Mott insulator states of ultracold atoms in optical resonators

TL;DR

This paper investigates the phase transitions of ultracold atoms in an optical resonator, revealing conditions for Mott insulator states, bistability, and superfluid phases influenced by cavity dynamics and pump parameters.

Contribution

It derives a one-dimensional Bose-Hubbard model incorporating cavity feedback and predicts novel bistable and competing Mott states near cavity resonance.

Findings

Identification of parameter regimes for Mott insulator states

Prediction of bistability near cavity resonance

Demonstration of superfluid phases outside specific regimes

Abstract

We study the low temperature physics of an ultracold atomic gas in the potential formed inside a pumped optical resonator. Here, the height of the cavity potential, and hence the quantum state of the gas, depends not only on the pump parameters, but also on the atomic density through a dynamical a.c.-Stark shift of the cavity resonance. We derive the Bose-Hubbard model in one dimension, and use the strong coupling expansion to determine the parameter regime in which the system is in the Mott-insulator state. We predict the existence of overlapping, competing Mott states, and bistable behavior in the vicinity of the shifted cavity resonance, controlled by the pump parameters. Outside these parameter regions, the state of the system is in most cases superfluid.