Multimode mean-field model for the quantum phase transition of a Bose-Einstein condensate in an optical resonator

TL;DR

This paper presents a mean-field model for ultracold atoms in an optical cavity, capturing the quantum phase transition of a Bose-Einstein condensate with a focus on excitation modes and atom-field entanglement.

Contribution

It introduces a comprehensive mean-field approach that extends beyond two-mode models to accurately describe the quantum phase transition and correlations in atom-light systems.

Findings

Model accurately describes the quantum phase transition.

Calculates second-order correlations including entanglement.

Goes beyond simple two-mode approximations.

Abstract

We develop a mean-field model describing the Hamiltonian interaction of ultracold atoms and the optical field in a cavity. The Bose-Einstein condensate is properly defined by means of a grand-canonical approach. The model is efficient because only the relevant excitation modes are taken into account. However, the model goes beyond the two-mode subspace necessary to describe the self-organization quantum phase transition observed recently. We calculate all the second-order correlations of the coupled atom field and radiation field hybrid bosonic system, including the entanglement between the two types of fields.