Full Counting Statistics of Cooper Pair Shuttling

TL;DR

This paper analyzes the full counting statistics of charge transfer in a Cooper pair shuttle, revealing that superconducting coherence persists even in incoherent regimes and challenging classical interpretations of charge transfer probabilities.

Contribution

It provides a detailed evaluation of the full counting statistics in the incoherent regime, highlighting the persistence of superconducting coherence.

Findings

Classical interpretation of FCS sometimes fails, showing negative and imaginary probabilities.

Superconducting coherence survives even in incoherent transport regimes.

Detailed analysis of current noise in the system.

Abstract

The Cooper pair shuttle is a simple model system that combines features of coherent and incoherent transport. We evaluate the full counting statistics (FCS) of charge transfer via the shuttle in the incoherent regime. We describe two limiting cases when the FCS allows for classical interpretation. Generally, the classical interpretation fails yielding negative and imaginary "probabilities". This signals that superconducting coherence survives even in incoherent regime. We evaluate the current noise in some detail.