding planar transmission line resonator is actively excited, while the other resonator exhibits minimal residual magnetic field as shown in FIGS. 5B and 5C. Fine- tuning the electrical length between the two planar transmisison line resonators 412A, 412B, as well as increasing the electrical length to 360 degrees, 540 degrees, or more, can further reduce this residual interaction. The input power is 1W.

[0095] FIG. 6 includes a plot showing S-parameters (S21) in dB as a function of frequency in GHz at different electrical lengths of the TL segments 404A / 404B separating the two microwave resonator units 402A, 402B in the example microwave resonator device 400 shown in FIGS. 4A-4B. For these simulations, the electrical lengths are 5.34 mm, 5.84mm and 6.34mm, respectively. The first and second planar transmission line resonators 412A, 412B have lengths of 5200 pm and 5100 pm, respectively. The coupling gaps of both planar transmission line resonators 412A, 412B are 250 pm. These results demonstrate that the Q factors of the first and second planar transmission line resonators 412A, 412B depend on the electrical length of the TL segments between them. The Q factor of the first planar transmission line resonator 412B remains mostly unaffected. In contrast, the Q factor of the first planar transmission line resonator 412A, which is closer to the input and output ports, changes significantly based on the electrical length of the transmission segment between the two planar transmission line resonators 412A, 412B.

[0096] FIG. 7A is a perspective view of an example microwave resonator device 700. As shown in FIG. 7A, the microwave resonator device 700 is a microwave resonator array,including a first microwave resonator unit 702A, a second microwave resonator unit 702B, and a third microwave resonator unit 702C, which are patterned on the same surface of a substrate 752. The first, second and third microwave resonator units 702A / 702B / 702C are connected in parallel between two feedlines 710A / 710B and spatially separated by a separation distance (d) defined by the electrical lengths of respective segments 704- 1A / 704-1B, 704-2A / 704-2B of the feedlines 710A, 710B. In some implementations, the first microwave resonator unit 702A includes a first planar transmission line resonator 712A which includes an array of conductive segments 722 and a ground plane on the substrate 752; the second microwave resonator unit 702B includes a second planar transmission line resonator 712B which includes an array of conductive segments 732 and a ground plane on the substrate 752; and the third microwave resonator unit 702C includes a third planar transmission line resonator 712C which includes an array of conductive segments 742 and a ground plane on the substrate 752. In some instances, the EPR samples can be positioned simultaneously on a sample cartridge at respective sample regions of the planar transmission line resonators l / l 12B / 712C; and can be tested in parallel or sequentially. In some instances, an EPR sample can be positioned and tested in a sample region of a planar transmission line resonator of the example microwave resonator device 700; and moved to and tested in a different sample region of a different planar transmission line resonator of the example microwave resonator device 700. The example microwave resonator device 700 can include additional or different features, and the features of the example microwave resonator device 700 may be arranged in the configuration shown or in another configuration. In some instances, the microwave resonator device 700 may be operated according to the operations in the example process 1000 or in another manner.

[0097] In some implementations, the microwave resonator device 700 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 700 to perform multiple resonance measurements of multiple electron spin centers in the multiple sample regions of the microwave resonator device 700. In some instances, the control system 114may operate the microwave resonator device 700 to perform double resonance measurements of the electron spins in the sample regions. For example, the microwave resonator device 700 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 700 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.

[0098] The first microwave resonator unit 702A includes a first terminal 728A and a second terminal 728B. The first and second terminals 728A / 728B, the first planar transmission line resonator 712A, and the ground plane can define planar transmission line structures in a first area on the substrate 752. The second microwave resonator unit includes a third terminal 738A and a fourth terminal 738B. The third and fourth terminals 738A / 738B, the second planar transmission line resonator 712B, and the ground plane can define planar transmission line structures in a second, distinct area on the substrate 752. The third microwave resonator unit 712C includes a fifth terminal 748A and a sixth terminal 748B. The fifth and sixth terminals 748A / 748B, the third planar transmission line resonator 712C, and the ground plane can define planar transmission line structures in a third, distinct area on the substrate 752.

[0099] As shown in FIG. 7A, the first terminal 728A has terminal segments 726A and a feedline 720A galvanically connected to the terminal segments 726A. The terminal segments 726A extend from the feedline 720A toward the first planar transmission line resonator 712A. The second terminal 720B has terminal segments 726B and a feedline 720B galvanically connected to the terminal segments 726B. The terminal segments 726B extend from the feedline 720B toward the first planar transmission line resonator 712A. Each of the first and second terminals 728A / 728B includes sixteen terminal segments 726A / 726B, each extending toward a respective conductive segment 722 of the first planar transmission line resonator 712A. In some implementations, the first and second terminals 728A / 728B include branching structures galvanically connecting the respective terminal segments 726A / 726B to the respective feedlines720A / 720B. A first end of each of theconductive segments 722 is capacitively coupled to a respective one of the terminal segments 726A of the first terminal 728A via a coupling gap 724A, while a second, opposite end of each of the conductive segments 722 is capacitively coupled to a respective one of coupling segments 726B of the second terminal 728B via a coupling gap 724B. In some instances, the first planar transmission line resonator 712A may be designed, fabricated and operated as the first planar transmission line resonator 412A, 912A in FIGS. 4A-4B, 9A- 9B, or in another manner.

[0100] As shown in FIG. 7A, the third terminal 738A has terminal segments 736A and a feedline 730A galvanically connected to the terminal segments 736A. The terminal segments 736A extend from the feedline 730A toward the second planar transmission line resonator 712B. The fourth terminal 738B has terminal segments 736B and a feedline 730B galvanically connected to the terminal segments 736B. Each of the third and fourth terminals 738A / 738B includes sixteen terminal segments 736A / 736B, each extending toward a respective conductive segment 732 of the second planar transmission line resonator 712B. The terminal segments 736A / 736B extend from the respective feedline 730A / 730B toward the second planar transmission line resonator 712B. In some implementations, the third and fourth terminals 738A / 738B include branching structures galvanically connecting the respective terminal segments 736A / 736B to the respective feedlines 730A / 730B. A first end of each of the conductive segments 732 is capacitively coupled to a respective one of the terminal segments 736A of the third terminal 738A via a coupling gap 734A, while a second, opposite end of each of the conductive segments 732 is capacitively coupled to a respective one of coupling segments 736B of the fourth terminal 738B via a coupling gap 734B. In some instances, the second planar transmission line resonator 712B may be designed, fabricated and operated as the second planar transmission line resonator 412B, 912B in FIGS. 4A-4B, 9A-9B, or in another manner.

[0101] As shown in FIG. 7A, the fifth terminal 748A has terminal segments 746A and a feedline 740A galvanically connected to the terminal segments 746A. The terminal segments 746A extend from the feedline 740A toward the third planar transmission line resonator 712C. The sixth terminal 748B has terminal segments 746B and a feedline 740B galvanically connected to the terminal segments 746B. Each of the fifth and sixth terminals748A / 748B includes sixteen terminal segments 746A / 746B, each extending toward a respective conductive segment 742 of the third planar transmission line resonator 712C. The terminal segments 746A / 746B extend from the respective feedline 740A / 740B toward the third planar transmission line resonator 712C. In some implementations, the fifth and sixth terminals 748A / 748B include branching structures galvanically connecting the respective terminal segments 746A / 746B to the respective feedlines 740A / 740B. A first end of each of the conductive segments 742 is capacitively coupled to a respective one of the terminal segments 746A of the fifth terminal 748A via a coupling gap 744A, while a second, opposite end of each of the conductive segments 742 is capacitively coupled to a respective one of coupling segments 746B of the sixth terminal 748B via a coupling gap 744B. In some instances, the third planar transmission line resonator 712C may be designed, fabricated and operated as the third planar transmission line resonator 912C, in FIGS. 9A-9B, or in another manner.

[0102] When the three planar transmission line resonators 712A / 712B / 712C of the different resonance frequencies are used with different coupling gaps, the quality factors and coupling factors of the three planar transmission line resonators 712A / 712B / 712C 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 bandwidth of 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 three planar transmission line resonators 712A / 712B / 712C can be made of superconducting materials to enable operations at low temperature, non- superconducting materials to enable operations at high temperature, or of different materials to enable operation at varying temperature ranges and with different kinetic inductance behavior.

[0103] In some instances, the first, second, and third planar transmission line resonators 712A / 712B / 712C may be designed to have resonance frequencies in the same frequency band (e.g., X-band). In some implementations, the size of the coupling gaps724A / 724B, 734A / 734B, 744A / 744B are different. As shown in FIG. 7A, each of the first, second, and third planar transmission line resonators 712A / 712B / 712C of the microwave resonator device 700 includes a 16-strip microstrip A / 2-resonator. The conductive segments 722 / 732 / 742 of the first, second, and third planar transmission line resonator 712A / 712B / 712C have a width w of 40 pm, and a spacing s0between neighboring microstrip lines of 100 pm. The conductive segments 722 of the first planar transmission line resonator 712A has a length of 5200 pm and a dimension of the coupling gaps 724A / 724B of 250 pm, whereas the conductive segments 732 of the second planar transmission line resonator 712B has a length of 5100 pm and a dimension of the coupling gaps 734A / 734B of 350 pm, and whereas the conductive segments 742 of the third planar transmission line resonator 712C has a length of 5000 pm and a dimension of the coupling gaps 744A / 744B of 450 pm. The resonant frequencies of the first, second, and third planar transmission line resonators 712A / 712B / 712C are 9.503 GHz, 9.698 GHz, and 9.907 GHz with Q factors of 875, 650, and 1100, respectively. The separation distance (d) between two neighboring resonators (e.g., the lengths of the feedline segments 704-1A / 704-1B; 704-2A / 704-2B) is 6 mm, corresponding to 180 degrees at 9.6 GHz. In some instances, the first, second, and third planar transmission line resonators 712A / 712B / 712C may be designed to have resonance frequencies in different frequency bands (e.g., X-band, Ku- band, and Q-band).

[0104] FIG. 7B is a plot 760 showing a full-wave simulation of scattering parameters (S- parameters) in dB as a function of frequency in GHz of the microwave resonator device 700 shown in FIG. 7A. In the simulation, the first, second, and third planar transmission line resonators 712A / 712B / 712C include superconducting material. The surface impedance of each superconducting resonator is assumed to be 2xl0’4£1. Curve 762 represents the Sil parameter which is measured between the two feedlines 710A / 710B at the input / output terminals 706A / 706B of the microwave resonator device 700; and curve 764 represents the S21 parameter which is measured between the two feedlines 710A / 710B at the input / output terminals 706A / 706B of the microwave resonator device 700.

[0105] FIG. 8A is a circuit diagram showing an equivalent circuit model of an example microwave resonator device 800. In some instances, the microwave resonator device 800may be used in an electron spin resonance system for performing ESR spectroscopy of multiple samples. The example microwave resonator device 800 includes an array of four microwave resonators 802A / 802B / 802C / 802D coupled in parallel between two nodes 810A / 810B. The microwave resonator 802A is coupled to the two nodes 810A / 810B through two respective capacitors 808-1A / 808-1B; the microwave resonator 802B is coupled to the two nodes 810A / 810B through two respective capacitors 808-2A / 808-2B; the microwave resonator 802C is coupled to the two nodes 810A / 810B through two respective capacitors 808-3A / 808-3B; and the microwave resonator 802D is coupled to the two nodes 810A / 810B through two respective capacitors 808-4A / 808-4B. The microwave resonators 802A / 802B / 802C / 802D are half-wavelength resonators having different intrinsic resonance frequencies of 9.5 GHz, 9.6 GHz, 9.7 GHz, and 9.8 GHz, respectively. The four microwave resonators 802A / 802B / 802C / 802D are separated by an electrical length of 6. The phase difference between two neighboring microwave resonators is 0=180 degrees at the frequency of 9.55 GHz. The node 810A is a source terminal connected to an excitation source 806; and the node 810B is a load terminal connected to a load. In some instances, each microwave resonator 802A / 802B / 802C / 802D can be implemented as the microwave resonator 202A / 202B / 202C / 202D, 302A / 302B in FIGS. 2, 3A, or in another manner.

[0106] FIG. 8B includes a plot 820 showing circuit analysis S-parameters (S21 and Sil) in dB as a function of frequency in GHz in the example microwave resonator device 800 shown in FIG. 8A. The capacitance values of the coupling capacitors 808-1A / 808-1B, 808- 2A / 808-2B, 808-3A / 808-3B, and 808-4A / 808-4B are equal to 8.2 fF. The source and the load impedance are 50 Ohm. The microwave resonators 802A / 802B / 802C / 802D can be modeled by a simple LC circuit, and the coupling capacitors at the end of each microwave resonators 802A / 802B / 802C / 802D can vary. As seen in this figure, there are four distinct resonant frequencies. As shown in FIG. 8B, resonances occur at shifted frequencies 9.215 GHz, 9.308 GHz, 9.401 GHz and 9.494 GHz.

[0107] FIG. 8C includes plots 860, 862, 864, 866 showing current in amps as a function of frequency in GHz in the respective microwave resonators 802A / 802B / 802C / 802D of the example microwave resonator device 800 shown in FIG. 8A. To calculate the magnitude ofthe current at the center of each transmission line resonator, where the current is maximum, the source and load impedance are chosen to be Rs= RL= 50 £1, and the peak-to- peak voltage of the 50-ohm source is Vs= 0.7 V, which is equivalent to 1 dBm input power available from the source. The first microwave resonator 802A only resonates at the frequency of 9.215 GHz, while the second, third and fourth microwave resonators 802B / 802C / 802D have no current at this frequency. Similarly, the second microwave resonator 802B resonates at 9.308 GHz, while the first, third and fourth microwave resonators 802A / 802C / 802D have no current at this frequency; the third microwave resonator 802C resonates at 9.401 GHz, while the first, second and fourth microwave resonators 802A / 802B / 802D have no current at this frequency; and the fourth microwave resonator 802D resonates at 9.494 GHz, while the first, second and third microwave resonators 802A / 802B / 802C have no current at this frequency. This result demonstrates the frequency selectivity of the array of microwave resonators, where only one microwave resonator generates the field (electrical current in the circuit analysis) to address the corresponding ESR sample. When one microwave resonator is selectively activated at a given excitation frequency, the other remains inactive. As shown in FIG. 8C, only one microwave resonator is excited at its resonance frequency and other microwave resonators behave as open circuits, enabling independent addressability of each microwave resonator. Each microwave resonator is active (maximally passing the current) only at its respective resonance frequency, while remaining inactive (open circuited) at other frequencies.

[0108] FIGS. 9A-9B include top and perspective views of an example microwave resonator device 900. As shown in FIGS. 9A-9B, the microwave resonator device 900 includes a microwave resonator array, including a first microwave resonator unit 902A, a second microwave resonator unit 902B, a third microwave resonator unit 902C, and a fourth microwave resonator unit 902D, which are patterned on the same surface of a substrate 962. The first, second, third, and fourth microwave resonator units 902A / 902B / 902C / 902D are connected in parallel between two feedlines 910A / 910B and spatially separated by electrical lengths of respective feedline segments 904-1A / 904-1B, 904-2A / 904-2B, 904-3A / 904-3B of the feedlines 910A / 910B. In some implementations, the first microwave resonator unit 902A includes a first planar transmission line resonator912A which includes an array of conductive segments 922 and a ground plane on the substrate 962; the second microwave resonator unit 902B includes a second planar transmission line resonator 912B which includes an array of conductive segments 932 and a ground plane on the substrate 962; the third microwave resonator unit 902C includes a third planar transmission line resonator 912C which includes an array of conductive segments 942 and a ground plane on the substrate 962; and the third microwave resonator unit 902D includes a fourth planar transmission line resonator 912D which includes an array of conductive segments 952 and a ground plane on the substrate 962. In some instances, the EPR samples can be positioned simultaneously on a sample cartridge at respective sample regions of the planar transmission line resonators 912A / 912B / 912C / 912D; and can be tested in parallel or sequentially. In some instances, an EPR sample can be positioned and tested in a sample region of a planar transmission line resonator of the example microwave resonator device 900; and moved to and tested in a different sample region of a different planar transmission line resonator of the example microwave resonator device 900. The example microwave resonator device 900 can include additional or different features, and the features of the example microwave resonator device 900 may be arranged in the configuration shown or in another configuration. In some instances, the microwave resonator device 900 may be operated according to the operations in the example process 1000, 1100 in FIGS. 10, 11, or in another manner.

[0109] In some implementations, the microwave resonator device 900 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 900 to perform multiple resonance measurements of multiple electron spin centers in the multiple sample regions of the microwave resonator device 900. In some instances, the control system 114 may operate the microwave resonator device 900 to perform double resonance measurements of the electron spins in the sample regions. The microwave resonator device 900 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 refocusespairwise interactions at varying times to reveal a distribution of coupling strength of the pairwise couplings.

[0110] The first microwave resonator unit 902A includes a first terminal 928A and a second terminal 928B. The first and second terminals 928A / 928B, the first planar transmission line resonator 912A, and the ground plane can define planar transmission line structures in a first area on the substrate 962. The second microwave resonator unit includes a third terminal 938A and a fourth terminal 938B. The third and fourth terminals 938A / 938B, the second planar transmission line resonator 912B, and the ground plane can define planar transmission line structures in a second, distinct area on the substrate 962. The third microwave resonator unit 912C includes a fifth terminal 948A and a sixth terminal 948B. The fifth and sixth terminals 948A / 948B, the third planar transmission line resonator 912C, and the ground plane can define planar transmission line structures in a third, distinct area on the substrate 962. The fourth microwave resonator unit 912D includes a seventh terminal 958A and an eighth terminal 958B. The seventh and eighth terminals 958A / 958B, the fourth planar transmission line resonator 912D, and the ground plane can define planar transmission line structures in a fourth, distinct area on the substrate 962.

[0111] As shown in FIG. 9A, the first terminal 928A has terminal segments 926A and a feedline 920A galvanically connected to the terminal segments 926A. The terminal segments 926A extend from the feedline 920A toward the first planar transmission line resonator 912A. The second terminal 920B has terminal segments 926B and a feedline 920B galvanically connected to the terminal segments 926B. The terminal segments 926B extend from the feedline 920B toward the first planar transmission line resonator 912A. Each of the first and second terminals 928A / 928B includes sixteen terminal segments 926A / 926B, each extending toward a respective conductive segment 922 of the first planar transmission line resonator 912A. In some implementations, the first and second terminals 928A / 928B include branching structures 927A / 927B galvanically connecting the respective terminal segments 926A / 926B to the respective feedlines 920A / 920B. A first end of each of the conductive segments 922 is capacitively coupled to a respective one of the terminal segments 926A of the first terminal 928A via a coupling gap 924A, while asecond, opposite end of each of the conductive segments 922 is capacitively coupled to a respective one of coupling segments 926B of the second terminal 928B via a coupling gap 924B.

[0112] As shown in FIG. 9A, the third terminal 938A has terminal segments 936A and a feedline 930A galvanically connected to the terminal segments 936A. The terminal segments 936A extend from the feedline 930A toward the second planar transmission line resonator 912B. The fourth terminal 938B has terminal segments 936B and a feedline 930B galvanically connected to the terminal segments 936B. Each of the third and fourth terminals 938A / 938B includes sixteen terminal segments 936A / 936B, each extending toward a respective conductive segment 932 of the second planar transmission line resonator 912B. The terminal segments 936A / 936B extend from the respective feedline 930A / 930B toward the second planar transmission line resonator 912B. In some implementations, the third and fourth terminals 938A / 938B include branching structures 937A / 937B galvanically connecting the respective terminal segments 936A / 936B to the respective feedlines 930A / 930B. A first end of each of the conductive segments 932 is capacitively coupled to a respective one of the terminal segments 936A of the third terminal 938A via a coupling gap 934A, while a second, opposite end of each of the conductive segments 932 is capacitively coupled to a respective one of coupling segments 936B of the fourth terminal 938B via a coupling gap 934B.

[0113] As shown in FIG. 9A, the fifth terminal 948A has terminal segments 946A and a feedline 940A galvanically connected to the terminal segments 946A. The terminal segments 946A extend from the feedline 940A toward the third planar transmission line resonator 912C. The sixth terminal 948B has terminal segments 946B and a feedline 940B galvanically connected to the terminal segments 946B. Each of the fifth and sixth terminals 948A / 948B includes sixteen terminal segments 946A / 946B, each extending toward a respective conductive segment 942 of the third planar transmission line resonator 912C. The terminal segments 946A / 946B extend from the respective feedline 940A / 940B toward the third planar transmission line resonator 912C. In some implementations, the fifth and sixth terminals 948A / 948B include branching structures 947A / 947B galvanically connecting the respective terminal segments 946A / 946B to the respective feedlines940A / 940B. A first end of each of the conductive segments 942 is capacitively coupled to a respective one of the terminal segments 946A of the fifth terminal 948A via a coupling gap 944A, while a second, opposite end of each of the conductive segments 942 is capacitively coupled to a respective one of coupling segments 946B of the sixth terminal 948B via a coupling gap 944B.

[0114] As shown in FIG. 9A, the seventh terminal 958A has terminal segments 956A and a feedline 950A galvanically connected to the terminal segments 956A. The terminal segments 956A extend from the feedline 950A toward the fourth planar transmission line resonator 912D. The eighth terminal 958B has terminal segments 956B and a feedline 950B galvanically connected to the terminal segments 956B. Each of the seventh and eighth terminals 958A / 958B includes sixteen terminal segments 956A / 956B, each extending toward a respective conductive segment 952 of the fourth planar transmission line resonator 912D. The terminal segments 956A / 956B extend from the respective feedline 950A / 950B toward the fourth planar transmission line resonator 912D. In some implementations, the seventh and eighth terminals 958A / 958B include branching structures 957A / 957B galvanically connecting the respective terminal segments 956A / 956B to the respective feedlines 950A / 950B. A first end of each of the conductive segments 952 is capacitively coupled to a respective one of the terminal segments 956A of the seventh terminal 958A via a coupling gap 954A, while a second, opposite end of each of the conductive segments 952 is capacitively coupled to a respective one of coupling segments 956B of the eighth terminal 958B via a coupling gap 954B.

[0115] When the four planar transmission line resonators 912A / 912B / 912C / 912D of the different resonance frequencies are used with different coupling gaps, the quality factors and coupling factors of the four planar transmission line resonators 912A / 912B / 912C / 912D 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 bandwidth of 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 EPRmeasurements. Additionally, the four planar transmission line resonators 912A / 912B / 912C / 912D can be made of superconducting materials to enable operations at low temperature, non-superconducting materials to enable operations at high temperature, or different materials to enable operation at varying temperature ranges and with different kinetic inductance behavior.

[0116] In some instances, the first, second, third, and fourth planar transmission line resonators 912A / 912B / 912C / 912D may be designed to have resonance frequencies in the same frequency band (e.g., X-band). In some implementations, the size of the coupling gaps 924A / 924B, 934A / 934B, 944A / 944B, 954A / 954B may be the same. As shown in FIG. 9A, each of the first, second, third, and fourth planar transmission line resonators 912A / 912B / 912C / 912D of the microwave resonator device 900 includes a 16-strip microstrip A / 2-resonator. The conductive segments 922 / 932 / 942 / 952 oft the first, second, third, and fourth planar transmission line resonators 912A / 912B / 912C / 912D have a width w of 40 pm, and a spacing s0between neighboring microstrip lines of 100 pm. The conductive segments 922 of the first planar transmission line resonator 912A has a length of 5250 pm and a dimension of the coupling gaps 924A / 924B of 250 pm, whereas the conductive segments 932 of the second planar transmission line resonator 912B has a length of 5150 pm and a dimension of the coupling gaps 934A / 934B of 250 pm, whereas the conductive segments 942 of the third planar transmission line resonator 912C has a length of 5050 pm and a dimension of the coupling gaps 944A / 944B of 250 pm, and whereas the conductive segments 952 of the fourth planar transmission line resonator 912D has a length of 4950 pm and a dimension of the coupling gaps 954A / 954B of 250 pm. The lengths of the feedline segments 904-1A / 904-1B. 904-2A / 904-2B, 904-3A / 904-3B between two neighboring resonators is 6 mm, corresponding to an electrical length of 180 degrees at 9.6 GHz. In some instances, the first, second, third, and fourth planar transmission line resonators 912A / 912B / 912C / 912D maybe designed to have resonance frequencies in different frequency bands (e.g., X-band, Ku-band, K-band, and Q-band).

[0117] FIG. 9C is a plot 970 showing a full-wave simulation of scattering parameters (S- parameters) in dB as a function of frequency in GHz of the microwave resonator device 900 shown in FIGS. 9A-9B. In the simulations, the first, second, third, and fourth planartransmission line resonators 912A / 912B / 912C / 912D include superconducting material.The surface impedance of each superconducting resonator is assumed to be 2xl0’4£1. Curve 972 represents the Sil parameter which is measured between the two feedlines 910A / 910B at the input / output terminals 906A / 906B of the microwave resonator device 900; and curve 974 represents the S21 parameter which is measured between the two feedlines 910A / 910B at the input / output terminals 906A / 906B of the microwave resonator device 900. These planar resonators are fabricated on an R-cut sapphire substrate measuring 24 mm by 26 mm and with a thickness of 0.43 mm. Four distinct resonances are clearly observed in FIG. 9C each corresponding to an individual resonator.

[0118] In some instances, the resonator distinguishability can be analyzed by examining the magnetic field structure over the resonators through the concept of spin-cavity coupling. This quantity, measured in Hz, is proportional to the magnetic field and can be viewed as a normalized magnetic field. The spin-cavity coupling, for one single spin, is calculated using the following equation:where y = 2.8024 MHz / G is the electron gyromagnetic ratio; p0is the vacuum permeability; h is the plank constant; a>ris the resonant frequency; lHmaxl is the maximum of the magnetic field magnitude; \H (r)| is the magnetic field magnitude at position r, and 1 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 closely matches its distribution. FIGS. 9D-9G include plots of the variation of t / 0(r) along lines at the center of each resonator and perpendicular to the surface of each resonator of the example microwave resonator device 900 in FIGS. 9A-9B as a function of distance in pm. FIGS. 9D-9G also includes data obtained from a reference microwave resonator device that includes a single 16-strip resonator. The single 16-strip resonator has a width w of 40 pm, a spacing s0between neighboring microstrip lines of 100 pm, a length of 5200 pm, and a dimension of the coupling gaps of250 pm. The single 16-strip resonator has a resonance frequency of 9.504 GHz. Each subplot corresponds to excitation at one of the resonant frequencies of the array.

[0119] Each subplot was calculated at one of the resonant frequencies obtained in the S- parameter analysis shown in FIG. 9C, which excites only one resonator. The g0values of the single 16-strip resonator are about 0.113 Hz at 100 pm above the resonator, shown by the dashed curves 980A, 982A, 984A, 986A. As shown in FIGS. 9D-9G, the g0values are approximately 0.1 Hz, 0.093 Hz, 0.095 Hz, and 0.105 Hz at 100 pm (distance = 100 pm) above the first, second, third, and fourth planar transmission line resonators 912A / 912B / 912C / 912D when excited at 9.424 GHz, 9.598 GHz, 9.776 GHz, and 9.988 GHz, respectively. As shown in FIGS. 9D-9G, there is some residual resonator crosstalk that leads to non-zero spin-cavity coupling g00) for resonators that are not directly excited. For example, when the first planar transmission line resonator 912A is excited the g0value for the second, third, and fourth planar transmission line resonators 912B / 912C / 912D would be 0.02 HZ, 0.006 Hz, and 0.001 Hz, respectively.

[0120] FIG. 10 is a flow chart showing aspects of an example process 1000 for operating a microwave resonator device. The example process 1000 can be used for performing an electron spin resonance process by operation of a microwave resonator device. In some implementations the microwave resonator device includes an array of transmission line resonators coupled to one another in parallel. In some instances, each transmission line resonator includes a single microstrip resonator, multiple microstrip resonators, a single coplanar waveguide resonator, or another type of transmission line resonator. In some instances, the transmission line resonators in the array may have different transmission line structures. In some implementations, the microwave resonator device may be implemented as the example microwave resonator devices 300, 700, 900 shown in FIGS. 3A-3B, 7A, 9A-9B, or another type of resonator device.

[0121] In some implementations, the microwave resonator device is designed to support multiple microwave resonant modes. The operations of the example process 1000 may be performed by operation of the electron spin resonance system 100 in FIG. 1. The example process 1000, individual operations of the process 1000, or groups of operations may be iterated or performed simultaneously to achieve a desired result. In some cases, theexample process 1000 may include the same, additional, fewer, or different operations performed in the same or a different order.

[0122] 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 a multiplexed 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 observer frequencies for measuring and demodulating detectable spin coherence. In some instances, the corresponding carrier frequencies may be demodulated in parallel by operation of a detection system. The mode structure of a 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.

[0123] At 1002, 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 above the transmission line resonator 412A / 412B, 712A / 712B / 712C, 912A / 912B / 912C / 912D in FIGS. 4A-4B, 7A, 9A-9B). In some instances, the geometrical parameters 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., ablood 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.

[0124] In some implementations, multiple resonance measurements are used in pulsed electron paramagnetic resonance (EPR) to examine the nature of multi-spin coupling networks in samples containing multiple unpaired electron spins. In contrast to single resonance measurements, microwave pulses are 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 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 serves to refocus pairwise couplings at varying times to reveal a distribution of coupling strengths of the pairwise couplings.

[0125] At 1004, two or more frequency channels are defined. In some implementations, the two or more frequency channels are defined as a set of modulated pulses with distinct carrier frequencies. In some implementations, the carrier frequencies can be in the microwave frequency, e.g., in a range of 2 to 90 GHz, or in another frequency range. In some instances, the carrier frequencies of the pulsed microwave signal are determined according to one of the multiple microwave resonant 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 frequencies 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.

[0126] At 1006, the frequency channels are assigned to one or more control hardware channels. The control system 114 can generate a hardware control sequencecorresponding 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.

[0127] At 1008, the frequency channels are assigned to one or more microwave resonators in 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.

[0128] In some instances, the pulsed microwave signal is generated externally (e.g., external to the microwave resonator device) and provided to the 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 the input port 206A, 312A, 406A, 706A, 810A, 906A of the example microwave resonator devices 200, 300, 400, 700, 800, 900 shown in FIGS. 2, 3A, 4A-4B, 7A, 8A, 9A-9B.

[0129] The pulsed microwave signal is provided to the array of microwave resonators in the microwave resonator device. When a transmission line resonator in the array includes multiple microstrip line resonators, the pulsed microwave signal can be delivered in-phase to each of the multiple microstrip line resonators of the transmission line resonator. In this case, all of the multiple microstrip line resonators can simultaneously receive the same signal with a common phase at each location on the conductive segments. As such, the phase of the signal on each conductive segment in a transmission line resonator can be substantially identical at each instant in time.

[0130] In some implementations, communicating the pulsed microwave signal from the input port to the output port across the array of transmission line resonators can create multiple microwave fields above the transmission line resonators. Each transmission line resonator in the array is configured to produce a corresponding microwave magnetic field (e.g., a drive magnetic field) in a respective sample region to allow exchange of magnetic field energy at a respective resonance frequency according to the pulsed microwave signal received. In some implementations, the magnetic field can be in-plane homogeneous in a sample region (e.g., a planar sample region), such that the magnetic field is uniform in planes crossing the sample region. This magnetic field can be substantially uniform in strength and may occupy a small mode volume well matched to the volume of the sample. The generated magnetic field can be applied to one or more samples in the sample region, for example, for pulsed ESR. In some instances, a transmission line resonator does not directly interact with the sample in a sample region that is not associated with itself (e.g., sample regions defined by other transmission line resonators). In some instances, the transmission line resonators may have the same resonance frequency or different resonance frequencies.

[0131] In some instances, the microwave magnetic field at multiple distinct carrier frequencies can be used to manipulate the electron spins in the multiple sample regions. The resonance frequencies of the magnetic fields 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, 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.

[0132] At 1010, 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 may be 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.

[0133] FIG. 11 is a flow chart showing aspects of an example process 1100 for operating a microwave resonator device. The example process 1100 can be used for performing an electron spin resonance process by operation of a microwave resonator device. In some implementations the microwave resonator device includes an array of transmission line resonators coupled to one another in parallel. In some instances, each transmission line resonator includes a single microstrip resonator, multiple microstrip resonators, a single coplanar waveguide resonator, or another type of transmission line resonator. In some instances, the transmission line resonators in the array may have different transmission line structures. In some implementations, the microwave resonator device may be implemented as the example microwave resonator devices 300, 700, 900, 1200, 1300, 1402 shown in FIGS. 3A-3B, 7A, 9A-9B, 12, 13, 14, or another type of resonator device.

[0134] At 1102, a sample is positioned in a first sample region of the microwave resonator device. At 1104, by operation of the first transmission line resonator, one or more control fields are applied to a first sample in the first sample region during a first time period. At 1106, a sample is positioned in a second sample region of a second microwave resonator device. At 1108, by operation of the second transmission line resonator, one or more control fields are applied to a second sample in the second sample region during a second, subsequent time period. In some instances, the second sample in the second sample region may be the first sample moved from the first sample region to the second sample region between the first and second time periods. In certain instances, the sample in the second sample region may be a second, distinct sample. In some instances, the first and second samples are positioned in the first and second sample regionssimultaneously, and control fields are applied to the respective first and second samples in parallel. In some instances, the first and second samples are positioned in the first and second sample regions simultaneously, and control fields are applied to the respective first and second samples sequentially.

[0135] During a parallel measurement, a sample cartridge containing multiple samples can be positioned over the microwave resonator device such that the multiple samples reside in respective sample regions of the microwave resonator device. In some cases, the external magnetic field (e.g., primary magnetic field) can be set such that one or more spin resonance frequencies are off-resonance with one or more resonance frequencies of the microwave resonator devices in the array. For example, the magnetic field may be set to a value where the resulting energy level splitting of the spins corresponds to the average resonance frequency of all the microwave resonator devices in the array. In this case, microwave control will be off-resonance with one or more spin transitions in the samples, which can be accounted for in design of control sequences. The spectrometer frequency may be configured to correspond to the average resonance frequency of all the microwave resonator devices in the array. A complete control and detection sequence with signal averaging on all samples simultaneously can be performed using the frequency multiplexing capability of the spectrometer IF.

[0136] During a sequential measurement, a sample cartridge containing multiple samples is positioned over the microwave resonator device such that the multiple samples reside in respective sample regions of the microwave resonator device. The position of the sample cartridge may stay fixed during the sequential measurement. In some implementations, the external magnetic field (e.g., primary magnetic field) may be set to a value where the resulting energy level splitting of the spins corresponds to the resonance frequency of a first microwave resonator. The spectrometer frequency may be set to correspond to the resonance frequency of the first microwave resonator. A control and detection sequence can be performed at the resonance frequency of the first microwave resonator. During the thermal relaxation time (T of the first spin sample (e.g., on the order of milliseconds in some cases), a current can be applied to a field adjustment coil (e.g., the field adjustment coil 1404 in the example ESR system 1400 shown in FIG. 14) witha response time significantly faster than the thermal relaxation time (Tx) (e.g., with a response time on the order of microseconds, in some cases) to adjust the external magnetic field to be resonant with the spin transitions corresponding to the resonance frequency of a second, distinct microwave resonator. The spectrometer frequency may then be set to correspond to the resonance frequency of the second microwave resonator. A control and detection sequence can be performed at the resonance frequency of the second microwave resonator. During the thermal relaxation time (T of both the first and second spin samples (e.g., on the order of milliseconds in some cases), a second current can be applied to the field adjustment coil with a response time (e.g., on the order of microseconds in some cases) to adjust the external magnetic field to be resonant with the spin transitions corresponding to the resonance frequency of the third microwave resonator. The measurement process can be repeated for a desired number of samples and microwave resonators in the array. In some instances, signal averaging can be performed a desired number of times using the same process.

[0137] In some implementations, during a sequential measurement, the sample container is positioned over the microwave resonator device 200 such that a single sample lies in the sample region of a single resonator in the array. The external magnetic field is set to a value where the resulting energy level splitting of the spins corresponds to the resonance frequency of a first microwave resonator. The spectrometer frequency can be set to correspond to the resonance frequency of the first microwave resonator. A complete control and detection sequence can be performed with signal averaging at the resonance frequency of the first microwave resonator. The external magnetic field can be then set to a value where the resulting energy level splitting of the spins corresponds to the resonance frequency of the second microwave resonator. The sample in the sample container can be moved or otherwise repositioned such that the sample resides in a second distinct sample region of a second, distinct microwave resonator in the microwave resonator device 200. The external magnetic field can then be set to a value where the resulting energy level splitting of the spins corresponds to the resonance frequency of the second microwave resonator. The spectrometer frequency can then be set to correspond to the resonance frequency of the second microwave resonator. A complete control and detection sequencecan be performed with signal averaging at the resonance frequency of the second microwave resonator. The sequential measurement can be repeated a desired number of times for different samples at different microwave resonators in the microwave resonator device 200.

[0138] FIG. 12 is a perspective view showing aspects of an example microwave resonator device 1200. In some implementations, the microwave resonator device 1200 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 1200 to perform multiple resonance measurements of multiple electron spin centers in multiple sample regions of the microwave resonator device 1200 at the same time. The microwave resonator device 1200 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.

[0139] As shown in FIG. 12, the microwave resonator device 1200 is a 2-dimensional (4 x 2) microwave resonator array, including a first transmission line resonator 1202-1A and a second transmission line resonator 1202-1B connected in series; a third transmission line resonator 1202-2A and a fourth transmission line resonator 1202-2B connected in series; a fifth transmission line resonator 1202-3A and a sixth transmission line resonator 1202-3B connected in series; and a seventh transmission line resonator 1202-4A and an eighth transmission line resonator 1202-4B connected in series. The first and second transmission line resonators 1202-1A / 1202-1B, the third and fourth transmission line resonators 1202-2A / 1202-2B, the fifth and sixth transmission line resonators 1202- 3A / 1202-3B, and the seventh and eighth transmission line resonators 1202-4A / 1202-4B are connected to between two common transmission lines 1208A, 1208B which are further connected to two respective ports 1206A, 1206B. The eight transmission line resonators of the microwave resonator array are patterned on the same surface of a substrate 1210 and configured to produce microwave drive fields in distinct sample regions above the respective transmission line resonators. In some implementations, each transmission lineresonator includes an array of conductive segments which are capacitively coupled to two separate sets of terminal segments of two terminals. In some instances, each transmission line resonator 1202-1A / 1202-1B, 1202-2A / 1202-2B, 1202-3A / 1202-3B, 1202-4A / 1202- 4B may be implemented as the transmission line resonator 402A / 402B, 702A / 702B / 702C, 902A / 902B / 902C / 902D shown in FIGS. 4A-4B, 7A, 9A-9B or in another manner. In some instances, the 2D microwave resonator array may be configured in another topology which may offer benefits such as in resonator selectivity, available device bandwidth, etc.

[0140] As shown in FIG. 12, the first and second transmission line resonators 1202- 1A / 1202-1B are separated from the third and fourth transmission line resonators 1202- 2A / 1202-2B by respective feedline segments 1204-1A / 1204-1B; the third and fourth transmission line resonators 1202-2A / 1202-2B are separated from the fifth and sixth transmission line resonators 1202-3A / 1202-3B by respective feedline segments 1204- 2A / 1204-2B; and the fifth and sixth transmission line resonators 1202-3A / 1202-3B are separated from the seventh and eighth transmission line resonators 1202-4A / 1202-4B by respective feedline segments 1204-3A / 1204-3B. In some instances, the feedline segments 1204-1A / 1204-1B, 1204-2A / 1204-2B, 1204-3A / 1204-3B may be implemented as the segments 404A / 404B, 704-1A / 704-1B, 704-2A / 704-2B, 904-1A / 904-1B, 904-2A / 904-2B, 904-3A / 904-3B in FIGS. 4A-4B, 7A, 9A-9B or in another manner. In some instances, the substrate 1210 may be implemented as the substrate 442, 752, 962 in FIGS. 4A-4B, 7A, 9A- 9B or in another manner.

[0141] In some instances, the eight transmission line resonators 1202-1A / 1202-1B, 1202-2A / 1202-2B, 1202-3A / 1202-3B, 1202-4A / 1202-4B may have different physical parameters and different properties. For example, the planar transmission line resonators of the transmission line resonators may have different coupling gaps, different number of microstrips, different widths, different spacings, different lengths, or made of different conductive materials. In some instances, the eight transmission line resonators 1202- 1A / 1202-1B, 1202-2A / 1202-2B, 1202-3A / 1202-3B, 1202-4A / 1202-4B may have different properties, e.g., different intrinsic resonance frequencies, different coupling (e.g., overcoupled, under-coupled, or critically coupled), or different quality factors. In someinstances, the microwave resonator device 1200 may be operated according to the operations in the example process 1000, 1100 in FIGS. 10, 11, or in another manner.

[0142] FIG. 13 is a perspective view showing aspects of an example microwave resonator device 1300. In some implementations, the microwave resonator device 1300 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 1300 to perform multiple resonance measurements of multiple electron spin centers in multiple sample regions of the microwave resonator device 1200 at the same time. The microwave resonator device 1300 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.

[0143] As shown in FIG. 13, the example microwave resonator device 1300 is a split- planar transmission line resonator including a first microwave resonator array 1302A patterned on a first surface of a first substrate 1310A; and a second microwave resonator array 1302B patterned on a second surface of a second substrate 1310B. In some implementations, the first microwave resonator array 1302A includes a first array of planar transmission line resonators connected between two ports 1306A, 1306B; and the second microwave resonator array 1302B includes a second array of planar transmission line resonators connected between two ports 1306C, 1306D. The example microwave resonator device 1300 includes four ports 1306A, 1306B, 1306C, 1306D; and thus, is a four-port device. Each of the first and second microwave resonator arrays 1302A may be implemented as the microwave resonator device 1200 shown in FIG. 12.

[0144] In the example shown in FIG. 13, the second substrate is oriented parallel to the first substrate with the second surface facing the first surface. The second surface is spaced apart from the first surface by a separation distance D. As shown in FIG. 13, respective planar transmission line resonators in the two microwave resonator arrays are aligned with each other along the Z axis such that a planar transmission line resonator from the first array and a corresponding planar transmission line resonator from the second arrayare directly facing each other along the Z axis and spaced apart by the separation distance. In some instances, the separation distance D can be adjusted to modify the field homogeneity within the sample region, to tune the resonance frequencies of the microwave resonator device, to tune the coupling between corresponding transmission line resonators from different arrays, or to modify other parameters of the microwave resonator device. In some implementations, the separation distance D is in a range of 0.5 to 3 mm.

[0145] In the example shown in FIG. 13, the two corresponding planar transmission line resonators on distinct substrates can generate microwave magnetic fields in a common sample region. In other words, the two planar transmission line resonators are capacitively and inductively coupled when microwave control signals are supplied. In some instances, the two planar transmission line resonators are configured to receive control signals to produce microwave fields to support distinct resonance modes, e.g., even and odd resonance modes, in a common sample region confined in cavity between the two planar transmission line resonators. In some cases, the microwave resonator device 1300 can enable two distinct resonance modes in a sample region for double-resonance measurements. The microwave fields generated by the two planar transmission line resonators that are facing each other may interact with a spin sample in the sample region independently. Although the transmission line resonators on the two substrates extend in the same direction in FIG. 13, in some cases the transmission line resonators on the two different substrates extend in different (e.g., orthogonal) directions. For example, transmission line resonators in the first array may extend long the X axis; and transmission line resonators in the second array may extend along the Y axis. In this case, the microwave resonator devices is a crossed split-planar microwave resonator device. In some instances, the microwave resonator device 1300 may be operated according to the operations in the example process 1000, 1100 in FIGS. 10, 11, or in another manner.

[0146] FIG. 14 is a schematic diagram showing an example electron spin resonance system 1400. The example ESR system 1400 includes a microwave resonator device 1402 placed in a field adjustment coil 1404. In some implementations, the field adjustment coil 1404 is configured to generate and adjust the primary magnetic field (in which the microwave resonator device 1402 resides) such that the energy level splitting of the spinsin the primary magnetic field corresponds to the resonance frequency of a particular transmission line resonator in the microwave resonator devicel402. For example, the field adjustment coil 1404 can be configured to produce a magnetic field that combines with the primary magnetic field generated by the primary magnet system 112 to generate a total primary magnetic field in which the energy level splitting of the spins corresponds to the resonance frequency of a first transmission line resonator 1412A during a first measurement period; and the field adjustment coil 1404 can be adjusted and tuned to produce a primary magnetic field in which the energy level splitting of the spins corresponds to the resonance frequency of a second transmission line resonator 1412B during a second measurement period.

[0147] In a general aspect of what is described above, a resonator system for electron spin resonance includes multiple transmission line resonators patterned on a substrate.

[0148] In a first example, a resonator system includes a first transmission line resonator, a second transmission line resonator, first and second feedlines. The first transmission line resonator is patterned on a substrate and configured to produce a first microwave field in a first sample region. The second transmission line resonator is patterned on the substrate and configured to produce a second microwave field in a second, distinct sample region. The first and second feedlines are patterned on the substrate. The first and second transmission line resonators are connected in parallel between the first and second feedlines.

[0149] Implementations of the first example may include one or more of the following features. The first transmission line resonator defines a first resonance frequency in a first frequency band; and the second transmission line resonator defines a second resonance frequency in a second, distinct frequency band. The first frequency band is X-band and the second frequency band is Q-band. The first and second resonance frequencies are in the same frequency band.

[0150] Implementations of the first example may include one or more of the following features. The first transmission line resonator has a first quality factor, and the second transmission line resonator has a second, distinct quality factor. The first transmission lineresonator is over-coupled, and the second transmission line resonator is under-coupled. The first transmission line resonator is critically coupled, and the second transmission line resonator is under-coupled. The first transmission line resonator is over-coupled, and the second transmission line resonator is critically coupled.

[0151] Implementations of the first example may include one or more of the following features. The first and second feedlines are configured to communicate magnetic resonance control signals from a transceiver to the first and second transmission line resonators in parallel, and the first and second feedlines are configured to communicate magnetic resonance response signals to the transceiver from the first and second transmission line resonators in parallel.

[0152] Implementations of the first example may include one or more of the following features. The resonator system includes an array of transmission line resonators patterned on the substrate. The transmission line resonators in the array are connected in parallel between the first and second feedlines. The transmission line resonators are arranged as a one-dimensional array of transmission line resonators on the substrate. The array of transmission line resonators are arranged as a two-dimensional array of transmission line resonators on the substrate.

[0153] Implementations of the first example may include one or more of the following features. The first and second transmission line resonators are made of superconducting material. The first and second transmission line resonators are made of non- superconducting material. The first transmission line resonators are made of superconducting material, and the second transmission line resonator is made of non- superconducting material.

[0154] Implementations of the first example may include one or more of the following features. Each of the first and second transmission line resonators includes a single microstrip resonator. The first transmission line resonator includes a first plurality of microstrip resonators, a first set of terminal segments capacitively coupled to first ends of the first plurality of microstrip resonators; a second set of terminal segments capacitively coupled to second, opposite ends of the first plurality of microstrip resonators, a firstbranching structure connected between the first feedline and the first set of terminal segments; and a second branching structure connected between the second feedline and the second set of terminal segments. The second transmission line resonator includes a second plurality of microstrip resonators, a third set of terminal segments capacitively coupled to first ends of the second plurality of microstrip resonators, and a fourth set of terminal segments capacitively coupled to second, opposite ends of the second plurality of microstrip resonators, a third branching structure connected between the first feedline and the third set of terminal segments, and a fourth branching structure connected between the second feedline and the fourth set of terminal segments.

[0155] Implementations of the first example may include one or more of the following features. The substrate is a first substrate including a first surface. The first and second transmission line resonators and the first and second feedlines are patterned on the first surface, and the resonator system includes a second substrate, a third transmission line resonator, a fourth transmission line resonator, third and fourth feedlines. The second substrate includes a second surface. The second substrate is oriented parallel to the first substrate with the second surface facing the first surface. The second surface is spaced apart from the first surface by a separation distance. The third transmission line resonator is patterned on the second surface and configured to produce a third microwave field in the first sample region. The fourth transmission line resonator is patterned on the second surface and configured to produce a fourth microwave field in the second sample region. The third and fourth feedlines are patterned on the second surface. The third and fourth transmission line resonators are connected in parallel between the third and fourth feedlines.

[0156] Implementations of the first example may include one or more of the following features. The resonator system includes an array of transmission line resonators patterned on the second substrate. The transmission line resonators in the array are connected in parallel between the third and fourth feedlines. The transmission line resonators are arranged as a one-dimensional array of transmission line resonators on the second substrate. The array of transmission line resonators are arranged as a two-dimensional array of transmission line resonators on the second substrate. The first sample region andthe second sample regions are distinct, non-overlapping volumes that are separated from each other by a distance.

[0157] In a second example, a resonator system includes an array of transmission line resonators patterned on a substrate and defining an array of respective sample regions; and first and second feedlines patterned on the substrate. The transmission line resonators in the array are connected in parallel between the first and second feedlines. The array of transmission line resonators may include the first and second transmission line resonators from the first example. The array of transmission line resonators may be configured as a one-dimensional array or a two-dimensional array.

[0158] In a third example, an electron resonance method includes positioning a sample in the first sample region of the resonator system of the first and second example; by operation of the first transmission line resonator, applying one or more control fields to the sample in the first sample region; positioning a sample in the second sample region; and by operation of the second transmission line resonator, applying one or more control fields to the sample in the second sample region.

[0159] Implementations of the third example may include one or more of the following features. The method includes by operation of the first transmission line resonator, applying one or more control fields to a first sample in the first sample region during a first time period; and by operation of the second transmission line resonator, applying one or more control fields to the first sample in the second sample region during a second, subsequent time period. Positioning the sample in the second sample region includes moving the first sample from the first sample region to the second sample region between the first and second time periods.

[0160] Implementations of the third example may include one or more of the following features. The method includes by operation of the first transmission line resonator, applying one or more control fields to a first sample in the first sample region; and by operation of the second transmission line resonator, applying one or more control fields to a second, distinct sample in the second sample region. The first and second samples are positioned in the first and second sample regions simultaneously, and control fields areapplied to the respective first and second samples in parallel. The first and second samples are positioned in the first and second sample regions simultaneously, and control fields are applied to the respective first and second samples sequentially.

[0161] 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 subcombination.

[0162] 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.

[0163] 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

1. CLAIMSWhat is claimed is:

1. A resonator system comprising: a first transmission line resonator patterned on a substrate and configured to produce a first microwave field in a first sample region; a second transmission line resonator patterned on the substrate and configured to produce a second microwave field in a second, distinct sample region; and first and second feedlines patterned on the substrate, wherein the first and second transmission line resonators are connected in parallel between the first and second feedlines.

2. The resonator system of claim 1, wherein the first transmission line resonator defines a first resonance frequency in a first frequency band, and the second transmission line resonator defines a second resonance frequency in a second, distinct frequency band.

3. The resonator system of claim 2, wherein the first frequency band is X-band and the second frequency band is Q-band.

4. The resonator system of claim 1, wherein the first transmission line resonator defines a first resonance frequency, the second transmission line resonator defines a second resonance frequency, and the first and second resonance frequencies are in the same frequency band.

5. The resonator system of claim 1, wherein the first transmission line resonator has a first quality factor, and the second transmission line resonator has a second, distinct quality factor.

6. The resonator system of claim 1, wherein the first transmission line resonator is over-coupled, and the second transmission line resonator is under-coupled.

7. The resonator system of claim 1, wherein the first transmission line resonator is critically coupled, and the second transmission line resonator is under-coupled.

8. The resonator system of claim 1, wherein the first transmission line resonator is over-coupled, and the second transmission line resonator is critically coupled.

9. The resonator system of claim 1, wherein the first and second feedlines are configured to communicate magnetic resonance control signals from a transceiver to the first and second transmission line resonators in parallel, and the first and second feedlines are configured to communicate magnetic resonance response signals to the transceiver from the first and second transmission line resonators in parallel.

10. The resonator system of claim 1, comprising an array of transmission line resonators patterned on the substrate, wherein the transmission line resonators in the array are connected in parallel between the first and second feedlines.

11. The resonator system of claim 10, wherein the transmission line resonators in the array are arranged as a one-dimensional array of transmission line resonators on the substrate.

12. The resonator system of claim 10, wherein the transmission line resonators in the array are arranged as a two-dimensional array of transmission line resonators on the substrate.

13. The resonator system of any of claims 1 through 12, wherein the first and second transmission line resonators are made of superconducting material.

14. The resonator system of any of claims 1 through 12, wherein the first and second transmission line resonators are made of non-superconducting material.

15. The resonator system of any of claims 1 through 12, wherein the first transmission line resonator is made of superconducting material, and the second transmission line resonator is made of non-superconducting material.

16. The resonator system of any of claims 1 through 12, wherein each of the first and second transmission line resonators comprises a single microstrip resonator.

17. The resonator system of any of claims 1 through 12, wherein: the first transmission line resonator comprises: a first plurality of microstrip resonators; a first set of terminal segments capacitively coupled to first ends of the first plurality of microstrip resonators;a second set of terminal segments capacitively coupled to second, opposite ends of the first plurality of microstrip resonators; a first branching structure connected between the first feedline and the first set of terminal segments; and a second branching structure connected between the second feedline and the second set of terminal segments; and the second transmission line resonator comprises: a second plurality of microstrip resonators; a third set of terminal segments capacitively coupled to first ends of the second plurality of microstrip resonators; a fourth set of terminal segments capacitively coupled to second, opposite ends of the second plurality of microstrip resonators; a third branching structure connected between the first feedline and the third set of terminal segments; and a fourth branching structure connected between the second feedline and the fourth set of terminal segments.

18. The resonator system of any of claims 1 through 12, wherein the substrate is a first substrate comprising a first surface, the first and second transmission line resonators and the first and second feedlines are patterned on the first surface, and the resonator system comprises: a second substrate comprising a second surface, the second substrate being oriented parallel to the first substrate with the second surface facing the first surface, the second surface being spaced apart from the first surface by a separation distance; a third transmission line resonator patterned on the second surface and configured to produce a third microwave field in the first sample region; a fourth transmission line resonator patterned on the second surface and configured to produce a fourth microwave field in the second sample region; and third and fourth feedlines patterned on the second surface, wherein the third and fourth transmission line resonators are connected in parallel between the third and fourth feedlines.

19. The resonator system of claim 18, comprising an array of transmission line resonators patterned on the second substrate, wherein the transmission line resonators in the array are connected in parallel between the third and fourth feedlines.

20. The resonator system of claim 19, wherein the transmission line resonators in the array are arranged as a one-dimensional array of transmission line resonators on the second substrate.

21. The resonator system of claim 19, wherein the transmission line resonators in the array are arranged as a two-dimensional array of transmission line resonators on the second substrate.

22. The resonator system of any of claims 1 through 12, wherein the first sample region and the second sample region are distinct, non-overlapping volumes that are separated from each other by a distance.

23. A resonator system comprising: an array of transmission line resonators patterned on a substrate and defining an array of respective sample regions; and first and second feedlines patterned on the substrate, wherein the transmission line resonators in the array are connected in parallel between the first and second feedlines.

24. The resonator system of claim 23, wherein the first and second feedlines are configured to communicate magnetic resonance control signals from a transceiver to the transmission line resonators in parallel, and the first and second feedlines are configured to communicate magnetic resonance response signals to the transceiver from the transmission line resonators in parallel.

25. The resonator system of claim 23, wherein the transmission line resonators in the array are arranged as a one-dimensional array of transmission line resonators on the substrate.

26. The resonator system of claim 23, wherein the transmission line resonators in the array are arranged as a two-dimensional array of transmission line resonators on the substrate.

1. The resonator system of claim 23, wherein the transmission line resonators in the array are made of superconducting material.

28. The resonator system of claim 23, wherein the transmission line resonators in the array are made of non-superconducting material.

29. The resonator system of claim 23, wherein the transmission line resonators in the array comprises a first transmission line resonator configured to produce a first microwave field in a first sample region, and a second transmission line resonator configured to produce a second microwave field in a second, distinct sample region.

30. The resonator system of claim 29, wherein the first transmission line resonator defines a first resonance frequency in a first frequency band, and the second transmission line resonator defines a second resonance frequency in a second, distinct frequency band.

31. The resonator system of claim 30, wherein the first frequency band is X-band and the second frequency band is Q-band.

32. The resonator system of claim 29, wherein the first transmission line resonator defines a first resonance frequency, the second transmission line resonator defines a second resonance frequency, and the first and second resonance frequencies are in the same frequency band.

33. The resonator system of claim 29, wherein the first transmission line resonator has a first quality factor, and the second transmission line resonator has a second, distinct quality factor.

34. The resonator system of claim 29, wherein the first transmission line resonator is over-coupled, and the second transmission line resonator is under-coupled.

35. The resonator system of claim 29, wherein the first transmission line resonator is critically coupled, and the second transmission line resonator is under-coupled.

36. The resonator system of claim 29, wherein the first transmission line resonator is over-coupled, and the second transmission line resonator is critically coupled.

37. The resonator system of claim 29, wherein the first transmission line resonator is made of superconducting material, and the second transmission line resonator is made of non-superconducting material.

38. The resonator system of claim 29, wherein each of the first and second transmission line resonators comprises a single microstrip resonator.

39. The resonator system of claim 29, wherein: the first transmission line resonator comprises: a first plurality of microstrip resonators; a first set of terminal segments capacitively coupled to first ends of the first plurality of microstrip resonators; a second set of terminal segments capacitively coupled to second, opposite ends of the first plurality of microstrip resonators; a first branching structure connected between the first feedline and the first set of terminal segments; and a second branching structure connected between the second feedline and the second set of terminal segments; and the second transmission line resonator comprises: a second plurality of microstrip resonators; a third set of terminal segments capacitively coupled to first ends of the second plurality of microstrip resonators; a fourth set of terminal segments capacitively coupled to second, opposite ends of the second plurality of microstrip resonators; a third branching structure connected between the first feedline and the third set of terminal segments; and a fourth branching structure connected between the second feedline and the fourth set of terminal segments.

40. The resonator system of any of claims 23 through 39, wherein the substrate is a first substrate comprising a first surface, the array of transmission line resonators is a first array of transmission line resonators, the first array of transmission line resonators and the first and second feedlines are patterned on the first surface, and the resonator systemcomprises: a second substrate comprising a second surface, the second substrate being oriented parallel to the first substrate with the second surface facing the first surface, the second surface being spaced apart from the first surface by a separation distance; a second array of transmission line resonators patterned on the second surface and configured to produce respective microwave fields in the respective sample regions; and third and fourth feedlines patterned on the second surface, wherein the second array of transmission line resonators are connected in parallel between the third and fourth feedlines.

41. An electron resonance method comprising, positioning a sample in a first sample region defined by a first transmission line resonator patterned on a substrate; by operation of the first transmission line resonator, applying one or more control fields to the sample in the first sample region; positioning a sample in a second sample region defined by a second transmission line resonator patterned on the substrate; and by operation of the second transmission line resonator, applying one or more control fields to the sample in the second sample region, wherein the resonator system further comprises first and second feedlines patterned on the substrate, and the first and second transmission line resonators are connected in parallel between the first and second feedlines.

42. The electron resonance method of claim 41, comprising: by operation of the first transmission line resonator, applying one or more first control fields to a first sample in the first sample region during a first time period; and by operation of the second transmission line resonator, applying one or more second control fields to the first sample in the second sample region during a second, subsequent time period, wherein positioning the sample in the second sample region comprises moving the first sample from the first sample region to the second sample region between the first and second time periods.

43. The electron resonance method of claim 41, comprising: by operation of the first transmission line resonator, applying one or more first control fields to a first sample in the first sample region; and by operation of the second transmission line resonator, applying one or more second control fields to a second, distinct sample in the second sample region.

44. The electron resonance method of claim 43, wherein the first and second samples are positioned in the first and second sample regions simultaneously, and the respective one or more first and second control fields are applied to the respective first and second samples in parallel.

45. The electron resonance method of claim 43, wherein the first and second samples are positioned in the first and second sample regions simultaneously, and the respective one or more first and second control fields are applied to the respective first and second samples sequentially.

46. The electron resonance method of any of claims 41 through 45, wherein the first transmission line resonator defines a first resonance frequency in a first frequency band, and the second transmission line resonator defines a second resonance frequency in a second, distinct frequency band.

47. The electron resonance method of any of claims 41 through 45, wherein the first transmission line resonator defines a first resonance frequency, the second transmission line resonator defines a second resonance frequency, and the first and second resonance frequencies are in the same frequency band.

48. The electron resonance method of any of claims 41 through 45, wherein the first transmission line resonator has a first quality factor, and the second transmission line resonator has a second, distinct quality factor.

49. The electron resonance method of any of claims 41 through 45, wherein the first transmission line resonator is over-coupled, and the second transmission line resonator is under-coupled.

50. The electron resonance method of any of claims 41 through 45, wherein the first transmission line resonator is critically coupled, and the second transmission line resonator is under-coupled.

51. The electron resonance method of any of claims 41 through 45, wherein the first transmission line resonator is over-coupled, and the second transmission line resonator is critically coupled.

52. The electron resonance method of any of claims 41 through 45, wherein the first and second transmission line resonators are made of superconducting material.

53. The electron resonance method of any of claims 41 through 45, wherein the first and second transmission line resonators are made of non-superconducting material.

54. The electron resonance method of any of claims 41 through 45, wherein the first transmission line resonator is made of superconducting material, and the second transmission line resonator is made of non-superconducting material.

55. The electron resonance method of any of claims 41 through 45, wherein each of the first and second transmission line resonators comprises a single microstrip resonator.

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