Effective Three-Body Interactions in Jaynes-Cummings-Hubbard Systems

TL;DR

This paper generalizes the Jaynes-Cummings-Hubbard model to include three-level systems, revealing controllable two- and three-body polariton interactions that significantly affect the system's phase diagram.

Contribution

It introduces a three-level system extension to the Jaynes-Cummings-Hubbard model, enabling tunable multi-body interactions and exploring their impact on quantum phases.

Findings

Two- and three-body polariton interactions are demonstrated.

Tuning transition dipoles controls interaction strength and sign.

Different interactions modify the superfluid-Mott insulator phase diagram.

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 $\Xi$-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.