Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

EPJ Quantum Technology

Gain, noise and intermodulation in a nonlinear superconducting resonator

Erik A. Tholén, Adem Ergül, David J. Schaeffer, David B. Haviland

Published Mar 7, 2014• 7 citations
Publisher

Abstract

A superconducting microwave resonator is modified with several weak links to make it nonlinear and operated as a phase-insensitive microwave amplifier. Signal gain is demonstrated by intermodulation with a strong pump. The gain is sharply frequency dependent, and we demonstrate phase dependence by examining correlations between the signal and one idler which is a 3rd order intermodulation product of the pump and signal tones. A calibration procedure is described which is based on measurement of both thermal and quantum noise, revealing that the following HEMT amplifier adds noise at 15 times the quantum limit. When operated as a phase-insensitive amplifier the nonlinear resonator added noise at 2.5 times the quantum limit. Significant power is found at intermodulation products beyond 3rd order, which may be responsible for the inability to reach the quantum limit. PACS Codes: 74.78.-w, 42.65.Yj, 85.25.Cp.

DOI
10.1140/epjqt5

Related papers

Intermodulation gain in nonlinear NbN superconducting microwave resonators

Baleegh Abdo, Eran Segev, Oleg Shtempluck +1 more

We report the measurement of intermodulation gain greater than unity in NbN superconducting stripline resonators. In the intermodulation measurements we inject two unequal tones into the oscillator—the pump and signal—both lying within the resonance band. At the onset of instability of the reflected pump we obtain a simultaneous gain of both the idler and the reflected signal. The measured gain in both cases can be as high as 15dB.

arXiv:cond-mat/0507056•Applied Physics Letters•Jan 9, 2006•23 citations

A Wideband, Low-Noise Superconducting Amplifier with High Dynamic Range

Byeong Ho Eom, Peter K. Day, Henry George LeDuc +1 more

Amplifiers are ubiquitous in electronics and play a fundamental role in a wide range of scientific measurements. From a user's perspective, an ideal amplifier has very low noise, operates over a broad frequency range, and has a high dynamic range - it is capable of handling strong signals with little distortion. Unfortunately, it is difficult to obtain all of these characteristics simultaneously. For example, modern transistor amplifiers offer multi-octave bandwidths and excellent dynamic range. However, their noise remains far above the fundamental limit set by the uncertainty principle of quantum mechanics. Parametric amplifiers, which predate transistor amplifiers and are widely used in optics, exploit a nonlinear response to transfer power from a strong pump tone to a weak signal. If the nonlinearity is purely reactive, ie. nondissipative, in theory the amplifier noise can reach the quantum-mechanical limit. Indeed, microwave frequency superconducting Josephson parametric amplifiers do approach the quantum limit, but generally are narrow band and have very limited dynamic range. In this paper, we describe a superconducting parametric amplifier that overcomes these limitations. The amplifier is very simple, consisting only of a patterned metal film on a dielectric substrate, and relies on the nonlinear kinetic inductance of a superconducting transmission line. We measure gain extending over 2 GHz on either side of an 11.56 GHz pump tone, and we place an upper limit on the added noise of the amplifier of 3.4 photons at 9.4 GHz. Furthermore, the dynamic range is very large, comparable to microwave transistor amplifiers, and the concept can be applied throughout the microwave, millimeter-wave and submillimeter-wave bands.

arXiv:1201.2392•Jan 1, 2012•0 citations

Parametric amplification with weak-link nonlinearity in superconducting microresonators

Erik A. Tholén, Adem Ergül, Kai Stannigel +2 more

Nonlinear kinetic inductance in a high Q superconducting coplanar waveguide microresonator can cause a bifurcation of the resonance curve. Near the critical pumping power and frequency for bifurcation, large parametric gain is observed for signals in the frequency band near resonance. We show experimental results on signal and intermodulation gain which are well described by a theory of parametric amplification based on a Kerr nonlinearity. Phase-dependent gain or signal squeezing is verified with a homodyne detection scheme.

arXiv:0906.2744•Physica Scripta•Dec 1, 2009•28 citations

Intermodulation measurements in Nb superconducting microstrip resonators

R. Monaco, A. Andreone, F. Palomba

The issue of intermodulation distortion in superconducting devices for rf and microwave applications is discussed. The classical frequency conversion theory for nonlinear two-port devices in the small signal limit is shown to apply to microstrip resonators regardless of their geometry and material. Two tone, third order intermodulation measurements allow more sensitive detection of nonlinearity compared to surface impedance measurements, provided a low noise, spurious free experimental setup is adopted. Measurements carried out on high quality Nb meanderline microstrip resonators show that at very low power level nonlinearity is dominated by intrinsic device properties. Film defects start to play a predominant role above a critical power level that strongly depends on the defect’s nature.

Journal of Applied Physics•Sep 1, 2000•23 citations

Parametric Microwave Amplification using a Tunable Superconducting Resonator

C. W. Sandbo Chang

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.

•Sep 2, 2015•0 citations

Intermodulation in nonlinear SQUID metamaterials: Experiment and theory

Daimeng Zhang, Melissa Trepanier, Thomas M. Antonsen +2 more

The response of nonlinear metamaterials and superconducting electronics to two-tone excitation is critical for understanding their use as low-noise amplifiers and tunable filters. A new setting for such studies is that of metamaterials made of radio frequency superconducting quantum interference devices (rf-SQUIDs). The two-tone response of self-resonant rf-SQUID meta-atoms and metamaterials is studied here via intermodulation (IM) measurement over a broad range of tone frequencies and tone powers. A sharp onset followed by a surprising strongly suppressed IM region near the resonance is observed. Using a two time scale analysis technique, we present an analytical theory that successfully explains our experimental observations. The theory predicts that the IM can be manipulated with tone power, center frequency, frequency difference between the two tones, and temperature. This quantitative understanding potentially allows for the design of rf-SQUID metamaterials with either very low or very high IM response.

arXiv:1606.09234•Physical review. B./Physical review. B•Nov 16, 2016•15 citations
A superconducting microwave resonator is modified with several weak links to make it nonlinear and operated as a phase-insensitive microwave amplifier. Signal gain is demonstrated by intermodulation with a strong pump. The gain is sharply frequency dependent, and we demonstrate phase dependence by examining correlations between the signal and one idler which is a 3rd order intermodulation product of the pump and signal tones. A calibration procedure is described which is based on measurement of both thermal and quantum noise, revealing that the following HEMT amplifier adds noise at 15 times the quantum limit. When operated as a phase-insensitive amplifier the nonlinear resonator added noise at 2.5 times the quantum limit. Significant power is found at intermodulation products beyond 3rd order, which may be responsible for the inability to reach the quantum limit. PACS Codes: 74.78.-w, 42.65.Yj, 85.25.Cp.
Amplifiers are ubiquitous in electronics and play a fundamental role in a wide range of scientific measurements. From a user's perspective, an ideal amplifier has very low noise, operates over a broad frequency range, and has a high dynamic range - it is capable of handling strong signals with little distortion. Unfortunately, it is difficult to obtain all of these characteristics simultaneously. For example, modern transistor amplifiers offer multi-octave bandwidths and excellent dynamic range. However, their noise remains far above the fundamental limit set by the uncertainty principle of quantum mechanics. Parametric amplifiers, which predate transistor amplifiers and are widely used in optics, exploit a nonlinear response to transfer power from a strong pump tone to a weak signal. If the nonlinearity is purely reactive, ie. nondissipative, in theory the amplifier noise can reach the quantum-mechanical limit. Indeed, microwave frequency superconducting Josephson parametric amplifiers do approach the quantum limit, but generally are narrow band and have very limited dynamic range. In this paper, we describe a superconducting parametric amplifier that overcomes these limitations. The amplifier is very simple, consisting only of a patterned metal film on a dielectric substrate, and relies on the nonlinear kinetic inductance of a superconducting transmission line. We measure gain extending over 2 GHz on either side of an 11.56 GHz pump tone, and we place an upper limit on the added noise of the amplifier of 3.4 photons at 9.4 GHz. Furthermore, the dynamic range is very large, comparable to microwave transistor amplifiers, and the concept can be applied throughout the microwave, millimeter-wave and submillimeter-wave bands.
Nonlinear kinetic inductance in a high Q superconducting coplanar waveguide microresonator can cause a bifurcation of the resonance curve. Near the critical pumping power and frequency for bifurcation, large parametric gain is observed for signals in the frequency band near resonance. We show experimental results on signal and intermodulation gain which are well described by a theory of parametric amplification based on a Kerr nonlinearity. Phase-dependent gain or signal squeezing is verified with a homodyne detection scheme.
The issue of intermodulation distortion in superconducting devices for rf and microwave applications is discussed. The classical frequency conversion theory for nonlinear two-port devices in the small signal limit is shown to apply to microstrip resonators regardless of their geometry and material. Two tone, third order intermodulation measurements allow more sensitive detection of nonlinearity compared to surface impedance measurements, provided a low noise, spurious free experimental setup is adopted. Measurements carried out on high quality Nb meanderline microstrip resonators show that at very low power level nonlinearity is dominated by intrinsic device properties. Film defects start to play a predominant role above a critical power level that strongly depends on the defect’s nature.
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.
The response of nonlinear metamaterials and superconducting electronics to two-tone excitation is critical for understanding their use as low-noise amplifiers and tunable filters. A new setting for such studies is that of metamaterials made of radio frequency superconducting quantum interference devices (rf-SQUIDs). The two-tone response of self-resonant rf-SQUID meta-atoms and metamaterials is studied here via intermodulation (IM) measurement over a broad range of tone frequencies and tone powers. A sharp onset followed by a surprising strongly suppressed IM region near the resonance is observed. Using a two time scale analysis technique, we present an analytical theory that successfully explains our experimental observations. The theory predicts that the IM can be manipulated with tone power, center frequency, frequency difference between the two tones, and temperature. This quantitative understanding potentially allows for the design of rf-SQUID metamaterials with either very low or very high IM response.