Analytic approximations to the phase diagram of the Jaynes-Cummings-Hubbard model with application to ion chains

TL;DR

This paper develops analytic approximations for the phase diagram of the Jaynes-Cummings-Hubbard model, applicable to ion chains and coupled cavity arrays, providing explicit phase boundary formulas and validating them against numerical data.

Contribution

It introduces new analytic expressions for phase boundaries in the JCH model, applicable to ion chains and cavity arrays, enhancing understanding of quantum phase transitions.

Findings

Derived approximate analytic phase boundaries for the JCH model.

Compared analytic approximations with DMRG numerical results.

Validated the effectiveness of the approximations for different system parameters.

Abstract

We discuss analytic approximations to the ground state phase diagram of the homogeneous Jaynes-Cummings-Hubbard (JCH) Hamiltonian with general short-range hopping. The JCH model describes e.g. radial phonon excitations of a linear chain of ions coupled to an external laser field tuned to the red motional sideband with Coulomb mediated hopping or an array of high-$Q$ coupled cavities containing a two-level atom and photons. Specifically we consider the cases of a linear array of coupled cavities and a linear ion chain. We derive approximate analytic expressions for the boundaries between Mott-insulating and superfluid phases and give explicit expressions for the critical value of the hopping amplitude within the different approximation schemes. In the case of an array of cavities, which is represented by the standard JCH model we compare both approximations to numerical data from density-matrix renormalization group (DMRG) calculations.