Superfluid-Mott Insulator Transition of Light in the Jaynes-Cummings Lattice

TL;DR

This paper investigates the quantum phase transition of polaritons in a Jaynes-Cummings lattice, revealing similarities to the Bose-Hubbard model and identifying multicritical points through mean-field and field-theory approaches.

Contribution

It provides a detailed mean-field analysis and analytical expressions for multicritical curves in the Jaynes-Cummings lattice, advancing understanding of its phase transition behavior.

Findings

Identification of superfluid to Mott insulator transition in Jaynes-Cummings arrays

Analytical expressions for multicritical points

Comparison with Bose-Hubbard model physics

Abstract

Regular arrays of electromagnetic resonators, in turn coupled coherently to individual quantum two-level systems, exhibit a quantum phase transition of polaritons from a superfluid phase to a Mott-insulating phase. The critical behavior of such a Jaynes-Cummings lattice thus resembles the physics of the Bose-Hubbard model. We explore this analogy by elaborating on the mean-field theory of the phase transition, and by presenting several useful mappings which pinpoint both similarities and differences of the two models. We show that a field-theory approach can be applied to prove the existence of multicritical curves analogous to the multicritical points of the Bose-Hubbard model, and we provide analytical expressions for the position of these curves.