# Full counting statistics of quantum phase slips

## TL;DR

This paper develops a microscopic theory for the full statistical distribution of voltage fluctuations caused by quantum phase slips in superconducting nanowires, revealing unique frequency-dependent behaviors.

## Contribution

It provides the first complete calculation of voltage fluctuation statistics, including higher cumulants, and links these to the nanowire's current-voltage characteristics.

## Key findings

- Voltage fluctuations follow Poisson statistics at zero frequency.
- Higher voltage cumulants are non-zero only due to quantum phase slips.
- Finite-frequency cumulants are explicitly calculated for short nanowires.

## Abstract

We work out a microscopic theory describing complete statistics of voltage fluctuations generated by quantum phase slips (QPS) in superconducting nanowires. We evaluate the cumulant generating function and demonstrate that shot noise of the voltage as well as the third and all higher voltage cumulants differ from zero only due to the presence of QPS. In the zero-frequency limit voltage fluctuations in superconducting nanowires are described by Poisson statistics just as in a number of other tunneling-like problems. However, at non-zero frequencies quantum voltage fluctuations in superconducting nanowires become much more complicated and are not anymore accounted for by Poisson statistics. In the case of short superconducting nanowires we explicitly evaluate all finite-frequency voltage cumulants and establish a non-trivial relation between these cumulants and the current-voltage characteristics of our system.