Quantum field theoretical study of an effective spin model in coupled optical cavity arrays

TL;DR

This paper investigates an effective spin model in coupled optical cavity arrays using quantum field theory, revealing phase transitions influenced by exchange anisotropy and detuning effects, supported by analytical and Hamiltonian analysis.

Contribution

It applies Abelian bosonization and renormalization group techniques to analyze phase transitions in cavity array systems, highlighting the impact of anisotropy and detuning.

Findings

Anisotropy changes the nature of the phase transition from Kosterlitz-Thouless to XY type.

A quantum phase transition occurs between Mott insulator and photonic superfluid phases.

Large detuning favors the photonic superfluid phase.

Abstract

Atoms trapped in microcavities and interacting through the exchange of virtual photons can model an anisotropic Heisenberg spin-1/2 lattice. We do the quantum field theoretical study of such a system using the Abelian bosonization method followed by the renormalization group analysis. We present interesting physics due to the presence of exchange anisotropy. An infinite order Kosterliz-Thouless-Berezinskii transition is replaced by second order XY transition even an infinitesimal a small anisotropy in exchange coupling is introduced. We predict a quantum phase transition between Mott insulating and photonic superfluid phase due to detuning between the cavity and laser frequency, a large detuning favours the photonic superfluid phase. We also do the analysis of Jaynes and Cumming Hamiltonian to support results of quantum field theoretical study.