# Two-photon Rabi-Hubbard and Jaynes-Cummings-Hubbard models: photon pair superradiance, Mott insulator and normal phases

## TL;DR

This paper investigates the phase diagrams of two-photon Rabi-Hubbard, Jaynes-Cummings-Hubbard, and Dicke models, revealing unique superradiant, Mott insulator, and normal phases through various computational methods.

## Contribution

It provides a comprehensive comparison of mean field predictions with exact QMC results and uncovers novel phase behaviors in two-photon models.

## Key findings

- Excellent agreement between mean field and QMC for Dicke model.
- JCH model shows a single Mott lobe with photon pair superfluid phase.
- No superradiant transition in the Rabi-Hubbard model with QMC.

## Abstract

We study the ground state phase diagrams of two-photon Dicke, the one-dimensional Jaynes-Cummings-Hubbard (JCH), and Rabi-Hubbard (RH) models using mean field, perturbation, quantum Monte Carlo (QMC), and density matrix renormalization group (DMRG) methods. We first compare mean field predictions for the phase diagram of the Dicke model with exact QMC results and find excellent agreement. The phase diagram of the JCH model is then shown to exhibit a single Mott insulator lobe with two excitons per site, a superfluid (SF, superradiant) phase and a large region of instability where the Hamiltonian becomes unbounded. Unlike the one-photon model, there are no higher Mott lobes. Also unlike the one-photon case, the SF phases above and below the Mott are surprisingly different: Below the Mott, the SF is that of photon {\it pairs} as opposed to above the Mott where it is SF of simple photons. The mean field phase diagram of the RH model predicts a transition from a normal to a superradiant phase but none is found with QMC.