Quantum Phase Transitions of the Bose-Hubbard Model inside a Cavity

TL;DR

This paper theoretically explores the phase diagram of the Bose-Hubbard model inside a cavity, revealing how strong correlations can change the nature of superradiant transitions from second to first order, guiding future experiments.

Contribution

It provides the first detailed phase diagram for the Bose-Hubbard model in a cavity, highlighting the impact of strong correlations on phase transition orders.

Findings

Superradiant transition can become first order near Mott transition due to strong correlations.

Phase boundaries between superfluid, Mott insulator, and superradiant phases are mapped.

Results suggest new experimental avenues for studying light-matter interactions in strongly correlated systems.

Abstract

The superfluid to Mott insulator transition and the superradiant transition are textbook examples for quantum phase transition and coherent quantum optics, respectively. Recent experiments in ETH and Hamburg succeeded in loading degenerate bosonic atomic gases in optical lattices inside a cavity, which enables the first experimental study of the interplay between these two transitions. In this letter we present the theoretical phase diagram for the ETH experimental setup, and determine the phase boundaries and the orders of the phase transitions between the normal superfluid phase, the superfluid with superradiant light, the normal Mott insulator and the Mott insulator with superradiant light. We find that in contrast to the second-order superradiant transition in a weakly interacting Bose condensate, strong correlations in the superfluid nearby a Mott transition can render the superradiant transition to a first order one. Our results will stimulate further experimental studies of interactions between cavity light and strongly interacting quantum matters.