Time Crystals in Coupled Exciton-Polariton Condensates

TL;DR

This paper demonstrates the emergence of time crystals in coupled exciton-polariton condensates driven by intrinsic gain and loss, with a full quantum description confirming their robustness and specific phase conditions.

Contribution

It introduces a quantum framework for time crystals in exciton-polariton systems and identifies the phase diagram and stability conditions for their formation.

Findings

Time crystals can form without external periodic driving.

The phase diagram depends on the ratio of Kerr nonlinearity to nonlinear dissipation.

Quantum corrections are small and periodic, confirming robustness.

Abstract

In this paper, we show that time crystals can emerge in coupled exciton-polariton condensates without periodic external driving, enabled instead by incoherent gain and dissipation channels inherent to semiconductor microcavities. We present a full quantum description of these processes that recovers the established effective theory at the mean-field level. We analytically determine the mean-field phase diagram for the time-crystalline phase and find that its emergence requires the ratio of Kerr nonlinearity to nonlinear dissipation to exceed $\sqrt{5/4}$. Within this regime, the periodic oscillation of the particle numbers forms an attractor that is insensitive to the initial conditions. Numerical bifurcation diagrams reveal transitions between the time-crystalline phase and various steady phases, in excellent agreement with the analytical results. Using Bogoliubov perturbation theory, we evaluate the leading-order quantum corrections and find that, over a wide parameter range, these corrections remain periodic and much smaller than the mean-field background, thereby establishing the robustness of the time crystal.