Abstract
A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a Ξ-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the mean field superfluid-Mott insulator phase diagram, with the possible emergence of a pair superfluid phase in the two-body attractive regime.
Highlights
There has been considerable effort applied to the study of solid-state phenomena in Jaynes-Cummings-Hubbard (JCH) systems
In this work we wish to consider the impact of three-body interactions and the interplay between two-body and three-body interactions on the properties of the mean-field superfluid-Mott insulator phase diagram
The discrepancy between the numeric and analytical predictions, for β > 2, is quite unlike what one observes in the Bose-Hubbard system20,34, or the JCH system5, or even the system in consideration for β ≤ 2. In these systems it was always assumed that the phase transition is second-order, that is, the order parameter ψ is continuous across the transition
Summary
There has been considerable effort applied to the study of solid-state phenomena in Jaynes-Cummings-Hubbard (JCH) systems These studies have predicted a superfluid-Mott insulator phase transition, supersolid and Bose-glass phases, metamaterial properties, and, in the presence of time-reversal-symmetry breaking, fractional quantum Hall states. These studies have predicted a superfluid-Mott insulator phase transition, supersolid and Bose-glass phases, metamaterial properties, and, in the presence of time-reversal-symmetry breaking, fractional quantum Hall states11–14 Almost all of these studies have focused on the case where each lattice element of the system is comprised of a two-level system interacting with a single photonic mode, resulting in the emergence of quasiparticles, referred to as polaritons. In this work we consider the properties of a generalised JCH system where each lattice element is comprised of a three-level system interacting with a single photon mode Such a model provides an opportunity to construct a Hamiltonian in which three-body interactions are dominant. Here, we consider a three-level JCH system which supports both two-body and three-body effective contact interactions, on each site of the JCH lattice, and analyse the zero-temperature phases that this system exhibits
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