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

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