Bose-Hubbard model: Relation between driven-dissipative steady states and equilibrium quantum phases

Alexandre Le Boité, Giuliano Orso, and Cristiano Ciuti
Phys. Rev. A 90, 063821 – Published 15 December 2014

Abstract

We present analytical solutions for the mean-field master equation of the driven-dissipative Bose-Hubbard model for cavity photons, in the limit of both weak pumping and weak dissipation. Instead of pure Mott-insulator states, we find statistical mixtures with the same second-order coherence g(2)(0) as a Fock state with n photons, but a mean photon number of n/2. These mixed states occur when n pump photons have the same energy as n interacting photons inside the nonlinear cavity and survive up to a critical tunneling coupling strength, above which a crossover to a classical coherent state takes place. We also explain the origin of both antibunching and superbunching predicted by P-representation mean-field theory at higher pumping and dissipation. In particular, we show that the strongly correlated region of the associated phase diagram cannot be described within the semiclassical Gross-Pitaevskii approach.

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  • Received 4 August 2014

DOI:https://doi.org/10.1103/PhysRevA.90.063821

©2014 American Physical Society

Authors & Affiliations

Alexandre Le Boité, Giuliano Orso, and Cristiano Ciuti

  • Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot-Paris 7 and CNRS, Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France

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Vol. 90, Iss. 6 — December 2014

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