# Unraveling the quantum nature of atomic self-ordering in a ring cavity

## TL;DR

This paper investigates quantum effects in atomic self-ordering within a modified ring cavity, demonstrating how quantum fluctuations influence phase transitions and stabilize atomic motion, revealing the quantum nature of the process.

## Contribution

It introduces a novel ring cavity geometry that highlights quantum dynamics and fluctuations near the phase transition, surpassing mean-field limitations.

## Key findings

- Quantum fluctuations are observable near the phase transition.
- The modified geometry reveals quantum stabilization of atomic motion.
- Mean-field predicts instability, but quantum model shows stabilization.

## Abstract

Atomic self-ordering to a crystalline phase in optical resonators is a consequence of the intriguing non-linear dynamics of strongly coupled atom motion and photons. Generally the resulting phase diagrams and atomic states can be largely understood on a mean-field level. However, close to the phase transition point, quantum fluctuations and atom-field entanglement play a key role and initiate the symmetry breaking. Here we propose a modified ring cavity geometry, in which the asymmetry imposed by a tilted pump beam reveals clear signatures of quantum dynamics even in a larger regime around the phase transition point. Quantum fluctuations become visible both in the dynamic and steady-state properties. Most strikingly we can identify a regime where a mean-field approximation predicts a runaway instability, while in the full quantum model the quantum fluctuations of the light field modes stabilize uniform atomic motion. The proposed geometry thus allows to unveil the "quantumness" of atomic self-ordering via experimentally directly accessible quantities.