# Quantum phase transitions of light in a dissipative Dicke-Bose-Hubbard model

## TL;DR

This paper investigates how environmental dissipation affects quantum phase transitions of light in a dissipative Dicke-Bose-Hubbard model, revealing photon localization, the disappearance of Mott lobes, and the transition towards classical behavior.

## Contribution

It provides an analytical formulation of the Hamiltonian and superfluid order parameter considering dissipation, extending understanding of quantum phase transitions in open photonic systems.

## Key findings

- Photon decay leads to evolution of the order parameter over time.
- Dissipation causes photons to localize, requiring higher hopping energy for phase coherence.
- Mott lobes vanish and the system becomes more classical with increasing atom number.

## Abstract

The impacts that the environment has on the quantum phase transition of light in the DickeBose-Hubbard model are investigated. Based on the quasibosonic approach, mean field theory and the perturbation theory, the formulation of the Hamiltonian, the eigenenergies and the superfluid order parameter are obtained analytically. Compared with the ideal cases, the order parameter of the system evolves with time as the photons naturally decay in their environment. When the system starts with the superfluid state, the dissipation makes the photons tend to localize, and a greater hopping energy of photon is required to restore the long-range phase coherence of the localized state of the system. Furthermore, the Mott lobes disappears and the system tends to be classical with the number of atoms increasing; however, the atomic number is far lower than that expected under ideal circumstances. Therefore, our theoretical results offer valuable insight into the quantum phase transition of a dissipative system.