Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions

TL;DR

This paper derives exact steady-state solutions for a driven-dissipative Kerr resonator with one- and two-photon processes, revealing controllable multimodal Wigner functions and phase transitions across various regimes.

Contribution

It provides an analytical solution for the steady state of a complex Kerr system, enabling exploration of regimes previously inaccessible with semiclassical methods.

Findings

Control of Wigner-function multimodality via driving parameters

Identification of dissipative phase transitions in large photon number limit

Analysis of photon blockade and multiphoton resonances

Abstract

We present exact results for the steady-state density matrix of a general class of driven-dissipative systems consisting of a nonlinear Kerr resonator in the presence of both coherent (one-photon) and parametric (two-photon) driving and dissipation. Thanks to the analytical solution, obtained via the complex P-representation formalism, we are able to explore any regime, including photon blockade, multiphoton resonant effects, and a mesoscopic regime with large photon density and quantum correlations. We show how the interplay between one- and two-photon driving provides a way to control the multimodality of the Wigner function in regimes where the semiclassical theory exhibits multistability. We also study the emergence of dissipative phase transitions in the thermodynamic limit of large photon numbers.