Non-equilibrium many-body effects in driven nonlinear resonator arrays

Abstract

We study the non-equilibrium behavior of optically driven dissipative coupled resonator arrays. Assuming each resonator is coupled with a two-level system via a Jaynes-Cummings interaction, we calculate the many-body steady state behavior of the system under coherent pumping and dissipation. We propose and analyze the many-body phases using experimentally accessible quantities such as the total excitation number, the emitted photon spectra and photon coherence functions for different parameter regimes. In parallel, we also compare and contrast the expected behavior of this system assuming the local nonlinearity in the cavities is generated by a generic Kerr effect rather than a Jaynes-Cummings interaction. We find that the behavior of the experimentally accessible observables produced by the two models differs for realistic regimes of interactions even when the corresponding nonlinearities are of similar strength. We analyze in detail the extra features available in the Jaynes-Cummings-Hubbard (JCH) model originating from the mixed nature of the excitations and investigate the regimes where the Kerr approximation would faithfully match the JCH physics. We find that the latter is true for values of the light-matter coupling and losses beyond the reach of current technology. Throughout the study we operate in the weak pumping, fully quantum mechanical regime where approaches such as mean field theory fail, and instead use a combination of quantum trajectories and the time evolving block decimation algorithm to compute the relevant steady state observables. In our study we have assumed small to medium size arrays (from 3 up to 16 sites) and values of the ratio of coupling to dissipation rate $g/\gamma \sim 20$ which makes our results implementable with current designs in Circuit QED and with near future photonic crystal set ups.

22 pages, 6 figures

References in corpus (25)

• Quantum nature of a strongly-coupled single quantum dot-cavity system
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Strongly Interacting Polaritons in Coupled Arrays of Cavities
• Quantum phase transitions of light
• Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays
• Single photons from coupled quantum modes
• Quantum Many-Body Phenomena in Coupled Cavity Arrays
• On the origin of strong photon antibunching in weakly nonlinear photonic molecules
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• Atomic three-body loss as a dynamical three-body interaction
• Mott-insulating and glassy phases of polaritons in 1D arrays of coupled cavities
• The quantum optical Josephson interferometer
• Fractional Quantum Hall State in Coupled Cavities
• Superfluid-Mott Insulator Transition of Light in the Jaynes-Cummings Lattice
• Many-body phenomena in QED-cavity arrays
• Non-equilibrium dynamics of coupled qubit-cavity arrays
• Photon correlations in a two-site non-linear cavity system under coherent drive and dissipation
• Low-lying bifurcations in cavity quantum electrodynamics
• Quantum phase transitions in photonic cavities with two-level systems
• Transport in open spin chains: A Monte Carlo wave-function approach
• Emission characteristics of laser-driven dissipative coupled-cavity systems
• Reproducing spin lattice models in strongly coupled atom-cavity systems
• Nonequilibrium phases in hybrid arrays with flux qubits and NV centers
• Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories
• Quantum phase transition in an array of coupled dissipative cavities

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• Photon blockade in non-Hermitian optomechanical systems with nonreciprocal couplings
• Disordered driven coupled cavity arrays: Non-equilibrium stochastic mean-field theory
• Quench dynamics of a disordered array of dissipative coupled cavities
• Phase diagram of a QED-cavity array coupled via a N-type level scheme
• Out-of-equilibrium physics in driven dissipative coupled resonator arrays