Interaction of a single mode field cavity with the 1D XY model: Energy spectrum

TL;DR

This paper analytically investigates the energy spectrum of a small 1D XY spin chain interacting with a single mode of light, revealing how different coupling regimes affect the system's quantum states.

Contribution

It provides exact analytical solutions for the energy spectrum of a 1D XY spin chain coupled to a single light mode, for chains up to four spins, considering various interaction configurations.

Findings

Exact energy spectra for chains of up to 4 spins

Dependence of spectrum on ferromagnetic or antiferromagnetic coupling

Analytical results for open and cyclic chain configurations

Abstract

In this work we use the fundamental in quantum optics Jaynes-Cummings model to study the response of spin $\tfrac12$ chain to a single mode of a laser light falling on one of the spins, a focused interaction model between the light and the spin chain. For the spin-spin interaction along the chain we use the XY model. We report here the exact analytical results, obtained with the help of a computer algebra system, for the energy spectrum in this model for chains of up to 4 spins with nearest neighbors interactions, either for open or cyclic chain configurations. Varying the sign and magnitude of the spin exchange coupling relative to the light-spin interaction we have investigated both cases of ferromagnetic or antiferromagnetic spin chains.