Driven-dissipative phase transition in a Kerr oscillator: From semiclassical $\mathcal{PT}$ symmetry to quantum fluctuations

TL;DR

This paper investigates a driven-dissipative Kerr oscillator, revealing a rich variety of critical phenomena including phase transitions, symmetry breaking, and quantum fluctuations, using multiple theoretical approaches.

Contribution

It provides a comprehensive analysis of the quantum phase transition in a Kerr oscillator, combining mean-field, exact diagonalization, and Keldysh formalism to understand critical behavior.

Findings

Identification of a continuous phase transition with Z2 symmetry breaking.

Demonstration of PT symmetry and state squeezing near criticality.

Analytical calculation of critical and finite-size scaling using quantum Langevin equations.

Abstract

We study a minimal model that has a driven-dissipative quantum phase transition, namely a Kerr non-linear oscillator subject to driving and dissipation. Using mean-field theory, exact diagonalization, and the Keldysh formalism, we analyze the critical phenomena in this system, showing which aspects can be captured by each approach and how the approaches complement each other. Then critical scaling and finite-size scaling are calculated analytically using the quantum Langevin equation. The physics contained in this simple model is surprisingly rich: it includes a continuous phase transition, $Z_{2}$ symmetry breaking, $\mathcal{PT}$ symmetry, state squeezing, and critical fluctuations. Due to its simplicity and solvability, this model can serve as a paradigm for exploration of open quantum many-body physics.