# Dissipation-induced instabilities of a spinor Bose-Einstein condensate inside an optical cavity

## TL;DR

This paper explores how dissipation causes instabilities in a spinor Bose-Einstein condensate within an optical cavity, revealing non-reciprocal dynamics and phase transitions driven by photon losses.

## Contribution

It introduces a detailed analysis of dissipative instabilities in a two-component Dicke model with complex couplings, highlighting the role of non-reciprocal interactions and exceptional points.

## Key findings

- Identification of dynamical limit cycles and instabilities
- Dissipation-induced non-reciprocal couplings between spins
- Potential for experimental observation of non-equilibrium phenomena

## Abstract

We investigate the dynamics of a spinor Bose-Einstein condensate inside an optical cavity, driven transversely by a laser with a controllable polarization angle. We focus on a two-component Dicke model with complex light-matter couplings, in the presence of photon losses. We calculate the steady-state phase diagram and find dynamical instabilities in the form of limit cycles, heralded by the presence of exceptional points and level attraction. We show that the instabilities are induced by dissipative processes which generate non-reciprocal couplings between the two collective spins. Our predictions can be readily tested in state-of-the-art experiments and open up the study of non-reciprocal many-body dynamics out of equilibrium.