Numerically exact treatment of many body self-organization in a cavity

TL;DR

This paper provides an exact quantum analysis of self-organization in ultracold bosonic atoms within an optical cavity, revealing complex steady states beyond mean-field predictions.

Contribution

It extends tensor network and adiabatic elimination methods to accurately study the global cavity coupling and open system dynamics.

Findings

Identification of mixed density wave and excited states in the self-organized phase

Discovery of a fully mixed atomic steady state at high dissipation

Demonstration of deviations from mean-field predictions in the long-time behavior

Abstract

We investigate the full quantum evolution of ultracold interacting bosonic atoms on a chain and coupled to an optical cavity. Extending the time-dependent matrix product state techniques and the many-body adiabatic elimination technique to capture the global coupling to the cavity mode and the open nature of the cavity, we examine the long time behavior of the system beyond the mean-field elimination of the cavity field. We investigate the many body steady states and the self-organization transition for a wide range of parameters. We show that in the self-organized phase the steady state consists in a mixture of the mean-field predicted density wave states and excited states with additional defects. In particular, for large dissipation strengths a steady state with a fully mixed atomic sector is obtained crucially different from the predicted mean-field state.