Nonequilibrium transition between dissipative time crystals

TL;DR

This paper investigates a dissipative phase transition in a driven nonlinear quantum oscillator, revealing two distinct types of time-crystal order and analyzing the transition between them through numerical, analytical, and semiclassical methods.

Contribution

It introduces the concept of a nonequilibrium transition between discrete and incommensurate time crystals, highlighting the role of quantum fluctuations and spectral singularities.

Findings

Identification of a phase transition between two time-crystal regimes.

Analysis of quantum fluctuations and their impact on time-crystal order.

Discovery of an exceptional point mediating the transition.

Abstract

We show a dissipative phase transition in a driven nonlinear quantum oscillator in which a discrete time-translation symmetry is spontaneously broken in two different ways. The corresponding regimes display either discrete or incommensurate time-crystal order, which we analyze numerically and analytically beyond the classical limit addressing observable dynamics, phenomenology in different (laboratory and rotating) frames, Liouvillian spectral features, and quantum fluctuations. Via an effective semiclassical description, we show that phase diffusion dominates in the incommensurate time crystal (or continuous time crystal in the rotating frame), which manifests as a band of eigenmodes with a lifetime growing linearly with the mean-field excitation number. Instead, in the discrete time crystal phase, the leading fluctuation process corresponds to quantum activation with a single mode that has an exponentially growing lifetime. Interestingly, the transition between these two regimes manifests itself already in the quantum regime as a spectral singularity, namely as an exceptional point mediating between phase diffusion and quantum activation. Finally, we discuss this transition between different time-crystal orders in the context of synchronization phenomena.