Nonlinear two-photon Rabi-Hubbard model: superradiance and photon/photon-pair Bose-Einstein condensate

TL;DR

This paper investigates a nonlinear two-photon Rabi-Hubbard model in one dimension, revealing that photon-photon interactions stabilize the system and lead to two distinct quantum phase transitions, including a photon pair superfluid phase.

Contribution

The study introduces a nonlinear photon-photon interaction term into the Rabi-Hubbard model, uncovering new phase transitions and symmetry-breaking phenomena not present in the linear model.

Findings

Photon-photon interaction stabilizes the system against spectral collapse.

Identification of two quantum phase transitions: normal to photon pair superfluid, and photon pair superfluid to single particle superfluid.

Spontaneous breaking of Z4 symmetry occurs in two stages during phase transitions.

Abstract

We study the ground state phase diagram of a nonlinear two-photon Rabi-Hubbard (RH) model in one dimension using quantum Monte Carlo (QMC) simulations and density matrix renormalization group (DMRG) calculations. Our model includes a nonlinear photon-photon interaction term. Absent this term, the RH model has only one phase, the normal disordered phase, and suffers from spectral collapse at larger values of the photon-qubit interaction or inter-cavity photon hopping. The photon-photon interaction, no matter how small, stabilizes the system which now exhibits {\it two} quantum phase transitions: Normal phase to {\it photon pair} superfluid (PSF) transition and PSF to single particle superfluid (SPSF). The discrete $Z_4$ symmetry of the Hamiltonian spontaneously breaks in two stages: First it breaks partially as the system enters the PSF and then completely breaks when the system finally enters the SPSF phase. We show detailed numerical results supporting this, and map out the ground state phase diagram.