# Dynamical spin-orbit coupling of a quantum gas

## TL;DR

This paper demonstrates the realization of dynamical one-dimensional spin-orbit coupling in a Bose-Einstein condensate within an optical cavity, revealing a superradiant phase transition that induces spinor-helix polariton condensates with potential for exploring exotic quantum states.

## Contribution

It introduces a novel method to generate dynamical spin-orbit coupling in a quantum gas using cavity QED, linking superradiance with spin-orbit effects in a controlled setting.

## Key findings

- Observation of superradiant phase transition with spin-orbit coupling
- Formation of spinor-helix polariton condensates
- Emergence of SOC through spin-resolved momentum imaging

## Abstract

We realize the dynamical 1D spin-orbit-coupling (SOC) of a Bose-Einstein condensate confined within an optical cavity. The SOC emerges through spin-correlated momentum impulses delivered to the atoms via Raman transitions. These are effected by classical pump fields acting in concert with the quantum dynamical cavity field. Above a critical pump power, the Raman coupling emerges as the atoms superradiantly populate the cavity mode with photons. Concomitantly, these photons cause a back-action onto the atoms, forcing them to order their spin-spatial state. This SOC-inducing superradiant Dicke phase transition results in a spinor-helix polariton condensate. We observe emergent SOC through spin-resolved atomic momentum imaging. Dynamical SOC in quantum gas cavity QED, and the extension to dynamical gauge fields, may enable the creation of Meissner-like effects, topological superfluids, and exotic quantum Hall states in coupled light-matter systems.