Diverging current fluctuations in critical Kerr resonators

TL;DR

This paper investigates how current fluctuations behave near critical points in Kerr resonators, revealing exponential divergence at discontinuous transitions and differing behaviors in measurement schemes, with new formulas linking quantum dynamics to fluctuations.

Contribution

It introduces formulas to compute diffusion coefficients from quantum master equations, connecting full counting statistics and stochastic trajectories in analyzing current fluctuations.

Findings

Current fluctuations diverge exponentially at discontinuous phase transitions.

Different measurement schemes reveal contrasting fluctuation behaviors near continuous transitions.

New computational methods link quantum master equations to long-time current fluctuation analysis.

Abstract

The parametrically pumped Kerr model describes a driven-dissipative nonlinear cavity, whose nonequilibrium phase diagram features both continuous and discontinuous quantum phase transitions. We consider the consequences of these critical phenomena for the fluctuations of the photocurrent obtained via continuous weak measurements on the cavity. Considering both direct photodetection and homodyne detection schemes, we find that the current fluctuations diverge exponentially at the discontinuous phase transition. However, we find strikingly different current fluctuations for these two detection schemes near the continuous transition, a behaviour which is explained by the complementary information revealed by measurements in different bases. To obtain these results, we develop formulas to efficiently compute the diffusion coefficient -- which characterises the long-time current fluctuations -- directly from the quantum master equation, thus connecting the formalisms of full counting statistics and stochastic quantum trajectories. Our findings highlight the rich features of current fluctuations near nonequilibrium phase transitions in quantum-optical systems.