The role of atomic interactions in cavity-induced continuous time crystals

TL;DR

This paper investigates how short-range atomic interactions influence the properties, stability, and dynamics of continuous time crystals in atom-cavity systems, revealing their role in phase transitions and inherent metastability.

Contribution

It demonstrates that atomic interactions modify the critical bifurcation and induce metastability in dissipative time crystals, providing analytical and numerical insights into their heating mechanisms.

Findings

Atomic interactions alter the nature of the critical bifurcation.

Short-range interactions cause inherent metastability of the time crystal.

Analytical predictions match numerical simulations of heating rates.

Abstract

We consider continuous time-crystalline phases in dissipative many-body systems of atoms in cavities, focusing on the role of short-range interatomic interactions. First, we show that the latter can alter the nature of the time crystal by changing the type of the underlying critical bifurcation. Second, we characterize the heating mechanism and dynamics resulting from the short-range interactions and demonstrate that they make the time crystal inherently metastable. We argue that this is generic for the broader class of dissipative time crystals in atom-cavity systems whenever the cavity loss rate is comparable to the atomic recoil energy. We observe that such a scenario for heating resembles the one proposed for preheating of the early universe, where the oscillating coherent inflation field decays into a cascade of exponentially growing fluctuations. By extending approaches for dissipative dynamical systems to our many-body problem, we obtain analytical predictions for the parameters describing the phase transition and the heating rate inside the time-crystalline phase. We underpin and extend the analytical predictions of the heating rates with numerical simulations.