Towards strongly correlated photons in arrays of dissipative nonlinear cavities under a frequency-dependent incoherent pumping

Abstract

We report a theoretical study of a quantum optical model consisting of an array of strongly nonlinear cavities incoherently pumped by an ensemble of population-inverted two-level atoms. Projective methods are used to eliminate the atomic dynamics and write a generalized master equation for the photonic degrees of freedom only, where the frequency-dependence of gain introduces non-Markovian features. In the simplest single cavity configuration, this pumping scheme gives novel optical bistability effects and allows for the selective generation of Fock states with a well-defined photon number. For many cavities in a weakly non-Markovian limit, the non-equilibrium steady state recovers a Grand-Canonical statistical ensemble at a temperature determined by the effective atomic linewidth. For a two-cavity system in the strongly nonlinear regime, signatures of a Mott state with one photon per cavity are found.

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• An Autonomous Stabilizer for Incompressible Photon Fluids and Solids
• Emergent Finite Frequency Criticality of Driven-Dissipative Correlated Lattice Bosons
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• Spectrum, Landau-Zener theory and driven-dissipative dynamics of a staircase of photons
• How to exploit driving and dissipation to stabilize and manipulate quantum many-body states
• Space-time first-order correlations of an open Bose-Hubbard model with incoherent pump and loss
• A solvable model for strongly interacting nonequilibrium excitons