# Dissipation Induced Nonstationarity in a Quantum Gas

## TL;DR

This paper demonstrates that a driven two-component Bose-Einstein condensate coupled to an optical cavity exhibits unavoidable dynamical instability and non-stationary behavior due to dissipation, leading to phenomena like squeezing, entanglement, and dissipative time crystals.

## Contribution

The authors solve the model in the thermodynamic limit, revealing persistent instability and non-stationarity not predicted by mean-field theory, and connect these to dissipative time crystal formation.

## Key findings

- System is always dynamically unstable in the thermodynamic limit.
- Higher-order correlations show instability, leading to squeezing and entanglement.
- Finite-size perturbation theory confirms non-stationary behavior.

## Abstract

Non-stationary long-time dynamics was recently observed in a driven two-component Bose-Einstein condensate coupled to an optical cavity [N. Dogra, et al. arXiv:1901.05974] and analyzed in mean-field theory. We solve the underlying model in the thermodynamic limit and show that this system is always dynamically unstable -- even when mean-field theory predicts stability. Instabilities always occur in higher-order correlation functions leading to squeezing and entanglement induced by cavity dissipation. The dynamics may be understood as the formation of a dissipative time crystal. We use perturbation theory for finite system sizes to confirm the non-stationary behaviour.