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Quantum many body properties of strongly correlated lattice bosons and polaritons

Michael Knap

Published Jan 1, 2009• 0 citations
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We present an analytic slave-boson approach to calculate the elementary excitations of the Jaynes-Cummings-Hubbard model (JCHM) describing strongly correlated polaritons on a lattice in various quantum optical systems. In the superfluid phase near the Mott transition we find a gapless, linear Goldstone mode and a gapped amplitude mode corresponding to phase and density fluctuations, respectively. The sound velocity of the Goldstone mode develops a peculiar anomaly as a function of detuning at low densities, which persists into the weakly interacting regime of a polariton BEC.
The experimental observation of quantum phenomena in strongly correlated many particle systems is difficult because of the short length- and timescales involved. Obtaining at the same time detailed control of individual constituents appears even more challenging and thus to date inhibits employing such systems as quantum information processing devices. Substantial progress to overcome these problems has been achieved with cold atoms in optical lattices, where a detailed control of collective properties is feasible. However it is very difficult to address and hence control or measure individual sites [1, 2]. In this work, we demonstrate that polaritons, combined atom and photon excitations, in an array of cavities can form a strongly interacting many body system [3]. This scheme has several advantages: First of all, individual particles can, by construction, be controlled and measured. In contrast to optical lattices, it therefore allows to create inhomogeneous systems where different phases may coexists in adjacent spatial regions. Finally not only an effective Bose- Hubbard Hamiltonian might be created but several different many body systems including spin chains.