Resonant Cooper-Pair Tunneling: Counting Statistics and Frequency-Dependent Current Noise

TL;DR

This paper investigates the counting statistics and frequency-dependent current noise in a superconducting single electron transistor at the double Josephson quasiparticle resonance, revealing phase-dependent effects and deriving shot noise from counting statistics.

Contribution

It introduces a method to derive full frequency-dependent shot noise from counting statistics in superconducting transistors, addressing phase-dependence issues.

Findings

Counting statistics are generally phase-dependent.

Full frequency-dependent shot noise can be obtained from counting statistics.

Phase-dependence complicates finite-frequency noise analysis.

Abstract

We discuss the counting statistics and current noise associated with the double Josephson quasiparticle resonance point in a superconducting single electron transistor. The counting statistics are in general phase-dependent, despite the fact that the average current has no dependence on phase. Focusing on parameter regimes where the counting statistics have no phase-dependence, we use a general relation first derived by MacDonald in 1948 to obtain the full frequency-dependent shot noise directly from the counting statistics, without any further approximations. We comment on problems posed by the phase-dependence of the counting statistics for the finite-frequency noise.