Phase diffusion and noise temperature of a microwave amplifier based on single unshunted Josephson junction

TL;DR

This paper develops a response theory for a microwave amplifier based on a Josephson junction, analyzing its noise and gain characteristics considering nonlinear dynamics and colored noise, with implications for quantum technology.

Contribution

It introduces a novel response theory for Josephson junction amplifiers that accounts for colored noise and nonlinear oscillations, enhancing understanding of their performance limits.

Findings

Derived expressions for gain and noise spectrum under colored noise.

Assessed the reliability of numerical simulation methods for nonlinear Langevin equations.

Identified potential errors in simulations affecting peak performance predictions.

Abstract

High-gain microwave amplifiers operating near quantum limit are crucial for development of quantum technology. However, a systematic theoretical modeling and simulations of their performance represent rather challenging tasks due to the occurrence of colored noises and nonlinearities in the underlying circuits. Here, we develop a response theory for such an amplifier whose circuit dynamics is based on nonlinear oscillations of an unshunted Josephson junction. The theory accounts for a subtle interplay between exponentially damped fluctuations around the stable limit cycle and the nonlinear dynamics of the limit cycle phase. The amplifier gain and noise spectrum are derived assuming a colored voltage noise at the circuit resistor. The derived expressions are generally applicable to any system whose limit cycle dynamics is perturbed by a colored noise and a harmonic signal. We also critically assess reliabilities of numerical methods of simulations of the corresponding nonlinear Langevin equations, where even reliable discretization schemes might introduce errors significantly affecting simulated characteristics at the peak performance.