Quantum phase transition of light in the Rabi–Hubbard model

Abstract

We discuss the physics of the Rabi-Hubbard model describing large arrays of coupled cavities interacting with two level atoms via a Rabi non-linearity. We show that the inclusion of counterrotating terms in the light-matter interaction, often neglected in theoretical descriptions based on Jaynes-Cumming models, is crucial to stabilize finite-density quantum phases of correlated photons with no need for an artificially engineered chemical potential. We show that the physical properties of these phases and the quantum phase transition occurring between them is remarkably different from those of interacting bosonic massive quantum particles. The competition between photon delocalization and Rabi non-linearity drives the system across a novel Z2 parity symmetry-breaking quantum phase transition between two gapped phases, a Rabi insulator and a delocalized superradiant phase.

Quantum Monte Carlo study of the Rabi-Hubbard model

“…The MF results obtained in [18,19] provide a qualitatively correct description of the transition line throughout the phase diagram. On the other hand, the simple ansatz Eq.…”

“…We also analysed this transition by doing the meanfield (MF) analysis previously performed by Schiró et al [19], which we brifely review here. As the kinetic terms are the only ones that couple sites, we can replace them, for each site, with a coupling to an external homogeneous field ψ = a i for all i.…”

“…However, it was recently remarked that, for larger values of g, these CR terms may modify deeply the physics of these systems [17][18][19]. In [18], Schiro et al introduced the Rabi-Hubbard (RH) model, which is equivalent to the JCH model with the addition of counter-rotating terms, both in the interaction and the hopping terms.…”

“…This model has different symmetry properties from the JCH model and consequently different transitions. The studies performed in [17][18][19][20] show that the RH model does not exhibit Mott insulating behavior, but rather an incoherent/coherent transition which resembles the superradiant transition of the Dicke model [21,22]. The out of equilibrium behavior of the RH model has been recently studied in Ref.…”

“…Whereas the JCH model has been studied with DMRG [9] and QMC [13] the RH model has mostly been studied with meanfield approximations [17][18][19]. Kumar et al [20] mapped the RH model onto the quantum Ising model in the strong coupling limit (g/ω l > 1) and compared their results with DMRG simulations.…”