Self-Ordered stationary states of driven quantum degenerate gases in optical resonators

TL;DR

This paper investigates how quantum statistics influence the self-ordering process of ultracold bosons and fermions in an optical resonator, revealing phase transitions and superradiant phenomena through numerical simulations.

Contribution

It provides the first detailed numerical analysis of quantum fluctuations and nonequilibrium dynamics in self-ordering ultracold gases within optical cavities, including fermionic cases.

Findings

Self-ordering transition from homogeneous to ordered phase.

Fermions exhibit a zero pump threshold for superradiance under specific conditions.

Quantum fluctuations and cavity cooling shape the stationary particle distribution.

Abstract

We study the role of quantum statistics in the self-ordering of ultracold bosons and fermions moving inside an optical resonator with transverse coherent pumping. For few particles we numerically compute the nonequilibrium dynamics of the density matrix towards the self-ordered stationary state of the coupled atom-cavity system. We include quantum fluctuations of the particles and the cavity field. These fluctuations in conjunction with cavity cooling determine the stationary distribution of the particles, which exhibits a transition from a homogeneous to a spatially ordered phase with the appearance of a superradiant scattering peak in the cavity output spectrum. At the same time the cavity field $Q$-function changes from a single to a double peaked distribution. While the ordering threshold is generally lower for bosons, we confirm the recently predicted zero pump strength threshold for superradiant scattering for fermions when the cavity photon momentum coincides with twice the Fermi momentum.