Radiation statistics of a degenerate parametric oscillator at threshold

TL;DR

This paper analyzes the radiation statistics of a degenerate parametric oscillator at threshold, revealing universal scaling laws and ratios of cumulants, with implications for experimental systems.

Contribution

It introduces a universal Liouvillian framework for the long-time dynamics near threshold, highlighting universal power-law scaling of cumulants and a system-independent ratio of the first three cumulants.

Findings

Cumulants obey universal power-law scaling with nonlinearity.

Fano factor peaks near but not at threshold.

First three cumulants ratio is system-independent.

Abstract

As a function of the driving strength, a degenerate parametric oscillator exhibits an instability at which spontaneous oscillations occur. Close to threshold, both the nonlinearity as well as fluctuations are vital to the accurate description of the dynamics. We study the statistics of the radiation that is emitted by the degenerate parametric oscillator at threshold. For a weak nonlinearity, we can employ a quasiclassical description. We identify a universal Liouvillian that captures the relevant long-time dynamics for large photon-numbers. We find that the cumulants obey a universal power-law scaling as a function of the nonlinearity. The Fano factor shows a maximum close, but not coinciding, with the threshold. Moreover, we predict a certain ratio of the first three cumulants to be independent of the microscopic details of the system and connect the results to experimental platforms.