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

¹ Institut für Theoretische Physik, Universität Innsbruck - Technikerstraße 25, A-6020 Innsbruck, Austria
² Department of Chemical Physics, Weizmann Institute of Science - Rehovot 7610001, Israel

^(a) Helmut.Ritsch@uibk.ac.at

Received: 2 July 2015
Accepted: 24 August 2015

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. 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.