-symmetry breaking in the steady state of microscopic gain–loss systems

Abstract

The phenomenon of ${ \mathcal P }{ \mathcal T }$ (parity- and time-reversal) symmetry breaking is conventionally associated with a change in the complex mode spectrum of a non-Hermitian system that marks a transition from a purely oscillatory to an exponentially amplified dynamical regime. In this work we describe a new type of ${ \mathcal P }{ \mathcal T }$ -symmetry breaking, which occurs in the steady-state energy distribution of open systems with balanced gain and loss. In particular, we show that the combination of nonlinear saturation effects and the presence of thermal or quantum noise in actual experiments results in unexpected behavior that differs significantly from the usual dynamical picture. We observe additional phases with preserved or ‘weakly’ broken ${ \mathcal P }{ \mathcal T }$ -symmetry, and an unconventional transition from a high-noise thermal state to a low-amplitude lasing state with broken symmetry and strongly reduced fluctuations. We illustrate these effects here for the specific example of coupled mechanical resonators with optically induced loss and gain, but the described mechanisms will be essential for a general understanding of the steady-state properties of actual ${ \mathcal P }{ \mathcal T }$ -symmetric systems operated at low amplitudes or close to the quantum regime.

Keywords

• P T -symmetry
• quantum optics
• nanomechanical systems
• phonon lasers