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Applied Physics Letters

Nonlinear response of a superconducting filter: To compress or not to compress

M. I. Salkola

Published May 11, 2005• 4 citations
Publisher

Abstract

Nonlinearities in passive superconducting filters give rise to gain and intermodulation distortions that can diminish their ability to attenuate large interfering signals. It is shown that the departure from gain linearity depends on the phase of a nonlinear interaction. If the nonlinear interaction arises from the kinetic inductance of a superconducting state, the signal frequency determines whether the superconducting filter exhibits gain expansion or compression. The absence of gain expansion is a signature of the nonlinear interaction that is mainly resistive.

DOI
10.1063/1.1931053

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Nonlinearities in passive superconducting filters give rise to gain and intermodulation distortions that can diminish their ability to attenuate large interfering signals. It is shown that the departure from gain linearity depends on the phase of a nonlinear interaction. If the nonlinear interaction arises from the kinetic inductance of a superconducting state, the signal frequency determines whether the superconducting filter exhibits gain expansion or compression. The absence of gain expansion is a signature of the nonlinear interaction that is mainly resistive.
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.
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.
The penetration depth and surface resistance of a superconductor depend upon the superfluid current density. This dependence gives rise to nonlinear mixing in a superconducting microstrip resonator. Here we discuss the problem of intermodulation in which two signals at ω1 and ω2, laying within the pass band of a microstrip cavity resonance, mix and generate a signal at 2ω1−ω2. An expression relating the power generated at 2ω1−ω2 to the power transmitted at ω1 and ω2 is given. We focus on the high-Tc superconductors where it is believed that the order parameter has dx2−y2 symmetry. We find for a resonator with a large unloaded Q that intermodulation arises dominantly from the reactive nonlinear inductance of the superconducting film.
The authors evaluate the frequency dependence of the nonlinear response in high-temperature superconductor YBa2Cu3O7−x thin films by simultaneously measuring the nonlinear intermodulation products and harmonic generation in broadband superconducting transmission lines at 76K. The frequencies of the two-tone incident signal are set to produce spurious signals from 1to21GHz. They extract a nonlinear term ∣ΔR2+jωΔL2∣ by applying a model of spurious signal generation in superconducting transmission lines to their measurement results. They found that this nonlinear term follows a linear dependence on frequency, indicating a dominant contribution of the nonlinear inductance ΔL2 over the nonlinear resistance ΔR2, (ωΔL2⪢ΔR2), for the superconducting nonlinear response.
At the resonant frequency, superconducting resonators produce intermodulation distortion (IMD), smaller unwanted signals near the resonant frequency. These signals are a measure of the ratio between fundamental frequencies and distortion products. By inducing external microwave signals, it is possible to analyse the patterns of IMD in several different types of superconducting resonators. These measurements can be used to complement the main peak values like quality factor and frequency shift in order to understand nonlinearities present in the material of the superconductor. Once IMD measurements are taken, they were combined into a 2-dimensional raster image of the resonator chip.