Frequency Combs in a Lumped-Element Josephson-Junction Circuit

TL;DR

This paper explores the dynamics of a driven Josephson junction coupled to an LC oscillator, revealing regimes of bistability and self-oscillations with frequency combs, and examines how quantum fluctuations affect these phenomena.

Contribution

It characterizes the full phase diagram of the system, identifying a novel frequency comb generation mechanism and analyzing quantum fluctuation effects on comb stability.

Findings

Identification of a regime with frequency combs in the spectrum.

Quantum fluctuations cause dephasing and broadening of spectral peaks.

Mechanism of comb generation differs from microcavity and laser systems.

Abstract

We investigate the dynamics of a microwave-driven Josephson junction capacitively coupled to a lumped element LC oscillator. In the regime of driving where the Josephson junction can be approximated as a Kerr oscillator, this minimal nonlinear system has been previously shown to exhibit a bistability in phase and amplitude. In the present study, we characterize the full phase diagram and show that besides a parameter regime exhibiting bistability, there is also a regime of self-oscillations characterized by a frequency comb in its spectrum. We discuss the mechanism of comb generation which appears to be different from those studied in microcavity frequency combs and mode-locked lasers. We then address the fate of the comb-like spectrum in the regime of strong quantum fluctuations, reached when nonlinearity becomes the dominant scale with respect to dissipation. We find that the nonlinearity responsible for the emergence of the frequency combs also leads to its dephasing, leading to broadening and ultimate disappearance of sharp spectral peaks. Our study explores the fundamental question of the impact of quantum fluctuations for quantum systems which do not possess a stable fixed point in the classical limit.