Strong coupling theory for the Jaynes-Cummings-Hubbard model

TL;DR

This paper develops an analytic strong-coupling framework to analyze the phase diagram and excitations of the Jaynes-Cummings-Hubbard model, revealing detailed particle/hole modes and phase boundaries.

Contribution

It introduces a strong-coupling approach with formulas for dispersion and spectral weights, extending beyond RPA to include quantum fluctuation corrections.

Findings

Identifies four particle/hole excitation modes in the Mott phase.

Derives explicit dispersion relations and spectral weights.

Calculates phase boundary including quantum fluctuation effects.

Abstract

We present an analytic strong-coupling approach to the phase diagram and elementary excitations of the Jaynes-Cummings-Hubbard model describing a superfluid-insulator transition of polaritons in an array of coupled QED cavities. In the Mott phase, we find four modes corresponding to particle/hole excitations with lower and upper polaritons, respectively. Simple formulas are derived for the dispersion relation and spectral weights within a strong-coupling random-phase approximation (RPA). The phase boundary is calculated beyond RPA by including the leading correction due to quantum fluctuations.