Current noise of a superconducting single electron transistor coupled to a resonator

TL;DR

This paper investigates the current and noise characteristics of a superconducting single electron transistor coupled to a resonator, revealing how resonator dynamics influence current noise and can indicate different operational regimes.

Contribution

It provides a detailed analysis of how resonator coupling affects current noise and identifies signatures of dynamical transitions and bistability in the system.

Findings

Current noise is sensitive to resonator-charge correlations.

Strong coupling induces limit cycle oscillations and bistability.

Resonator energy fluctuations impact the SSET current noise.

Abstract

We analyze the current and zero-frequency current noise properties of a superconducting single electron resonator (SSET) coupled to a resonator, focusing on the regime where the SSET is operated in the vicinity of the Josephson quasiparticle resonance. We consider a range of coupling strengths and resonator frequencies to reflect the fact that in practice the system can be tuned to quite a high degree with the resonator formed either by a nanomechanical oscillator or a superconducting stripline fabricated in close proximity to the SSET. For very weak couplings the SSET acts on the resonator like an effective thermal bath. In this regime the current characteristics of the SSET are only weakly modified by the resonator. Using a mean field approach, we show that the current noise is nevertheless very sensitive to the correlations between the resonator and the SSET charge. For stronger couplings, the SSET can drive the resonator into limit cycle states where self-sustained oscillation occurs and we find that regions of well-defined bistability exist. Dynamical transitions into and out of the limit cycle state are marked by strong fluctuations in the resonator energy, but these fluctuations are suppressed within the limit cycle state. We find that the current noise of the SSET is strongly influenced by the fluctuations in the resonator energy and hence should provide a useful indicator of the resonator's dynamics.