# Superfluid-Mott-insulator phase transition of light in a two-mode cavity array with ultrastrong coupling

## TL;DR

This paper introduces a novel cavity array model with ultrastrong coupling that exhibits a superfluid-Mott-insulator phase transition of light, influenced by a unique symmetry and atom-photon interactions, with potential implementation in circuit QED.

## Contribution

The work presents a new two-mode cavity array model with ultrastrong coupling, supporting stable Mott-lobe structures and a continuous symmetry, expanding understanding of strongly-correlated photonic systems.

## Key findings

- Supports a global conserved excitation and continuous U(1) symmetry.
- Displays stable Mott-lobe structures of photons.
- Predicts a second-order superfluid-Mott-insulator phase transition.

## Abstract

In this paper we construct a new type of cavity array, in each cavity of which multiple two-level atoms interact with two independent photon modes. This system can be totally governed by a two-mode Dicke-lattice model, which includes all of the counter-rotating terms and therefore works well in the ultrastrong coupling regime achieved in recent experiments. Attributed to its special atom-photon coupling scheme, this model supports a global conserved excitation and a continuous $U(1)$ symmetry, rather than the discrete $Z_{2}$ symmetry in the standard Dicke-lattice model. This distinct change of symmetry via adding an extra photon mode strongly impacts the nature of photon localization/delocalization behavior. Specifically, the atom-photon interaction features stable Mott-lobe structures of photons and a second-order superfluid-Mott-insulator phase transition, which share similarities with the Jaynes-Cummings-lattice and Bose-Hubbard models. More interestingly, the Mott-lobe structures predicted here depend crucially on the atom number of each site. We also show that our model can be mapped into a continuous $XX$ spin model. Finally, we propose a scheme to implement the introduced cavity array in circuit quantum electrodynamics. This work broadens our understanding of strongly-correlated photons.