Nonlinear two-photon Rabi-Hubbard model: Superradiance, photon, and photon-pair Bose-Einstein condensates

Shifeng Cui,B Grémaud,Wenan Guo,G G Batrouni

doi:10.1103/physreva.102.033334

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.

Highlights

Light-matter interaction is ubiquitous in nature and is, the focus of much theoretical and experimental work
We show that the photon-photon interaction term stabilizes the system by ensuring that the Hamiltonian is always bounded from below, eliminating spectral collapse, which leads to the appearance of two quantum phase transitions; the first is the transition from the disordered phase to the pair superfluid (PSF) phase where the Z4 symmetry partially breaks, and the second is the transition between the PSF and the single-particle superfluid (SPSF) phases where the Z4 symmetry is completely broken
The results we present here were obtained using DMRG and SGF quantum Monte Carlo (QMC) depending on the physical quantities being studied and the boundary conditions: Open boundary conditions were typically used with DMRG and periodic ones were typically used with SGF

Summary

INTRODUCTION

Light-matter interaction is ubiquitous in nature and is, the focus of much theoretical and experimental work. When the CR terms are restored, the symmetry of the Hamiltonian is reduced from U(1) to Z4 and it was found that the two-photon RH model does not exhibit any quantum phase transitions; it has only the disordered phase and the spectral collapse region [46]. I.e., photon-photon interactions, have attracted experimental and theoretical interest as a means to generate topological photon pairs [47,48,49] which have robust transport properties To this end we exploit the density-matrix renormalization group [50,51] (DMRG) with open boundary conditions using the ALPS library [52], and the stochastic Green’s-function [53,54] (SGF) quantum Monte Carlo method, with periodic boundary conditions, to study the phase diagram of the two-photon RH model with a nonlinear photon term.

MODEL AND METHOD

RESULTS

CONCLUSIONS