Spectral properties and exact solutions for Rabi-coupled noninteracting fermions in a spin-dependent anharmonic trapping potential

Abstract

Abstract We investigate the effect of spin-motion coupling on the spectral properties of Rabi-coupled noninteracting fermions in a spin-dependent harmonic trapping potential plus an anharmonic term. It is shown that when the spin-motion coupling becomes strong, fermions tend to stay in one of the two components. In the limit of the strong spin-motion coupling, the entire energy spectrum exhibits a sequence of near degeneracy. In particular, in the case of the sextic anharmonic term, the system admits the exact analytical energies and wave functions of the bound states for an infinite number of the specific parameter conditions. The properties of the energy spectrum have also been discussed on basis of these obtained exact analytical solutions.