Ginzburg-Landau Theory for the Jaynes-Cummings-Hubbard Model

Details Ginzburg-Landau Theory for the Jaynes-Cummings-Hubbard Model Ginzburg-Landau Theory for the Jaynes-Cummings-Hubbard Model

2012-01-29

arxiv.org/abs/1201.6060v1

Physics

Condensed Matter

Quantum Gases

Scientific paper

We develop a Ginzburg-Landau theory for the Jaynes-Cummings-Hubbard model which effectively describes both static and dynamic properties of photons evolving in a cubic lattice of cavities, each filled with a two-level atom. To this end we calculate the effective action to first-order in the hopping parameter. Within a Landau description of a spatially and temporally constant order parameter we calculate the finite-temperature mean-field quantum phase boundary between a Mott insulating and a superfluid phase of polaritons. Furthermore, within the Ginzburg-Landau description of a spatio-temporal varying order parameter we determine the excitation spectra in both phases and, in particular, the sound velocity of light in the superfluid phase.

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