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arXiv:quant-ph/0606097 · Nature Physics

Strongly interacting polaritons in coupled arrays of cavities

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

Published Nov 26, 2006• 960 citations
arXivHTMLPDF
DOI
10.1038/nphys462

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We propose a new type of spatially periodic structure, i.e. polaritonic crystal (PolC), to observe a "slow"/"stopped" light phenomenon due to coupled atom-field states (polaritons) in a lattice. Under the tightbinding approximation, such a system realizes an array of weakly coupled trapped two-component atomic ensembles interacting with optical field in a tunnel-coupled one dimensional cavity array. We have shown that the phase transition to the superfluid Bardeen-Cooper-Schrieffer state, a so-called (BCS)-type state of low branch polaritons, occurs under the strong coupling condition. Such a transition results in the appearance of a macroscopic polarization of the atomic medium at non-zero frequency. The principal result is that the group velocity of polaritons depends essentially on the order parameter of the system, i.e. on the average photon number in the cavity array.
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.