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

TL;DR

This paper presents a theoretical analysis of an array of dissipative nonlinear cavities with frequency-dependent incoherent pumping, revealing novel optical bistability, Fock state generation, and Mott state signatures in non-Markovian regimes.

Contribution

It introduces a new model for nonlinear cavity arrays with frequency-dependent gain, showing how non-Markovian effects influence steady states and quantum phases.

Findings

Optical bistability and Fock state generation in single cavities.

Recovery of Grand-Canonical ensemble in many-cavity systems.

Observation of Mott state signatures in strongly nonlinear two-cavity systems.

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.