# Photon waiting time distributions: a keyhole into dissipative quantum chaos

## TL;DR

This paper investigates how photon waiting time distributions can reveal chaotic versus regular behavior in a driven Kerr-nonlinear cavity, providing a non-invasive method to identify quantum chaos through photon emission statistics.

## Contribution

It introduces a novel approach to distinguish chaotic and regular regimes in open quantum systems using photon waiting time distributions and quantum Lyapunov exponents.

## Key findings

- Chaotic regimes show power-law asymptotics in photon waiting times.
- Photon emission monitoring can differentiate chaotic and regular states.
- Method enables non-invasive chaos detection in quantum optical systems.

## Abstract

Open quantum systems can exhibit complex states, which classification and quantification is still not well resolved. The Kerr-nonlinear cavity, periodically modulated in time by coherent pumping of the intra-cavity photonic mode, is one of the examples. Unraveling the corresponding Markovian master equation into an ensemble of quantum trajectories and employing the recently proposed calculation of quantum Lyapunov exponents [I.I. Yusipov {\it et al.}, Chaos {\bf 29}, 063130 (2019)], we identify `chaotic' and `regular' regimes there. In particular, we show that chaotic regimes manifest an intermediate power-law asymptotics in the distribution of photon waiting times. This distribution can be retrieved by monitoring photon emission with a single-photon detector, so that chaotic and regular states can be discriminated without disturbing the intra-cavity dynamics.