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arXiv:0706.2251 · New Journal of Physics

A polaritonic two-component Bose–Hubbard model

M J Hartmann, Fernando G. S. L. Brandão, Martin Bodo Plenio

Published Mar 6, 2008• 32 citations
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Abstract

We demonstrate that polaritons in an array of interacting micro-cavities with strong atom–photon coupling can form a two-component Bose–Hubbard model in which both polariton species are protected against spontaneous emission as their atomic part is stored in two ground states of the atoms. The parameters of the effective model can be tuned via the driving strength of external lasers and include attractive and repulsive polariton interactions. We also describe a method to measure the number statistics in one cavity for each polariton species independently.

DOI
10.1088/1367-2630/10/3/033011

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We propose a scheme to observe the crossover from weakly to strongly bound pairs with stationary polaritons. We first show how stationary light-matter excitations (polaritons) can realize an optically tunable two-component Bose-Hubbard model with repulsive intraspecies interactions and attractive interspecies interactions. We then discuss the feasibility of generating an effective Fermi-Hubbard model of polaritons exhibiting the crossover behavior. The predicted behavior of the system characterized by a crossover from short- to long-range spatial correlations as interactions are tuned can be efficiently observed by measuring correlation functions on the light exiting the waveguide.
A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a Ξ-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the mean field superfluid-Mott insulator phase diagram, with the possible emergence of a pair superfluid phase in the two-body attractive regime.
We present a scheme for engineering the extended two-component Bose-Hubbard model using polariton condensate supported by an optical microcavity. Compared to the usual two-component Bose-Hubbard model with only Kerr nonlinearity, our model includes a nonlinear tunneling term which depends on the number difference of the particle in the two modes. In the mean-field treatment, this model is an analog to a nonrigid pendulum with a variable pendulum length whose sign can be also changed. We study the dynamic and ground-state properties of this model and show that there exists a first-order phase transition as the strength of the nonlinear tunneling rate is varied. Furthermore, we propose a scheme to obtain the polariton condensate wave function.
A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a Ξ-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the mean field superfluid-Mott insulator phase diagram, with the possible emergence of a pair superfluid phase in the two-body attractive regime.