Phase diagram of incoherently driven strongly correlated photonic lattices

Abstract

We explore theoretically the nonequilibrium photonic phases of an array of coupled cavities in presence of incoherent driving and dissipation. In particular, we consider a Hubbard model system where each site is a Kerr nonlinear resonator coupled to a two-level emitter, which is pumped incoherently. Within a Gutzwiller mean-field approach, we determine the steady-state phase diagram of such a system. We find that, at a critical value of the intercavity photon hopping rate, a second-order nonequilibrium phase transition associated with the spontaneous breaking of the U(1) symmetry occurs. The transition from an incompressible Mott-like photon fluid to a coherent delocalized phase is driven by commensurability effects and not by the competition between photon hopping and optical nonlinearity. The essence of the mean-field predictions is corroborated by finite-size simulations obtained with matrix product operators and corner-space renormalization methods

Dynamical properties of dissipative XYZ Heisenberg lattices

“…Dissipative processes are usually at odds with the unitary Hamiltonian evolution of the quantum system and the competition between the incoherent and the coherent dynamics can give rise to criticality for the steady state in the thermodynamic limit [33]. Dissipative phase transitions have been discussed theoretically for single cavity photonic systems [34][35][36], as well as for lattices of cavities with mean field methods [37][38][39] or full-size lattice simulations [40,41]. An experimental observation of these critical phenomena seems feasible with state-of-the-art techniques, and some remarkable results have already been obtained [42][43][44].…”

Generation and spectroscopic signatures of a fractional quantum Hall liquid of photons in an incoherently pumped optical cavity

“…In the present work, we rely on a different pumping scheme based on a frequency-selective incoherent drive as proposed in [15,16] and further investigated in [17,18] in view of preparing correlated many-body states with a well-defined particle number, e.g. Mott insulators.…”

Localization to delocalization crossover in a driven nonlinear cavity array

“…Given the limited lifetime of photons trapped in a cavity, it is however more natural to explore many-body phases in a non-equilibrium setting taking into account input drives and dissipation. Following this route, auxiliary systems together with specific driving mechanisms have recently been considered to generate effective chemical potentials for photons [18][19][20][21] and resulting phase diagrams have been explored [22].…”