Critical dynamical properties of a first-order dissipative phase transition

TL;DR

This paper analyzes the critical properties of a driven-dissipative nonlinear photon mode, revealing a first-order phase transition with an exponentially vanishing Liouvillian gap in the large excitation limit.

Contribution

It provides an exact quantum solution for the phase transition in a single-mode cavity, connecting it to many-cavity systems and analyzing spectral gap behavior.

Findings

Liouvillian gap vanishes exponentially in the thermodynamic limit

Disappearance of bimodality in the photon Wigner function

Connection established between single-mode and many-cavity limits

Abstract

We theoretically investigate the critical properties of a single driven-dissipative nonlinear photon mode. In a well-defined thermodynamical limit of large excitation numbers, the exact quantum solution describes a first-order phase transition in the regime where semiclassical theory predicts optical bistability. We study the behavior of the complex spectral gap associated with the Liouvillian superoperator of the corresponding master equation. We show that in this limit the Liouvillian gap vanishes exponentially and that the bimodality of the photon Wigner function disappears. The connection between the considered thermodynamical limit of large photon numbers for the single-mode cavity and the thermodynamical limit of many cavities for a driven-dissipative Bose-Hubbard system is discussed.