Two coupled nonlinear cavities in a driven-dissipative environment

TL;DR

This paper explores the behavior of two coupled nonlinear cavities under driven-dissipative conditions, revealing how semiclassical symmetry breaking states are affected by quantum fluctuations and providing analytical solutions for steady-state correlations.

Contribution

It offers a comprehensive analysis combining semiclassical, quantum, and analytical methods to understand symmetry breaking and bistability in coupled nonlinear cavities.

Findings

Semiclassical states show symmetry breaking and bistability.

Quantum fluctuations suppress symmetry breaking states.

Analytical steady-state solutions are derived using complex P-representation.

Abstract

We investigate two coupled nonlinear cavities that are coherently driven in a dissipative environment. We perform semiclassical, numerical and analytical quantum studies of this dimer model when both cavities are symmetrically driven. In the semiclassical analysis, we find steady-state solutions with different photon occupations in two cavities. Such states can be considered analogs of the closed system double well symmetry breaking states. We analyze the occurrence and properties of these localized states in the system parameter space and examine how the symmetry breaking states, in form of a bistable pair, are associated to the single cavity bistable behavior. In a full quantum calculation of the master equation dynamics that includes quantum fluctuations, the symmetry breaking states and bistability disappear due to the quantum fluctuations. In quantum trajectory picture, we observe enhanced quantum jumps and switching which indicate the presence of the underlying semiclassical symmetry breaking states. Finally, we present a set of analytical solutions for the steady state correlation functions using the complex P-representation and discuss its regime of validity.