Polariton Mott insulator with trapped ions or circuit QED

TL;DR

This paper explores extended Jaynes-Cummings-Hubbard models with long-range hopping for polariton Mott insulators in trapped ions and circuit QED, analyzing phase boundaries and excitation spectra.

Contribution

It introduces models with next-nearest-neighbor and long-range hopping, providing new insights into phase boundaries and spectral properties in these systems.

Findings

Long-range hopping enlarges the Mott phase in trapped ions.

It reduces the Mott phase in stripline resonators.

Critical hopping varies significantly with added hopping terms.

Abstract

We consider variants of the Jaynes-Cummings-Hubbard model of lattice polaritons, taking into account next-nearest-neighbor, diagonal and long-range photon hopping in one and two dimensions. These models are relevant for potential experimental realizations of polariton Mott insulators based on trapped ions or microwave stripline resonators. We obtain the Mott-superfluid phase boundary and calculate excitation spectra in the Mott phase using numerical and analytical methods. Including the additional hopping terms leads to a larger Mott phase in the case of trapped ions, and to a smaller Mott phase in the case of stripline resonators, compared to the original model with nearest-neighbor hopping only. The critical hopping for the transition changes by up to about 50 percent in one dimension, and by up to about 20 percent in two dimensions. In contrast, the excitation spectra remain largely unaffected.