# Mean-field phase diagram of ultracold atomic gases in cavity quantum electrodynamics

## TL;DR

This paper maps the phase diagram of ultracold bosonic atoms in a 2D optical lattice coupled to a cavity, revealing the stability of supersolid phases and comparing with previous theoretical and numerical studies.

## Contribution

It provides a comprehensive mean-field analysis of the phase diagram for a 2D Bose-Hubbard model with infinite-range interactions, including analytical and numerical results.

## Key findings

- Agreement with previous phase diagrams from literature
- Identification of stability regions for supersolid phases
- Discussion of differences with dipolar boson systems

## Abstract

We investigate the mean-field phase diagram of the Bose-Hubbard model with infinite-range interactions in two dimensions. This model describes ultracold bosonic atoms confined by a two-dimensional optical lattice and dispersively coupled to a cavity mode with the same wavelength as the lattice. We determine the ground-state phase diagram for a grand-canonical ensemble by means of analytical and numerical methods. Our results mostly agree with the ones reported in Dogra et al. [PRA 94, 023632 (2016)], and have a remarkable qualitative agreement with the quantum Monte Carlo phase diagrams of Flottat et al. [PRB 95, 144501 (2017)]. The salient differences concern the stability of the supersolid phases, which we discuss in detail. Finally, we discuss differences and analogies between the ground state properties of strong long-range interacting bosons with the ones predicted for repulsively interacting dipolar bosons in two dimensions.