# Dicke time crystals in driven-dissipative quantum many-body systems

## TL;DR

This paper explores the stability and emergence of Dicke time crystals in driven-dissipative quantum many-body systems, especially when short-range interactions break the mean-field approximation, revealing complex dynamical phases.

## Contribution

It demonstrates the existence of long-lived and metastable Dicke time crystals in a driven-dissipative setting with short-range interactions, extending the understanding beyond mean-field models.

## Key findings

- Time crystalline behavior persists with ferromagnetic interactions at strong coupling.
- Dissipation can cool many-body heating, stabilizing time crystals.
- Rich dynamical responses emerge from the interplay of drive, dissipation, and interactions.

## Abstract

The Dicke model -- a paradigmatic example of superradiance in quantum optics -- describes an ensemble of atoms which are collectively coupled to a leaky cavity mode. As a result of the cooperative nature of these interactions, the system's dynamics are captured by the behavior of a single mean-field, collective spin. In this mean-field limit, it has recently been shown that the interplay between photon losses and periodic driving of light-matter coupling can lead to time-crystalline-like behavior of the collective spin. In this work, we investigate whether such a Dicke time crystal is stable to perturbations that explicitly break the mean-field solvability of the conventional Dicke model. In particular, we consider the addition of short-range interactions between atoms, which breaks the collective coupling and leads to complex many-body dynamics. In this context, the interplay between periodic driving, dissipation and interactions yields a rich set of dynamical responses including long-lived and metastable Dicke time crystals, where losses can cool down the many-body heating resulting from the continuous pump of energy from the periodic drive. Specifically, when the additional short-range interactions are ferromagnetic, we observe time crystalline behavior at non-perturbative values of the coupling strength, suggesting the possible existence of stable dynamical order in a driven-dissipative quantum many-body system. These findings illustrate the rich nature of novel dynamical responses with many-body character in quantum optics platforms.