We study the ground-state phase diagram of a nonlinear two-photon Rabi-Hubbard (RH) model in one dimension using quantum Monte Carlo simulations and density-matrix renormalization-group 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 intercavity photon hopping. The photon-photon interaction, no matter how small, stabilizes the system, which now exhibits two quantum phase transitions: Normal phase to 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 it 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.

• Received 30 June 2020
• Accepted 25 August 2020

DOI:https://doi.org/10.1103/PhysRevA.102.033334

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society