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Physical Review Applied

Low-noise microwave parametric amplifier based on self-heated nonlinear impedance with subnanosecond thermal response

Michael Will, Mohammad Tasnimul Haque, Yuvraj Chaudhry, Dmitry S. Golubev, Pertti Juhani Hakonen

Published Jan 17, 2025• 0 citations
Publisher

Abstract

Low-noise amplifiers are of great significance in the field of quantum technologies. We study a thermally driven parametric amplifier based on a superconductor-insulator-graphene-insulator-superconductor ($S$-$I$-$G$-$I$-$S$) junction coupled to a superconducting microwave cavity. The strong nonlinearity in the temperature dependence of our device leads to thermal self-modulation that produces impedance oscillations at frequencies around twice the angular cavity resonance frequency ${\ensuremath{\omega}}_{\mathrm{r}}$. In particular, reactance modulation of the effective capacitance yields a gain of 18.6 dB over a frequency span of 125 kHz with a minimum noise temperature of ${T}_{\mathrm{N}}=1.4\phantom{\rule{0.2em}{0ex}}\mathrm{K}$. Our theoretical modeling gives insight into the exact mixing processes, confirmation of the electron-phonon coupling parameter and possible improvements of the studied system.

DOI
10.1103/physrevapplied.23.014037

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Low-noise parametric microwave amplifier based on self-heated nonlinear impedance with sub-nanosecond thermal response

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Low-noise amplifiers are of great importance in the field of quantum technologies. We study a thermally driven parametric amplifier based on a superconductor-insulator-graphene-insulator-superconductor (SIGIS) junction coupled to a superconducting microwave cavity. The strong non-linearity in the temperature dependence of our device leads to thermal self-modulation that produces impedance oscillations at frequencies around twice the angular cavity resonance frequency $ω_\mathrm{r}$. In particular, reactance modulation of the effective capacitance yields a gain of 18.6 dB over a frequency span of 125 kHz with a minimum noise temperature of $T_\mathrm{N} = 1.4$ K. Our theoretical modelling gives insight into the exact mixing processes, confirmation of the electron-phonon coupling parameter and possible improvements of the studied system.

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We report the lowest noise temperature of any microwave amplifier except the maser. This amplifier is a nearly degenerate superconducting parametric amplifier at X-band consisting of a low β, thin film, single junction SQUID, a monolithic 50 Ω to 1 Ω impedance matching network, and a cooled circulator. Nb/Nb2O5/Pb alloy junctions were incorporated into Nb and Pb-in circuitry on 1×2 cm silicon chips. The SQUID was phase-biased near 90° and driven by an external pump at approximately twice the operating frequency. The self-resonance frequency of the SQUID inductance and junction capacitance was set at the operating frequency of 8.2GHz. The operating charac teristics depended on the pump amplitude, the junction phase bias, and the SQUID parameters. For small values of\beta < 1, the maximum gain in both the signal and idler channels was ≈10dB, the bandwidth = 170MHz, and the single-sidehand noise temperature was 6K with an uncertainty of (+15 to -7)K. For higher β, the gain increased to nearly 30dB with increased noise and parametric oscillations occurring near the pump subharmonic frequency.

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Graphene-based superconducting quantum circuits : the Josephson parametric amplifier

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With a large portfolio of elemental quantum components, superconducting quantum circuits have contributed to dramatic advances in microwave quantum optics. Of these elements, quantum-limited parametric amplifiers have proven to be essential for low noise readout of quantum systems whose energy range is intrinsically low (tens of µeV). They are also used to generate non classical states of light that can be a resource for quantum enhanced detection. Superconducting parametric amplifiers, like quantum bits, typically utilize a Josephson junction as a source of magnetically tunable and dissipation-free nonlinearity. The magnetic control is not an industry standard for devices and starts already to be an issue in large scale circuits. In recent years, efforts have been made to introduce semiconductor weak links as electrically tunable nonlinear elements, with demonstrations of microwave resonators and quantum bits using semiconductor nanowires, a two dimensional electron gas, carbon nanotubes and graphene. However, given the challenge of balancing nonlinearity, dissipation, participation, and energy scale, parametric amplifiers have not yet been implemented with a semiconductor weak link. The work presented in this PhD thesis demonstrates the design, fabrication and performances of a parametric amplifier leveraging a graphene Josephson junction.The graphene is encapsulated in between hBN flakes in order to improve its quality. Using such high quality junctions, we demonstrate amplification with 20 dB gain which is the milestone for overcoming noise of the classical amplifiers in the rest of the amplification chain. The Josephson parametric amplifier being based on a resonant structure (around 6 GHz) suffers from the gain bandwidth product limiting the amplification to a few MegaHertz frequency range. The use of a side gate to electrically tune the graphene gives control of the Josephson junction inductance and thus the resonant frequency of the amplifier. We demonstrate a near 1 GHz tunability of the amplification frequency with the use of a side gate which is as good as the tunability offered by using a magnetic flux on a SQUID for similar amplifier designs. Moreover, graphene has shown to exhibit nonlinear loss under a strong microwave irradiation arising because of dynamics in the Andreev states. Dissipation is known to add intrinsic noise on quantum amplifiers and could be a problem for quantum limited parametric amplification. We demonstrate that despite the presence of nonlinear loss, graphene based Josephson parametric amplifiers can reach near quantum limited amplification. A two photon loss model was used to describe the behaviour of the device but we show that a more complex model is required in order to take into account the nonlinear dissipation and the non-sinusoidal current phase relation. We also studied the dynamic range and showed that the graphene based Josephson parametric amplifier can reach a 1 dB compression point of -123 dBm which is as good as single tunnel junctions based parametric amplifiers. Our results expand the toolset for electrically tunable superconducting quantum circuits and offer new opportunities for the development of quantum technologies such as quantum computing, quantum sensing and fundamental science.

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In this Master thesis, I present a theoretical description and experimental measurements of a tunable microwave resonator operated as a parametric amplifier. Superconducting parametric amplifiers have attracted great interest in recent years as it has been demonstrated that they can operate with a noise performance at the standard quantum limit. \nParametric amplification is achieved in the devices by modulating the electrical length of the resonator at twice the resonance frequency. The device measured in this thesis consists of a quarter-wavelength microwave resonator fabricated in a thin-film aluminum coplanar waveguide geometry. With a termination to ground through a Superconducting Quantum Interference Device (SQUID), the boundary condition of the resonator becomes sensitive to an applied magnetic field. This enables the tuning of the resonance frequencies, using a DC magnetic field, over a wide frequency range of 670MHz. Similarly, an AC magnetic field then allows for the modulation of the resonator electrical length at microwave frequencies. \nWe characterized the device by first measuring the DC tuning curves of the 2nd and 3rd harmonics of the resonator, around 4 GHz and 6 GHz respectively. We then studied parametric amplification in the device when the electrical length was modulated at approximately twice the resonance frequency of one of the modes. We scanned the pump frequency and pump power over a wide range to study the region in parameters which gives parametric gain. We performed an in-depth parameter sweep over this region, identifying pump parameters that provided maximum gain and maximum system noise improvements compared the following HEMT amplifier. \nWe find that the use of the parametric amplifier can improve the system noise temperature by more than 10 dB compared to a start-of-the-art commercial HEMT amplifier. This implies a performance near the standard quantum limit.

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Experimental results are reported on a Josephson parametric upconverting amplifier which is self-pumped via the internal Josephson oscillations derived from a dc bias voltage. A niobium point-contact SQUID is simultaneously coupled to a 115-MHz tank circuit and a 9-GHz cavity. Josephson oscillations at 9 GHz produce parametric upconversion of power in the 115-MHz circuit to sidebands at 9±0.115 GHz with measured power gain of 25. The amplifier noise temperature, referred to the input at 115 MHz, was established to be <15 K by varying the temperature of an input termination from 4.2 to 300 K. This result establishes the behavior of self-pumped SQUID upconverters at microwave frequencies and demonstrates that the achievable noise performance is not greatly in excess of the thermal limit.

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The high-frequency amplification properties of transformer coupled, resistively shunted Josephson tunnel junctions have been investigated. The importance of the shunt loop inductance is stressed. It allows a high cutoff frequency, of significance for good high-frequency performance. The self-pumped parametric amplifier showed none of the excessive noise rise, which has hitherto plagued the development of externally pumped Josephson junction amplifiers. Around 10 GHz, we estimated a noise temperature less than 30 K for an amplifier pumped by a Josephson oscillation with a frequency well above twice the signal frequency. The corresponding gain of 5 dB may be increased in a better impedance matched circuit. The gain was very stable against variations in the bias conditions. A gain-bandwidth product as high as 0.3 was registered. The experimental results agreed well with the established theory for self-pumped parametric Josephson amplifiers. It should be possible to extend the low noise amplification by this device to mm wave frequencies. A relaxation oscillation occurred at a subharmonic of the Josephson frequency when the shunt loop inductance became large. The amplification in this mode followed closely the predictions of a simple model, where the signal modulated the switching of the sawtooth-like (relatively low frequency) relaxation current. Gains of about 15 dB were measured around 10 GHz, but the amplification was sensitive to bias conditions and noisy in this case where the relaxation frequency fell well below the signal frequency. Much improved properties were registered when the inductance was decreased so that the relaxation frequency approached the Josephson frequency and exceeded twice the signal frequency. The behavior then resembled that of a Josephson mode parametric amplifier, but the high content of harmonics of a relaxation oscillation meant that the amplifier became noisier due to converted noise from the many idler frequencies.

Journal of Applied Physics•Jul 1, 1982•26 citations
Low-noise amplifiers are of great significance in the field of quantum technologies. We study a thermally driven parametric amplifier based on a superconductor-insulator-graphene-insulator-superconductor (SSS-III-GGG-III-SSS) junction coupled to a superconducting microwave cavity. The strong nonlinearity in the temperature dependence of our device leads to thermal self-modulation that produces impedance oscillations at frequencies around twice the angular cavity resonance frequency \ensuremathωr{\ensuremath{\omega}}_{\mathrm{r}}\ensuremathωr​. In particular, reactance modulation of the effective capacitance yields a gain of 18.6 dB over a frequency span of 125 kHz with a minimum noise temperature of TN=1.4K{T}_{\mathrm{N}}=1.4\phantom{\rule{0.2em}{0ex}}\mathrm{K}TN​=1.4K. Our theoretical modeling gives insight into the exact mixing processes, confirmation of the electron-phonon coupling parameter and possible improvements of the studied system.
Low-noise amplifiers are of great importance in the field of quantum technologies. We study a thermally driven parametric amplifier based on a superconductor-insulator-graphene-insulator-superconductor (SIGIS) junction coupled to a superconducting microwave cavity. The strong non-linearity in the temperature dependence of our device leads to thermal self-modulation that produces impedance oscillations at frequencies around twice the angular cavity resonance frequency ωrω_\mathrm{r}ωr​. In particular, reactance modulation of the effective capacitance yields a gain of 18.6 dB over a frequency span of 125 kHz with a minimum noise temperature of TN=1.4T_\mathrm{N} = 1.4TN​=1.4 K. Our theoretical modelling gives insight into the exact mixing processes, confirmation of the electron-phonon coupling parameter and possible improvements of the studied system.
We report the lowest noise temperature of any microwave amplifier except the maser. This amplifier is a nearly degenerate superconducting parametric amplifier at X-band consisting of a low β, thin film, single junction SQUID, a monolithic 50 Ω to 1 Ω impedance matching network, and a cooled circulator. Nb/Nb2O5/Pb alloy junctions were incorporated into Nb and Pb-in circuitry on 1×2 cm silicon chips. The SQUID was phase-biased near 90° and driven by an external pump at approximately twice the operating frequency. The self-resonance frequency of the SQUID inductance and junction capacitance was set at the operating frequency of 8.2GHz. The operating charac teristics depended on the pump amplitude, the junction phase bias, and the SQUID parameters. For small values of\beta < 1, the maximum gain in both the signal and idler channels was ≈10dB, the bandwidth = 170MHz, and the single-sidehand noise temperature was 6K with an uncertainty of (+15 to -7)K. For higher β, the gain increased to nearly 30dB with increased noise and parametric oscillations occurring near the pump subharmonic frequency.
With a large portfolio of elemental quantum components, superconducting quantum circuits have contributed to dramatic advances in microwave quantum optics. Of these elements, quantum-limited parametric amplifiers have proven to be essential for low noise readout of quantum systems whose energy range is intrinsically low (tens of µeV). They are also used to generate non classical states of light that can be a resource for quantum enhanced detection. Superconducting parametric amplifiers, like quantum bits, typically utilize a Josephson junction as a source of magnetically tunable and dissipation-free nonlinearity. The magnetic control is not an industry standard for devices and starts already to be an issue in large scale circuits. In recent years, efforts have been made to introduce semiconductor weak links as electrically tunable nonlinear elements, with demonstrations of microwave resonators and quantum bits using semiconductor nanowires, a two dimensional electron gas, carbon nanotubes and graphene. However, given the challenge of balancing nonlinearity, dissipation, participation, and energy scale, parametric amplifiers have not yet been implemented with a semiconductor weak link. The work presented in this PhD thesis demonstrates the design, fabrication and performances of a parametric amplifier leveraging a graphene Josephson junction.The graphene is encapsulated in between hBN flakes in order to improve its quality. Using such high quality junctions, we demonstrate amplification with 20 dB gain which is the milestone for overcoming noise of the classical amplifiers in the rest of the amplification chain. The Josephson parametric amplifier being based on a resonant structure (around 6 GHz) suffers from the gain bandwidth product limiting the amplification to a few MegaHertz frequency range. The use of a side gate to electrically tune the graphene gives control of the Josephson junction inductance and thus the resonant frequency of the amplifier. We demonstrate a near 1 GHz tunability of the amplification frequency with the use of a side gate which is as good as the tunability offered by using a magnetic flux on a SQUID for similar amplifier designs. Moreover, graphene has shown to exhibit nonlinear loss under a strong microwave irradiation arising because of dynamics in the Andreev states. Dissipation is known to add intrinsic noise on quantum amplifiers and could be a problem for quantum limited parametric amplification. We demonstrate that despite the presence of nonlinear loss, graphene based Josephson parametric amplifiers can reach near quantum limited amplification. A two photon loss model was used to describe the behaviour of the device but we show that a more complex model is required in order to take into account the nonlinear dissipation and the non-sinusoidal current phase relation. We also studied the dynamic range and showed that the graphene based Josephson parametric amplifier can reach a 1 dB compression point of -123 dBm which is as good as single tunnel junctions based parametric amplifiers. Our results expand the toolset for electrically tunable superconducting quantum circuits and offer new opportunities for the development of quantum technologies such as quantum computing, quantum sensing and fundamental science.
In this Master thesis, I present a theoretical description and experimental measurements of a tunable microwave resonator operated as a parametric amplifier. Superconducting parametric amplifiers have attracted great interest in recent years as it has been demonstrated that they can operate with a noise performance at the standard quantum limit. \nParametric amplification is achieved in the devices by modulating the electrical length of the resonator at twice the resonance frequency. The device measured in this thesis consists of a quarter-wavelength microwave resonator fabricated in a thin-film aluminum coplanar waveguide geometry. With a termination to ground through a Superconducting Quantum Interference Device (SQUID), the boundary condition of the resonator becomes sensitive to an applied magnetic field. This enables the tuning of the resonance frequencies, using a DC magnetic field, over a wide frequency range of 670MHz. Similarly, an AC magnetic field then allows for the modulation of the resonator electrical length at microwave frequencies. \nWe characterized the device by first measuring the DC tuning curves of the 2nd and 3rd harmonics of the resonator, around 4 GHz and 6 GHz respectively. We then studied parametric amplification in the device when the electrical length was modulated at approximately twice the resonance frequency of one of the modes. We scanned the pump frequency and pump power over a wide range to study the region in parameters which gives parametric gain. We performed an in-depth parameter sweep over this region, identifying pump parameters that provided maximum gain and maximum system noise improvements compared the following HEMT amplifier. \nWe find that the use of the parametric amplifier can improve the system noise temperature by more than 10 dB compared to a start-of-the-art commercial HEMT amplifier. This implies a performance near the standard quantum limit.
Experimental results are reported on a Josephson parametric upconverting amplifier which is self-pumped via the internal Josephson oscillations derived from a dc bias voltage. A niobium point-contact SQUID is simultaneously coupled to a 115-MHz tank circuit and a 9-GHz cavity. Josephson oscillations at 9 GHz produce parametric upconversion of power in the 115-MHz circuit to sidebands at 9±0.115 GHz with measured power gain of 25. The amplifier noise temperature, referred to the input at 115 MHz, was established to be <15 K by varying the temperature of an input termination from 4.2 to 300 K. This result establishes the behavior of self-pumped SQUID upconverters at microwave frequencies and demonstrates that the achievable noise performance is not greatly in excess of the thermal limit.
The high-frequency amplification properties of transformer coupled, resistively shunted Josephson tunnel junctions have been investigated. The importance of the shunt loop inductance is stressed. It allows a high cutoff frequency, of significance for good high-frequency performance. The self-pumped parametric amplifier showed none of the excessive noise rise, which has hitherto plagued the development of externally pumped Josephson junction amplifiers. Around 10 GHz, we estimated a noise temperature less than 30 K for an amplifier pumped by a Josephson oscillation with a frequency well above twice the signal frequency. The corresponding gain of 5 dB may be increased in a better impedance matched circuit. The gain was very stable against variations in the bias conditions. A gain-bandwidth product as high as 0.3 was registered. The experimental results agreed well with the established theory for self-pumped parametric Josephson amplifiers. It should be possible to extend the low noise amplification by this device to mm wave frequencies. A relaxation oscillation occurred at a subharmonic of the Josephson frequency when the shunt loop inductance became large. The amplification in this mode followed closely the predictions of a simple model, where the signal modulated the switching of the sawtooth-like (relatively low frequency) relaxation current. Gains of about 15 dB were measured around 10 GHz, but the amplification was sensitive to bias conditions and noisy in this case where the relaxation frequency fell well below the signal frequency. Much improved properties were registered when the inductance was decreased so that the relaxation frequency approached the Josephson frequency and exceeded twice the signal frequency. The behavior then resembled that of a Josephson mode parametric amplifier, but the high content of harmonics of a relaxation oscillation meant that the amplifier became noisier due to converted noise from the many idler frequencies.