Impact of the Confinement Strength on the Energy Spectra of Two Atoms Interacting via Zero-Range or Realistic Potentials

This work analyzes the influence of an external confinement on the energy spectrum of two interacting ultracold atoms, considering either a regularized contact or a more realistic Born-Oppenheimer potential. For two harmonically confined particles with contact interaction, the known analytical solution exhibits universality in the sense that the energy spectra solely depend on the ratio of the confinement length to the scattering length. In this work it is shown that this type of universality breaks down for realistic interatomic interactions, leading to an explicit trap-size dependence of the energy spectrum. This effect is especially pronounced for very tight confinement. On the other hand, using first-order perturbation theory it is shown analytically that the here discussed universality persists for the contact interaction even in the case of anharmonic confinement, this result being also verified numerically beyond perturbation theory for a sextic trap potential. These findings demonstrate limitations of the popular contact-interaction model and highlight the necessity of considering more realistic finite-range interactions under tight trapping conditions.