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IEEE Toronto International Conference Science and Technology for Humanity

Small and large signal analyses of Josephson nonlinear inductance for superconductive parametric amplifier

Hamid Reza Mohebbi, A. Hamed Majedi

Published Sep 1, 2009• 1 citation
Publisher

Abstract

Due to the inherent nonlinearity in the Josephson junction (JJ) element, there is great potential to develop nonlinear parametric devices, such as amplifiers and mixers. In this paper, we investigate the time domain small-signal and large-signal analysis on the nonlinear flux-current characteristics of an array of lumped JJs. The procedure is similar to that applied on the nonlinear current-voltage characteristics of a semiconductor p-n junction diode, and results are presented in closed-form equations. The gain improvement due to parametric interaction of the pump with the signal is also discussed at the end of the paper.

DOI
10.1109/tic-sth.2009.5444531

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Due to the inherent nonlinearity in the Josephson junction (JJ) element, there is great potential to develop nonlinear parametric devices, such as amplifiers and mixers. In this paper, we investigate the time domain small-signal and large-signal analysis on the nonlinear flux-current characteristics of an array of lumped JJs. The procedure is similar to that applied on the nonlinear current-voltage characteristics of a semiconductor p-n junction diode, and results are presented in closed-form equations. The gain improvement due to parametric interaction of the pump with the signal is also discussed at the end of the paper.
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Superconducting parametric amplifiers have great promise for quantum-limited readout of superconducting qubits and detectors. Until recently, most superconducting parametric amplifiers had been based on resonant structures, limiting their bandwidth and dynamic range. Broadband traveling-wave parametric amplifiers based both on the nonlinear kinetic inductance of superconducting thin films and on Josephson junctions are in development. By modifying the dispersion property of the amplifier circuit, referred to as dispersion engineering, the gain can be greatly enhanced and the size can be reduced. We present two theoretical frameworks for analyzing and understanding such parametric amplifiers: 1) generalized coupled-mode equations and 2) a finite difference time domain (FDTD) model combined with a small signal analysis. We show how these analytical and numerical tools may be used to understand device performance.
We have developed and measured a high-gain quantum-limited microwave parametric amplifier based on a superconducting lumped LC resonator with the inductor L including an array of eight superconducting quantum interference devices (SQUIDs). This amplifier is parametrically pumped by modulating the flux threading the SQUIDs at twice the resonator frequency. Around 5 GHz, a maximum gain of 31 dB, a product amplitude gain $\ifmmode\times\else\texttimes\fi{}$ bandwidth above 60 MHz, and a 1 dB compression point of $\ensuremath{-}123$ dBm at 20 dB gain are obtained in the nondegenerate mode of operation. Phase-sensitive amplification-deamplification is also measured in the degenerate mode and yields a maximum gain of 37 dB. The compression point obtained is 18 dB above what would be obtained with a single SQUID of the same inductance, due to the smaller nonlinearity of the SQUID array.
An analysis is presented describing four-photon parametric amplification in an unbiased Josephson junction. Central to the theory is the model of the Josephson effect as a nonlinear inductance. Linear, small signal analysis is applied to the « two fluid » model of the Josephson junction. The gain, gain-bandwidth product, high frequency limit and effective noise temperature is calculated for a cavity reflection amplifier. The analysis is extended to multiple (series-connected) junctions and sub-harmonic pumping.
Josephson parametric amplification is a tool of paramount importance in circuit-QED especially for the quantum-noise-limited single-shot read-out of superconducting qubits. We developed a Josephson parametric amplifier (JPA) based on a lumped-element LC resonator, in which the inductance L is composed by a geometric inductance and an array of 4 superconducting quantum interference devices (SQUIDs). We characterized the main figures of merit of the device, obtaining a −3 dB bandwidth BW = 15 MHz for a gain G = 21 dB and a 1 dB compression point P1dB = −115 dBm. The obtained results are promising for the future use of such JPA as the first stage of amplification for single-shot readout of superconducting qubits.
Nearly quantum limited Josephson parametric amplifiers (JPAs) are essential components in superconducting quantum circuits. However, higher order nonlinearities of the Josephson cosine potential are known to cause gain compression, therefore limiting scalability. In an effort to reduce the fourth order, or Kerr nonlinearity, we realize a parametric amplifier with an Al-InAs superconductor–semiconductor hybrid Josephson junction (JJ). We extract the Kerr nonlinearity of the Al-InAs JJ from two different devices and show that it is three orders of magnitude lower compared to an Al-AlOX junction with identical Josephson inductance. We then demonstrate a four-wave-mixing (4WM) parametric amplifier made with an Al-InAs junction that achieves more than 20 dB of gain and −119 dBm of compression power, which outperforms single resonant JPAs based on Al junctions.