Fluorescence Spectrum and Thermalization in a Driven Coupled Cavity Array

Abstract

We calculate the fluorescence spectra of a driven lattice of coupled cavities. To do this, we extend methods of evaluating two-time correlations in infinite lattices to open quantum systems; this allows access to momentum resolved fluorescence spectrum. We illustrate this for a drivendissipative transverse field anisotropic XY model. By studying the fluctuation dissipation theorem, we find the emergence of a quasi-thermalized steady state with a temperature dependent on system parameters; for blue detuned driving, we show this effective temperature is negative. In the low excitation density limit, we compare these numerical results to analytical spin-wave theory, providing an understanding of the form of the distribution function and the origin of quasi-thermalization. regime, with a two-photon pump that creates pairs of photons in adjacent sites (see Fig. 6). J κ J J J

Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator

“…Finally, we stress that in general, T eff (ω) for a non-equilibrium system will both be frequency dependent and operator dependent. That is, if one defined T eff (ω) using the FDT relation for Green's functions corresponding to operators other thanˆˆ † a a , , one would in general obtain a different function T eff (ω) [15,45].…”

“…One is then naturally interested in understanding the Greenʼs functions that describe the linear response of the system to external perturbations. For Markovian systems, these correlations functions can be readily computed using the quantum regression theorem, and have been studied in a variety of different contexts, from the standard example of resonance fluorescence of a driven two-level atom [12][13][14], recently discussed in the case of arrays of coupled qubits [15], to the second-order correlations probing bunching/anti-bunching of time-delayed photons (see, e.g. [16]).…”

On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices

“…They have subsequently been extended to finite temperatures [7,8], and to open quantum systems and density-matrix evolution [9,10]. Such methods have been very fruitful in exploring the nonequilibrium steady states (NESS) of driven-dissipative one-dimensional systems, using matrix product operators (MPO) [11][12][13][14][15][16][17][18][19][20][21]. These methods can also be extended beyond one dimension, either by mapping a finite two-dimensional lattice onto a one-dimensional chain [22]-see Ref.…”

Strong-coupling limit of the driven dissipative light-matter interaction

“…Critical behavior in quantum optical systems where the particle number is not conserved (see e.g. [1][2][3][4][5]) presents substantial interest as well as conceptual challenges (for a recent discussion see [6] and references therein). In order to address the issue, a thermodynamic limit can be formulated via the number of system excitations for which the displayed nonlinearity responsible for criticality can no longer be treated as a negligible perturbation [7].…”