Photon counting statistics of a microwave cavity

TL;DR

This paper analyzes photon counting statistics in a microwave cavity, revealing how waiting time distributions and factorial cumulants provide insights into quantum processes and heat transport, with implications for quantum technology development.

Contribution

It introduces a novel analysis of photon waiting times and factorial cumulants in microwave cavities, linking quantum bosonic behavior to photon emission statistics and heat transport.

Findings

Waiting time distributions reveal information about few-photon processes.

Factorial cumulants remain positive, indicating bosonic quantum nature.

Derived a fluctuation-dissipation relation for heat noise spectra.

Abstract

The development of microwave photon detectors is paving the way for a wide range of quantum technologies and fundamental discoveries involving single photons. Here, we investigate the photon emission from a microwave cavity and find that distribution of photon waiting times contains information about few-photon processes, which cannot easily be extracted from standard correlation measurements. The factorial cumulants of the photon counting statistics are positive at all times, which may be intimately linked with the bosonic quantum nature of the photons. We obtain a simple expression for the rare fluctuations of the photon current, which is helpful in understanding earlier results on heat transport statistics and measurements of work distributions. Under non-equilibrium conditions, where a small temperature gradient drives a heat current through the cavity, we formulate a fluctuation-dissipation relation for the heat noise spectra. Our work suggests a number of experiments for the near future, and it offers theoretical questions for further investigation.