Energy spectra of a spin-$\tfrac12$ XY spin molecule interacting with a single mode field cavity: Numerical study

TL;DR

This paper numerically investigates the energy spectra of spin-$\tfrac{1}{2}$ XY molecules with up to 10 spins interacting with a single mode field, exploring parameter effects for quantum computing applications.

Contribution

It extends previous analytical work by numerically analyzing larger spin molecules with both nearest-neighbour and long-range interactions.

Findings

Energy spectra depend strongly on the number of spins (even or odd).

The invariant operator's behavior varies with system parameters.

Results inform parameter choices for quantum computing suitability.

Abstract

In a previous paper [J. Phys.: Conf. Ser. 682 (2016) 012032}, arXiv:1605.05593] we studied analytically the energy spectra of a finite-size spin $\tfrac12$ XY chain (molecule) coupled at an arbitrary spin site to a single mode of an electromagnetic field via the Jaynes-Cummings model. We considered spin rings and open spin molecules with up to 4 spins and an interaction restricted to nearest-neighbours. Here we extend our investigation, addressing numerically the energy spectra of molecules of up to 10 spins with nearest-neighbour or long-range interaction. Furthermore we analyze the behaviour of an invariant operator, constructed by combining the magnetization of the spin-chain and the total number of photons in the system. We found a strong dependence on the number (even or odd) of sites in the molecules. This study is aimed at finding the appropriate combination of the physical parameters that could make the system suitable for use in quantum computations.