Elementary modes of excitation caused by the quadratic Zeeman term and the sensitivity of spin structures of small spin-2 condensates against the magnetic field

The response of spin-2 small condensates to an external magnetic field $B$ is studied. The parameters of the interaction are considered as variable. The emphasis is placed on clarifying the modes of excitation caused by the quadratic Zeeman term. The theoretical method used is beyond the mean field theory. A set of eigenstates with the $U(5)\supset SO(5)\supset SO(3)$ symmetry is introduced to facilitate the analysis. To obtain a quantitative evaluation on the response, the fidelity susceptibility and the $B$ -dependent average populations of spin-components have been calculated. Mostly the particle number N=30 is assumed. The effect with a larger or smaller $N$ is also considered. It was found that the sensitivity of the response depends strongly both on the interaction and on the inherent symmetry.