Spectral properties of a resonator driven by a superconducting single-electron transistor

TL;DR

This paper studies how a resonator's spectral features are affected when coupled to a superconducting single-electron transistor near resonance, revealing narrow linewidths and phase diffusion effects similar to laser physics.

Contribution

It provides a detailed analysis of the spectral properties and phase diffusion in a resonator driven by an SSET, highlighting new regimes of phase noise behavior and measurement methods.

Findings

Linewidth becomes very narrow in the limit-cycle regime

Phase diffusion dominates linewidth, influenced by amplitude fluctuations

Current noise can measure linewidth and energy relaxation rate

Abstract

We analyze the spectral properties of a resonator coupled to a superconducting single electron transistor (SSET) close to the Josephson quasiparticle resonance. Focussing on the regime where the resonator is driven into a limit-cycle state by the SSET, we investigate the behavior of the resonator linewidth and the energy relaxation rate which control the widths of the main features in the resonator spectra. We find that the linewidth becomes very narrow in the limit-cycle regime, where it is dominated by a slow phase diffusion process, as in a laser. The overall phase diffusion rate is determined by a combination of direct phase diffusion and the effect of amplitude fluctuations which affect the phase because the resonator frequency is amplitude dependent. For sufficiently strong couplings we find that a regime emerges where the phase diffusion is no longer minimized when the average resonator energy is maximized. Finally we show that the current noise of the SSET provides a way of measuring both the linewidth and energy relaxation rate.