Few-mode geometric description of a driven-dissipative phase transition in an open quantum system

TL;DR

This paper introduces a geometric framework using two Liouvillian eigenmodes to describe hysteresis in driven-dissipative phase transitions, simplifying analysis and expanding computational capabilities.

Contribution

It presents a novel geometric approach based on two collective eigenmodes to analyze driven-dissipative phase transitions in open quantum systems.

Findings

Accurately describes hysteresis phenomena using two eigenmodes

Simplifies the analysis of driven-dissipative phase transitions

Extends computationally accessible parameter regimes

Abstract

By example of the nonlinear Kerr-mode driven by a laser, we show that hysteresis phenomena in systems featuring a driven-dissipative phase transition (DPT) can be accurately described in terms of just two collective, dissipative Liouvillian eigenmodes. The key quantities are just two components of a nonabelian geometric connection, even though a single parameter is driven. This powerful geometric approach considerably simplifies the description of driven-dissipative phase transitions, extending the range of computationally accessible parameter regimes, and providing a new starting point for both experimental studies and analytical insights.