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

TL;DR

This paper develops a Ginzburg-Landau theoretical framework to analyze static and dynamic properties of photons in a lattice of cavities with atoms, elucidating phase transitions and excitation spectra in the Jaynes-Cummings-Hubbard model.

Contribution

It introduces a Ginzburg-Landau approach to the Jaynes-Cummings-Hubbard model, enabling analysis of phase boundaries and excitation spectra.

Findings

Calculated the finite-temperature phase boundary between Mott insulator and superfluid phases.

Determined the excitation spectra and sound velocity of light in the superfluid phase.

Developed a first-order effective action in the hopping parameter.

Abstract

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.