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.

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

“…As it is discussed in detail in [16] and the Appendices therein, this can be accomplished by placing in the cavity a large number of population-inverted two-level emitters of transition frequency ω at , in order to obtain an effectively Lorenzian emission spectrum. More precisely, we assume that the emitters are quickly pumped to their excited state at a rate Γ p much larger than the collective Rabi frequency Ω R of the collective cavity field-emitter coupling.…”

“…In the formalism of [16], this frequency selectivity is included by the modified field operatorΨ(r) defined as…”

“…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.…”

Spectrum, Landau–Zener theory and driven-dissipative dynamics of a staircase of photons

“…The control and the preparation of multi-photon states is of paramount importance for a progress towards a many-body physics of coupled light and matter in these platforms. Single-and multi-photon preparation has a long history in cavity QED [24][25][26][27][28][29][30], including photon generation in high quality cavities [31], the control of single-photon states emitted by polaritons [32], as well as the conversion of collective atomic excitations into single photonic states within optical resonators [33], encompassing quantum homodyne tomography [34] and preparation of photon states in the driven-dissipative dynamics of cavity arrays [35,36].…”

Spontaneous Beliaev-Landau scattering out of equilibrium

“…For systems far from equilibrium no such claims can be made. Although some similarities can exist [1][2][3], driving and dissipation in general prevent the system from approaching a complete thermal equilibrium [4]. As a result, the phase-space distribution of out-of-equilibrium systems is typically much more sensitive to the actual microscopic driving, dissipation and equilibration processes that drive the system towards the steady-state.…”