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arXiv:1212.5602 · Physical Review A

Disordered driven coupled cavity arrays: Nonequilibrium stochastic mean-field theory

Gytis Kulaitis, Frank Krüger, Felix Nissen, Jonathan Keeling

Published Jan 29, 2013• 19 citations
arXivHTMLPDF

Abstract

We study the interplay of disorder with pumping and decay in coupled qubit-cavity arrays, the Jaynes-Cummings-Hubbard model. We find that relatively weak disorder can wash out the bistability present in the clean pumped system and that moreover the combination of disorder in on-site energies and decay can lead to effective phase disorder. To explore these questions, we present a nonequilibrium generalization of stochastic mean-field theory, providing a simple tool to address such questions. This technique is developed for rather general forms of light-matter coupling, driving, dissipation, and on-site disorder, making it applicable to a wide range of systems.

DOI
10.1103/physreva.87.013840

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We study the interplay of disorder with pumping and decay in coupled qubit-cavity arrays, the Jaynes-Cummings-Hubbard model. We find that relatively weak disorder can wash out the bistability present in the clean pumped system and that moreover the combination of disorder in on-site energies and decay can lead to effective phase disorder. To explore these questions, we present a nonequilibrium generalization of stochastic mean-field theory, providing a simple tool to address such questions. This technique is developed for rather general forms of light-matter coupling, driving, dissipation, and on-site disorder, making it applicable to a wide range of systems.
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We analyze equilibrium properties of coupled-doped cavities described by the Jaynes–Cummings–Hubbard Hamiltonian. In particular, we characterize the entanglement of the system in relation to the insulating–superfluid phase transition. We point out the existence of a crossover inside the superfluid phase of the system when the excitations change from polaritonic to purely photonic. Using an ensemble statistical approach for small systems and stochastic mean-field theory for large systems, we analyze static disorder of the characteristic parameters of the system and explore the ground state-induced statistics. We report on a variety of glassy phases deriving from the hybrid statistics of the system. On-site strong disorder induces insulating behavior through two different mechanisms. For disorder in the light–matter detuning, low-energy cavities dominate the statistics, allowing the excitations to localize and bunch in such cavities. In the case of disorder in the light–matter coupling, sites with strong coupling between light and matter become very significant, which enhances the Mott-like insulating behavior. Inter-site (hopping) disorder induces fluidity and the dominant sites are strongly coupled to each other.
We study the coherence and fluorescence properties of the coherently pumped and dissipative Jaynes-Cummings-Hubbard model describing polaritons in a coupled-cavity array. At weak hopping we find strong signatures of photon blockade similar to single-cavity systems. At strong hopping the state of the photons in the array depends on its size. While the photon blockade persists in a dimer consisting of two coupled cavities, a coherent state forms on an extended lattice, which can be described in terms of a semiclassical model.
In recent years, the control of photon-photon interactions in optical nonlinear media has led to the realization of quantum fluids of light. One of the current challenges is to increase the strength of these interactions and enter the so-called strongly correlated regime. To achieve this goal, arrays of nonlinear cavities are a very promising candidate. In this thesis, theoretical results on arrays of nonlinear cavities described by a driven-dissipative Bose-Hubbard model are presented. In particular, a general method to compute the mean-field phase diagram of this model is described. Due to the finite life time of photons, the system is intrinsically dissipative: cavity losses must be compensated by an external driving field. This nonequilibrium nature gives rise to interesting features, such as a transition between monostable and bistable phases induced by tunneling. In the limit of weak dissipation and weak driving, analytical results describing generalized Mott insulating phases are derived. These states survive up to a critical tunneling strength, above which a crossover to a classical coherent state takes place. Finally, the issue of how to go beyond the mean-field approximation is addressed by performing exact numerical simulations. Large arrays of cavities were simulated by implementing a new method specifically tailored for driven-dissipative systems.
We explore theoretically the nonequilibrium photonic phases of an array of coupled cavities in presence of incoherent driving and dissipation. In particular, we consider a Hubbard model system where each site is a Kerr nonlinear resonator coupled to a two-level emitter, which is pumped incoherently. Within a Gutzwiller mean-field approach, we determine the steady-state phase diagram of such a system. We find that, at a critical value of the intercavity photon hopping rate, a second-order nonequilibrium phase transition associated with the spontaneous breaking of the U(1)\text{U}(1)U(1) symmetry occurs. The transition from an incompressible Mott-like photon fluid to a coherent delocalized phase is driven by commensurability effects and not by the competition between photon hopping and optical nonlinearity. The essence of the mean-field predictions is corroborated by finite-size simulations obtained with matrix product operators and corner-space renormalization methods.
We discuss a nonequilibrium dynamical mean-field framework for simulating inhomogeneous Hubbard models with local disorders. Our approach treats electron interactions and disorders on equal footing, by considering only local dynamical fluctuations. The theory reduces to nonequilibrium dynamical mean-field theory in the presence of only electron-electron interactions and to the coherent potential approximation in noninteracting systems with disorders. Both time-dependent and steady-state problems are treated by implementing the theory on the three-branch Kadanoff-Baym contour and two-branch Schwinger-Keldysh contour, respectively. Benchmarks on a eight-site cube show that the method yields rather accurate spectral functions in both the weakly and strongly interacting regimes. In a cubic lattice, we demonstrate energy conservation after an interaction quench and thermalization after just a few hopping times in both clean and disordered systems. As an application, we study transport through a serial double quantum-dot sandwiched between two leads, focusing on the current and dot occupations after a voltage quench.