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arXiv:1202.0737 · New Journal of Physics

Equilibrium and disorder-induced behavior in quantum light–matter systems

Eduardo Mascarenhas, Libby Heaney, M C O Aguiar, Marcelo França Santos

Published Apr 25, 2012• 11 citations

Abstract

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.

DOI: 10.1088/1367-2630/14/4/043033

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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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The superfluid to Mott insulator transition in cavity polariton arrays is analyzed using the variational cluster approach, taking into account quantum fluctuations exactly on finite length scales. Phase diagrams in one and two dimensions exhibit important non-mean-field features. Single-particle excitation spectra in the Mott phase are dominated by particle and hole bands separated by a Mott gap. In contrast to Bose-Hubbard models, detuning allows for changing the nature of the bosonic particles from quasilocalized excitons to polaritons to weakly interacting photons. The Mott state with density one exists up to temperatures T/g > or = 0.03, implying experimentally accessible temperatures for realistic cavity couplings g.

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