Charge noise at Cooper-pair resonances

TL;DR

This paper investigates charge noise in a superconducting single-electron transistor at Cooper-pair resonances, revealing characteristic spectral features and implications for coupled oscillator measurements.

Contribution

It introduces an approximate Hamiltonian model and master equation to analyze charge noise spectra, highlighting the structure of noise peaks at resonances.

Findings

Charge noise spectrum shows asymmetric triplet peaks.

Sharp current peaks occur at Cooper-pair resonances.

Charge noise can be probed via coupled oscillator measurements.

Abstract

We analyze the charge dynamics of a superconducting single-electron transistor (SSET) in the regime where charge transport occurs via Cooper-pair resonances. Using an approximate description of the system Hamiltonian, in terms of a series of resonant doublets, we derive a Born-Markov master equation describing the dynamics of the SSET. The average current displays sharp peaks at the Cooper-pair resonances and we find that the charge noise spectrum has a characteristic structure which consists of a series of asymmetric triplets of peaks. The strongest feature in the charge noise spectrum is the triplet of peaks centered at zero frequency which has a peak spacing equal to the level separation within the doublets and is similar to the triplet in the spectrum of a driven, damped, two-level system. We also explore the back-action that the SSET charge noise would have on an oscillator coupled to the island charge, measurement of which provides a way of probing the charge noise spectrum.