Dynamic inductive parametric amplifier

Abstract

The present disclosure relates to a dynamic inductive parametric amplifier comprising an input port arranged to receive a pump tone, a DC bias and an input signal, an output port arranged to provide an amplified version of the input signal, a tunable stepped impedance component arranged to attenuate and / or filter a predetermined frequency band, and a high dynamic inductor line. The tunable stepped impedance component is tuned at a frequency that allows the amplifier to resonate at a predetermined frequency, and the pump tone has a frequency higher than the input signal, and the DC bias signal is sent to the high dynamic inductor line.

Description

Technical Field

[0001] The technology of the present invention relates to a parametric amplifier based on superconducting materials. In particular, the technology of the present invention relates to a dynamic inductance parametric amplifier. Background Art

[0002] Parametric amplification is a widely used technique in microwave engineering and optics. It provides gain by varying circuit parameters, such as capacitance or inductance. Specifically, it relies on nonlinear reactive elements (capacitors or inductors for microwaves, nonlinear refraction in optics) to mix two AC signals.

[0003] Power can be transferred from one mode (the "pump") to another (the "signal"), thereby amplifying the signal. One advantage of this amplification is that there is no dissipation in purely reactive components, which means minimal added noise.

[0004] For example, parametric amplifiers using reverse-biased semiconductor diodes have been shown to achieve very low noise performance in the microwave region. However, even in this type of amplifier, thermal noise generated in the semiconductor's extended resistance is unavoidable.

[0005] There are many applications, such as amplifying small signals (e.g., single photons) such as those arising during the readout of qubits in a quantum processor, that require parametric amplifiers that provide low-noise performance under quantum processor operating conditions and are compatible with the quantum processor architecture.

[0006] Parametric amplification of Josephson junction devices is used in quantum computing architectures based on Josephson junction superconducting qubits. Josephson junctions behave like highly nonlinear inductors.

[0007] To increase the amplification bandwidth, Josephson junctions can be incorporated into broadband transmission lines, a class of devices known as traveling-wave parametric amplifiers (TWPAs). Because mixing and amplification occur across many wavelengths in a TWPA, dispersion engineering must be performed to maintain phase matching between the pump and signal. Furthermore, Josephson junction-based parametric amplifiers are extremely sensitive to magnetic fields and are unsuitable for applications requiring them.

[0008] Another approach to parametric amplification using superconducting circuits is to exploit the inertia of copper pairs, which provides an effective "kinetic inductance" that depends on the current passing through the superconductor. Kinetic inductance is an intrinsic property of superconductors and can be large enough to facilitate parametric amplification in materials with large normal-state resistivity, such as NbN, TiN, and NbTiN. Kinetic inductance TWPAs have recently attracted significant interest due to their ease of fabrication (they do not contain any Josephson junctions) and their high dynamic range (resulting from the high critical current they support). The quadratic nonlinearity of the kinetic inductance supports a four-wave mixing process, in which two pump photons combine to create a signal photon and an idler photon.

[0009] Recently, it has been demonstrated that biasing a dynamic inductive TWPA with a DC current results in three-wave mixing (TWM) and lower pump power requirements. Three-wave mixing is advantageous because it involves a single pump photon at approximately twice the signal frequency, making it easy to filter out this single pump photon in the measurement chain.

[0010] Until now, three-wave mixing in dynamic inductor parametric amplifiers could only be achieved using traveling-wave geometry, because these devices must combine currents over a wide frequency range, covering DC, frequencies f s The signal and about 2f s The dynamic inductance TWPA is very long, ranging from 20cm to 2m, which poses a challenge to the integration of manufacturing microelectronic circuits. Summary of the Invention

[0011] According to a first aspect, the present invention provides a dynamic inductor parametric amplifier comprising: an input port arranged to receive a pump tone, a DC bias signal and an input signal; an output port arranged to provide an amplified version of the input signal; a tunable step impedance component arranged to attenuate and / or filter a predetermined frequency band; and a high dynamic inductance line; wherein the tunable step impedance component is tuned to a frequency allowing the amplifier to resonate at a predetermined frequency, and the pump tone has a frequency higher than the input signal, and the DC bias signal is sent to the high dynamic inductance line.

[0012] In an embodiment, the tunable stepped impedance component comprises a coplanar waveguide (CPW) microwave band-stop filter.

[0013] In an embodiment, the high dynamic inductance line is shorted to ground. In an alternative embodiment, the high dynamic inductance line forms a quarter wavelength resonator (or a harmonic thereof).

[0014] In an embodiment, the high dynamic inductance line resonates at a frequency in a stop band of the tunable stepped impedance component.

[0015] In an embodiment, the frequency response of the tunable stepped impedance has a continuous centerline that allows DC current to pass and provides three-wave mixing.

[0016] In an embodiment, the high dynamic inductance line comprises NbTiN.

[0017] In an embodiment, the high dynamic inductance line comprises a single layer of NbTiN.

[0018] In an embodiment, the step impedance is tunable.

[0019] According to a second aspect, the present invention provides a method for performing parametric amplification using a dynamic inductor parametric amplifier, the method comprising the following steps: providing a dynamic inductor parametric amplifier according to any one of the preceding claims; applying a DC signal configured to modify one or more filtering characteristics of the dynamic inductor and stepped impedance components; applying a pump tone and an input signal to an input port; and detecting an amplified version of the input signal at the output port.

[0020] In an embodiment, the one or more filtering characteristics of the tunable stepped impedance component include the band-stop frequency and attenuation value and / or quality factor.

[0021] In an embodiment, the dynamic inductive parametric amplifier is a two-port device with large port coupling asymmetry (ie, with port coupling rates differing by more than one order of magnitude).

[0022] In an embodiment, the high dynamic inductance line is between two asymmetrically coupled ports. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Although there are any other forms that may fall within the scope of the present invention, for a clearer understanding of the technology of the present invention, embodiments of the technology of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0024] Figure 1: Shows a circuit schematic of an amplifier (a); an embodiment of an amplifier implemented using a coplanar waveguide (b); and example transmission S-parameters of a stepped impedance filter / Bragg mirror (c).

[0025] Figure 2 Shown are the measurement results of the signal gain reflected from the dynamic inductance parametric amplifier.

[0026] Figure 3 is a flow chart outlining the steps for performing amplification using the amplifier shown in FIG1 .

[0027] Figure 4A simplified setup for cooling a KIPA below its superconducting critical temperature and operating it as an amplifier is shown.

[0028] Figure 5a shows the phase-sensitive gain curve of the amplifier.

[0029] Figure 5b shows the output power of the amplifier at 1dB gain compression point.

[0030] FIG6 a is a schematic diagram illustrating the amplification and de-amplification of phase-scanned coherence states and the squeezing of vacuum noise.

[0031] FIG6 b shows the measurement results of amplification and de-amplification of the phase-scanned coherence state for different pump powers.

[0032] Figure 7A The spin echo signal measured using an amplifier is shown.

[0033] Figure 7B The phase dependence of the amplified echo signal on the pump phase is shown for different pump powers.

[0034] Figure 8 An example optical cavity for introducing parametric coupling between two modes with different resonant frequencies is described.

[0035] Figure 9A Shown is a reflected S-parameter measurement of an amplifier centered on its first harmonic.

[0036] Figure 9B Shown is a reflected S-parameter measurement of an amplifier centered on its fundamental mode. DETAILED DESCRIPTION

[0037] When two waves pass through a nonlinear medium, the amplitude of one wave periodically changes a parameter (related to the nonlinearity) that controls the propagation of the other wave, resulting in a power transfer between them. The frequency of the first wave (the pump) should be twice or approximately the same as the frequency of the second wave (the signal), depending on the order of the nonlinearity. In order for this amplification to add only the noise required by quantum mechanics (which is said to be quantum limited), the nonlinear elements and other amplifier components should not dissipate energy.

[0038] When superconducting materials are cooled to a temperature below their critical temperature, they enter a superconducting phase in which electric current can pass through them with almost no dissipation.

[0039] Superconducting circuits utilizing kinetic inductance can be used for parametric amplification using materials such as NbN, TiN, and NbTiN. In recent years, kinetic inductor traveling-wave parametric amplifiers have been studied due to their ease of fabrication (they do not contain any Josephson junctions) and their high dynamic range (resulting from the high critical current they support). The quadratic nonlinearity of the kinetic inductance supports a four-wave mixing process, in which two pump photons combine to create a signal photon and an idler photon.

[0040] An embodiment of the present invention provides a dynamic inductive parametric amplifier (KIPA) implemented in a resonant structure. The device is based on a microwave transmission line geometry that forms a resonator and allows both DC and high frequencies to pass through the structure.

[0041] Figure 1(a) shows a schematic circuit representation of amplifier 100. The design has a single port 102 that serves as the input port for the pump tone, signal, and DC signal. The same port 102 also serves as the output port. Amplifier 100 also includes stepped impedance coplanar waveguide (CPW) microwave band-rejection filters 104, 104', shorted to ground by a high-dynamic inductance line 106. The high-dynamic inductance section 106 is decoupled from the input / output port 102 by the band-rejection filters 104, 104' and resonates at a frequency that depends on several factors (e.g., geometry, amount of dynamic inductance, etc.). The band-rejection filter is formed by varying the impedance of the CPW between two or more values, and its parameters (attenuation, bandwidth) can be tuned by varying the impedance, cross-sectional length, and number of repetitions of the stepped impedance. This configuration can also be viewed as a Bragg cavity in optics, where microwaves are confined within the high-dynamic inductance line (cavity) by a Bragg mirror (the stepped impedance CPW).

[0042] Figure 1(b) shows an embodiment of an amplifier implemented using a CPW 150. The input port 152 is directly connected to a waveguide, which comprises a distributed impedance arrangement 154. The coplanar waveguide feeds a high dynamic inductor section 156.

[0043] Figure 1(c) shows a simulation of microwave transmission through an exemplary stepped impedance filter, such as impedance filter / Bragg reflector 104, 104'. In one embodiment, the cavity length is selected to produce resonance somewhere in the first stopband, such as at the dashed line. Because the CPW has a continuous centerline, it passes DC current to generate three-wave mixing. In addition, the filter passes the pump signal at double the frequency (dashed line in Figure 1(c)).

[0044] The external coupling rate of the high dynamic inductor section 156 to the feed line 152 sets the bandwidth of the resonator and, therefore, the bandwidth of the amplifier. The external coupling rate can be controlled by the design of the band-stop filter 154. In general, reducing the attenuation of the band-stop filter increases the bandwidth of the amplifier.

[0045] In another embodiment, the ground connection of high dynamic inductor section 156 can be replaced with a second Bragg reflector and a port with a lower coupling rate than first ports 152, 154. In this embodiment, the coupling rate of the second port is more than an order of magnitude lower than that of the first port. For example, the coupling rate can be reduced by increasing the number of repetitions of the stepped impedance structure in the band-stop filter / Bragg mirror. The input signal is applied to either port 1 or port 2, and due to the asymmetric coupling rate, the input signal will preferentially exit the device through the more strongly coupled port 1. The pump tone can be applied through either port 1 or port 2.

[0046] Figure 2 The gain is shown for a microwave signal reflected from a single-port NbTiN KIPA in the presence of a pump signal and a DC current. In addition to the DC current (which was varied in this experiment), a pump tone approximately twice the signal frequency was applied. The measurements were performed at a temperature of 400 mK and a parallel magnetic field of 200 mT, which is possible due to the high critical field of NbTiN and the absence of a Josephson junction.

[0047] Figure 3 An example process is shown utilizing amplifier 100. Specifically, the process begins at step 302 where a dynamic inductor parametric amplifier as described above is provided.

[0048] At step 304, a DC signal is applied to the input port 102 of the amplifier 100. The DC signal is configured to modify one or more filtering characteristics of the dynamic inductance and the stepped impedance component.

[0049] At step 306, a pump tone and an input signal are applied to the input port 102. The pump tone may have a frequency that is twice the frequency of the input signal.

[0050] Finally, at step 308 , an amplified version of the input signal is detected at an output port (the same as input port 102 ).

[0051] Embodiments of the present disclosure can be used to amplify small signals (e.g., single photons), such as those that occur during qubit readout in a quantum processor. In an embodiment, the device is made of a single layer of NbTiN and a single exposure lithography manufacturing process, so it can be cost-effectively and mass-produced. In addition, because it is a resonant amplifier, it is much shorter (<2 cm) than other NbTiN dynamic inductance amplifiers, thereby improving yield. Since there is no Josephson junction in the device, it can operate in large magnetic fields and high temperatures, opening up more application areas. In an embodiment, the large critical current of the film provides a high dynamic range, with a 1 dB compression point exceeding –60 dBm.

[0052] The device's amplifying element is actually a microwave resonator that can be used to perform electron spin resonance (ESR) spectroscopy on small samples at cryogenic temperatures. The signal-to-noise ratio (SNR) is one of the most important parameters in spin resonance experiments because it has a significant impact on measurement time. Losses between the input signal and the first amplifier in the measurement chain degrade the SNR. Because the KIPA described in this article can operate in a magnetic field and is quantum noise limited, it provides an integrated ESR resonator / amplifier solution (with no additional losses between the ESR resonator and the amplifier) ​​that can be advantageously used to perform high-sensitivity ESR spectroscopy.

[0053] In certain configurations, the resonator can also be used to relax the spins via the so-called Purcell effect. This enables fast measurements of repetition times that would otherwise be very slow (due to the long spin relaxation times at these temperatures and magnetic fields).

[0054] The DC current used to promote three-wave mixing also enables rapid control of the resonator frequency.

[0055] Furthermore, in embodiments, the DC current can also be used to change the quality factor of the resonator. This is accomplished by changing the impedance of the band-stop filter portion and / or the relative position of the resonator frequency to the band-stop region. Advantageously, this capability enables reaching a state known as critical coupling (where the quality factor is matched to the loss), where the device is most sensitive in detecting spin resonance.

[0056] Phase-sensitive amplification and squeezing

[0057] The amplifier 100 described herein acts as a nearly ideal degenerate three-wave mixing device, thereby allowing phase-sensitive amplification and squeezing. By choosing a pump frequency that is exactly twice the input signal frequency, ω p =2ω s , the output signal reflected from the amplifier 100 may be amplified or de-amplified depending on the phase relationship between the pump and input signals.

[0058] Phase-sensitive power gain Depends on the signal power gain G s and the relative pump / signal phase for

[0059]

[0060] when The input signal is amplified, however, if The input signal is then de-amplified.

[0061] Under the limitation of large signal gain, G(0)≈4G s And G(π / 2)≈1 / 4G s . Amplifier 100 can be used Figure 4 The example setup shown in operates as a phase-sensitive amplifier. Specifically, Figure 4 As shown, the amplifier 100 is mounted on a mixing chamber plate of a dilution refrigerator to achieve quantum-limited noise performance. For applications that do not require quantum-limited system noise, the amplifier can also be mounted and operated at higher temperatures (e.g., at 4K) if desired. A pump signal generator 402 is connected to the amplifier 100 via a duplexer 404, while a DC bias current is connected to the signal path via a bias tee 406. In addition, the output port is connected to one or more amplifier stages 408 via a circulator 410. The amplifier stage is connected to a measurement setup 412. It should be appreciated that this simplified setup 400 is merely exemplary. Other measurement setups may also be used.

[0062] In use, input microwave signal (frequency ω s , phase ) and the pump tone (frequency ω p ) can be generated by a pump signal generator 402 and a scanning phase The input signal generator 414 is applied to the amplifier 100. The output power is monitored and measured by the measuring device 412.

[0063] The resulting phase-sensitive gain curve is shown in Figure 5a. Specifically, the graph shows the phase dependence of the gain of the amplifier 100 operating in degenerate mode. Relative to the fixed input signal phase It is step-by-step. The signal is de-amplified at At 100 dBm, amplifier 100 experiences maximum gain. Different traces use different pump powers (ranging from -36 dBm to -26 dBm at the KIPA input), corresponding to different maximum gains. As shown, the gain is highest (approximately 50 dB) at a pump power of -26 dBm, while the gain is approximately 10 dB at an input power of -30 dBm.

[0064] Figure 5b shows the maximum gain for each trace in Figure 5a as a function of input signal power. Inset 502 depicts the output power at which the maximum gain is reduced by 1 dB (1 dB compression point).

[0065] In addition to achieving exceptionally large gains (up to 50 dB), the 1 dB compression point output power was found to be greater than -45 dBm (Figure 5b), which is approximately 5-6 orders of magnitude higher than the 1 dB compression point of typical JPA-based parametric amplifiers.

[0066] Figure 6 plots the output field quadrature curves of an amplified microwave signal applied to the amplifier input, measured using homodyne detection. Specifically, Figure 6a depicts the amplification and de-amplification of a phase-sweep signal and the squeezing of vacuum noise. Figure 6b illustrates the trajectory of a circle in the IQ plane, as the signal phase is swept at a constant signal amplitude. With the introduction of a pump signal, the circle stretches into an ellipse, demonstrating the squeezing capability of amplifier 100.

[0067] Selecting the Local Oscillator Phase The amplified field quadrature is aligned with the I-axis of the output IQ plane, while the de-amplified field quadrature is aligned along the Q-axis of the output IQ plane. As the pump power increases, the microwave tones (or so-called coherence states) - which trace a circle in the IQ plane when the amplifier 100 is turned off - are stretched into ellipses, as shown in FIG. Figure 6A and Figure 6B shown.

[0068] When no signal is applied and the amplifier 100 is in a state satisfying At temperature T, the input field is in its quantum mechanical ground state and undergoes zero-point fluctuations. This is a direct consequence of the uncertainty principle of the quantum harmonic oscillator.

[0069] The field quadratures in the ground state (labeled X and Y) obey uncertainty relations (in units of photons).

[0070] δX 2 δY 2 ≥1 / 16

[0071] That is, each quadrature has an uncertainty of 1 / 4 photon. This uncertainty is imposed on all signals and represents the quantum limit of noise in the measurement. The phase-sensitive gain of amplifier 100 can be used to de-amplify or "squeeze" this noise in one quadrature at the expense of amplifying it in another quadrature. For example, noise can be de-squeezed in either the X or Y quadrature to reduce uncertainty in the other quadrature.

[0072] This can be used to improve the signal-to-noise ratio in measurements of small microwave signals, for example, in qubit readout, spin resonance spectroscopy, and axion searches.

[0073] In Josephson junction-based amplifiers, squeezing levels exceeding 12 dB have so far been hampered by the presence of high-order nonlinearities. The resulting squeezed state becomes highly non-Gaussian at large gains.

[0074] The semiclassical measurements of Figure 6b show that a high degree of squeezing can be performed using amplifier 100, with no visible distortion at gains up to 30 dB. This high level of squeezing is achieved in part by the amplifier's weak higher-order nonlinearities.

[0075] In addition to being useful in measurements, these high levels of squeezing can also be used to achieve fault-tolerant quantum computations with continuously variable cluster states. In a qubit-based error correction scheme, a threshold of 20.5 dB of squeezing was achieved for fault-tolerant measurement-based quantum computation.

[0076] Spin resonance spectroscopy

[0077] The high magnetic field compatibility of the amplifier 100 also opens up applications in spin resonance spectroscopy. Electron spin resonance (ESR) spectroscopy is a widely used technique in biology, medicine, chemistry, and materials science. It is used to reveal the underlying structure and function of materials. In traditional ESR, approximately 1 billion electron spins are typically required to produce a signal above the system noise level at room temperature. Recent advances have seen superconducting resonators and JPAs used to push the sensitivity of ESR spectroscopy to the quantum limit, with detection capabilities reaching levels of 10 spins.

[0078] In current quantum-confined ESR spectrometers, a spin sample is coupled to a high-quality superconducting planar resonator and placed in a moderate magnetic field (e.g., ~0.34 T for X-band spectrometers). The spins emit a signal into the resonator, which is then routed to a separate JPA for amplification. The JPA is extremely sensitive to magnetic fields and must be housed in multiple layers of magnetic field shielding. In addition, a microwave circulator is required to connect the resonator to the JPA, which increases insertion loss, which reduces the signal-to-noise ratio of the measurement.

[0079] The amplifier 100 is a (nonlinear) resonator that can be coupled to the spins and placed in a moderate magnetic field (~0.34 T). Thus, the spin signal emitted in a pulsed ESR experiment can be amplified within the amplifier 100 by applying a properly timed pump tone, eliminating the need for an external JPA and any associated insertion losses between the cavity and the first amplifier. Furthermore, since the amplifier and the ESR resonator are the same device, their frequencies are matched.

[0080] FIG7 shows an example of amplification of a spin echo signal within the amplifier 100. Specifically, Figure 7AThe spin echo signal measured using the amplifier 100 is shown without amplification (blue trace) and with amplification (red trace). The amplification is performed in degenerate mode. Figure 7A As shown, the echo area is significantly enhanced with magnification. Figure 7B The amplified echo signal is presented for different pump powers and pump phases. Phase dependence of , where regions of amplification and de-amplification (relative to the pump-off data in orange) are evident.

[0081] Parametric spin cooling

[0082] In optomechanics, parametric coupling between optical cavities and mechanical resonators can be used to perform many useful tasks, from frequency conversion to quantum non-destructive measurements and cooling. Specifically, optomechanical cooling has been used to reduce the hot population of mechanical resonators to bring them close to their quantum mechanical ground state, or equivalent temperature in the microkelvin range.

[0083] Figure 8 A conventional optical cavity 800 is shown for introducing parametric coupling. Specifically, optical cavity 800 includes two mirrors—mirror 802 and mirror 804. Parametric coupling can be introduced by connecting a mirror of optical cavity 800 (e.g., mirror 804) to a spring 806—the mirror 804 now acts as a mechanical resonator whose resonant frequency is determined by the mass and spring constant of the connected spring 806. When the mechanical resonator oscillates, it changes the length of the optical cavity and, thereby, its resonant frequency. Quantum mechanically, this interaction is described by the Hamiltonian:

[0084]

[0085] in, is the photon number operator of the optical cavity, and is proportional to the displacement operator of the mechanical resonator. This type of interaction is called optomechanical coupling.

[0086] Cooling is achieved by the cavity frequency difference ω d This is achieved by introducing a drive into the coupled system at ω = ω1 - ω0, where ω0 is the mechanical resonant frequency and ω1 is the optical frequency. Phonons in the mechanical resonator are upconverted by the driver into photons in the optical mode, and vice versa. Because the linewidth (or dissipation rate) of the mechanical mode (κ0) is typically several orders of magnitude smaller than that of the optical cavity (κ1), the upconverted photons are dissipated through the optical cavity. If the effective rate of phonon removal exceeds the rate at which the mechanical mode thermalizes to its environment (κ0), the mechanical resonator is cooled.

[0087] The above conversion process can also be regarded as the coupling between the mechanical mode and the optical mode, which are driven at the frequency ω d degenerates in the rotated frame. Invoking the "linearized" approximation, the interaction becomes:

[0088]

[0089] That is, the pattern and The coupling between them and their strength is where n d is the number of photons in the driver.

[0090] In this application, amplifier 100 is fabricated from a short-circuit terminated quarter-wavelength resonator, as shown in Figure 1. In other examples, amplifier 100 can be constructed in which the ground terminal is replaced by a second port. The resonator is inherently multimodal, with a resonance at a frequency kω0, where k is a positive integer. In the case of a short-circuit terminated amplifier, k is a positive odd integer. Furthermore, the nonlinear dynamic inductance creates a natural coupling between the modes: that is, the current in one mode changes the dynamic inductance along the resonator and shifts the frequency of another mode, similar to optomechanical coupling. Therefore, low-frequency modes can be cooled by parametrically coupling them with a driver to higher harmonics of the resonator.

[0091] Figure 9 shows the fundamental mode of amplifier 100 (at ω0 / 2π≈7.2 GHz) coupled to the first harmonic (at ω1 / 2π=3ω0 / 2π≈21.6 GHz). Specifically, Figure 9 shows an S-parameter reflection measurement of the amplifier, centered around two different modes, with a strong drive tone present. Figure 9A shows the first harmonic, while Figure 9B The fundamental mode is shown. The driving tone frequency varies along the horizontal axis. When the driving frequency is equal to the difference between the mode frequencies, the modes become mixed (at ), indicating the onset of strong coupling.

[0092] The high power handling capability of the amplifier 100 means that large drive signals can be applied, even to achieve a strong coupling between the modes (g>κ0,κ1). Furthermore, by modifying the impedance along the length of the resonator (introducing dispersion), the frequencies of the harmonics can be tailored. The frequency of the first harmonic mode can be shifted so that the drive frequency that couples it to the fundamental mode is not twice the fundamental frequency, i.e., ω d / 2π≠ω0 / π. This is important because degenerate amplification occurs in the fundamental mode when driven at ω0 / π, a competing process that limits cooling efficiency. The coupling rate of the harmonics to the external port can also be selected by carefully positioning the mode frequency within its stopband, or by modifying the stopband's characteristics, such as attenuation and bandwidth.

[0093] Thus, the amplifier 100 can be used to achieve an optomechanical-like interaction and cool any mode of the resonator to below the effective temperature of the measurement system. This is a useful capability that can be used to reduce the temperature of auxiliary systems that are thermalized to the cooling mode.

[0094] Recent advances in quantum confined ESR spectroscopy have shown that spins coupled to superconducting resonators can relax via the spontaneous emission of microwave photons into the resonator, the so-called Purcell effect. It has been further demonstrated that in this case, the spins do in fact thermalize into the modes of the resonator to which they are coupled. Therefore, the amplifier 100 can be used to cool the spins (either collectively or individually) coupled to one of the amplifier modes. This is very useful in ESR spectroscopy, where it provides enhanced polarization and, therefore, a larger signal. The amplifier can operate at high temperatures (up to ~5K) and in a magnetic field, so this cooling process can be performed under typical conditions of X-band ESR (2K, 0.34T). One can also envision using parametric cooling to initialize large registers of spin qubits in spin-based quantum processors.

[0095] For parametric spin cooling to be effective, a strong single-spin-to-photon coupling rate g is required. s The rate of spin relaxation / thermalization is given by is given and is greater than the other rates of energy relaxation. In order to increase g s , the low resonator impedance enhances the zero-point magnetic field fluctuations of the mode. In one method of achieving this, the large dynamic inductance of the resonator can be compensated by including interdigital capacitance on the ground plane 156.

[0096] As used herein, the term "comprising" (and grammatical variations thereof) is used in the inclusive sense of "having" or "including," rather than in the sense of "consisting only of."

[0097] It will be appreciated by those skilled in the art that various changes and / or modifications may be made to the invention shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. Therefore, the embodiments herein are considered in all respects to be illustrative and not restrictive.

Claims

1. A dynamic inductance parametric amplifier, comprising: an input port arranged to receive a pump tone, a DC bias signal, and an input signal; an output port arranged to provide an amplified version of said input signal; a tunable stepped impedance component comprising a coplanar waveguide (CPW) microwave band-stop filter arranged to attenuate and / or filter a predetermined frequency band; as well as High dynamic inductance line; wherein the tunable stepped impedance component is tuned at a frequency that allows the dynamic inductance parametric amplifier to resonate at a predetermined frequency, and wherein the pump tone has a frequency higher than a frequency of the input signal, and wherein the DC bias signal is sent to the high dynamic inductance line.

2. The dynamic inductance parametric amplifier according to claim 1, wherein: The high dynamic inductance line is shorted to ground.

3. The dynamic inductance parametric amplifier according to claim 2, wherein: The high dynamic inductance line resonates at a frequency in the stop band of the tunable stepped impedance component.

4. The dynamic inductance parametric amplifier according to any one of claims 1 to 3, wherein: The frequency response of the tunable stepped impedance has a continuous centerline that allows DC current to pass and provides three-wave mixing.

5. The dynamic inductance parametric amplifier according to any one of claims 1 to 3, wherein: The high dynamic inductance line includes NbTiN.

6. The dynamic inductance parametric amplifier according to any one of claims 1 to 3, wherein: The high dynamic inductance line includes a single layer of NbTiN.

7. A method for performing parametric amplification using a dynamic inductor parametric amplifier, the method The following steps are involved: Providing a dynamic inductance parametric amplifier according to any one of the preceding claims; applying a DC signal configured to modify one or more filtering characteristics of the dynamic inductor and the stepped impedance component; Applying a pump tone and an input signal to the input port; An amplified version of the input signal is detected at the output port.

8. The method according to claim 7, wherein: The one or more filtering characteristics of the tunable stepped impedance component include a stopband frequency and an attenuation value and / or a quality factor.

9. A dynamic inductance parametric amplifier for performing phase-sensitive amplification, the amplifier comprising: an input port configured to receive a pump tone, a DC bias signal, and an input signal; an output port configured to provide an amplified or de-amplified version of the input signal; a tunable stepped impedance component comprising a coplanar waveguide (CPW) microwave band-stop filter configured to attenuate and / or filter a predetermined frequency band; as well as High dynamic inductance line; wherein the tunable stepped impedance component is tuned at a frequency that allows the amplifier to resonate at a predetermined frequency, and wherein the pump tone has a frequency twice that of the input signal, and wherein the DC bias signal is sent to the high dynamic inductance line.

10. The amplifier of claim 9, mounted on a mixing chamber board of a dilution refrigerator.

11. The amplifier according to any one of claims 9 to 10, wherein: The input port is connected to a pump signal generator via a duplexer, and the input port is connected to a DC bias current via a bias tee.

12. The amplifier according to any one of claims 9 to 10, wherein: The output ports are connected to one or more amplification stages via one or more cryocirculators, and the amplification stages are connected to a measurement setup.

13. The amplifier according to claim 9, wherein The amplifier is used as a resonator in electron spin resonance (ESR) spectroscopy to amplify the spin signal.

14. The amplifier of claim 9, wherein the amplifier is used to assist in parametric cooling of a system, The amplifier is a short-circuit terminated multi-mode resonator.

15. The amplifier of claim 9, wherein the amplifier is used to assist in parametric cooling of a system, The amplifier is a two-port multi-mode resonator with asymmetric port coupling rates.

16. The amplifier according to claim 14 or 15, wherein The nonlinear dynamic inductance created by the amplifier produces a natural coupling between the modes of the multi-mode resonator, causing the current in one mode to change the frequency in another mode.

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