Quantum stability of self-organized atomic insulator-like states in optical resonators

TL;DR

This paper explores the stability of atomic insulator-like states in a cavity QED system with ultracold atoms, revealing bistability and parameter regions for stable Mott-like states influenced by cavity feedback.

Contribution

It derives an effective Bose-Hubbard model for atoms in a cavity, analyzing the stability and bistability of insulator-like states with cavity feedback effects.

Findings

Identification of parameter regions with stable insulator states

Prediction of bistability controlled by pump intensity

Analysis of crossover between superfluid and Mott insulator states

Abstract

We investigate a paradigm example of cavity quantum electrodynamics with many body systems: an ultracold atomic gas inside a pumped optical resonator. In particular, we study the stability of atomic insulator-like states, confined by the mechanical potential emerging from the cavity field spatial mode structure. As in open space, when the optical potential is sufficiently deep, the atomic gas is in the Mott-like state. Inside the cavity, however, the potential depends on the atomic distribution, which determines the refractive index of the medium, thus altering the intracavity field amplitude. We derive the effective Bose-Hubbard model describing the physics of the system in one dimension and study the crossover between the superfluid -- Mott insulator quantum states. We determine the regions of parameters where the atomic insulator states are stable, and predict the existence of overlapping stability regions corresponding to competing insulator-like states. Bistable behavior, controlled by the pump intensity, is encountered in the vicinity of the shifted cavity resonance.