Statistics of radiation at Josephson parametric resonance

TL;DR

This paper provides a theoretical analysis of the full counting statistics of radiation emitted below the Josephson parametric resonance threshold, revealing photon bunching and correlation properties relevant for experimental detection.

Contribution

It derives a closed-form expression for the full counting statistics in the long measurement time limit, highlighting photon burst behavior and correlation features in Josephson junction circuits.

Findings

Radiation exhibits photon bunching due to uncorrelated bursts of 2N photons.

Derived explicit formulas for burst rates and time correlations.

Identified experimental signatures via frequency-resolved cross-correlations.

Abstract

Motivated by recent experiments, we study theoretically the full counting statistics of radiation emitted below the threshold of parametric resonance in a Josephson junction circuit. In contrast to most optical systems, a significant part of emitted radiation can be collected and converted to an output signal. This permits studying the correlations of the radiation. To quantify the correlations, we derive a closed expression for full counting statistics in the limit of long measurement times. We demonstrate that the statistics can be interpreted in terms of uncorrelated bursts each encompassing 2N photons, this accounts for the bunching of the photon pairs produced in course of the parametric resonance. We present the details of the burst rates. In addition, we study the time correlations within the bursts and discuss experimental signatures of the statistics deriving the frequency-resolved cross-correlations.