Scattering of particles in the presence of harmonic confinement perturbed by a complex absorbing potential

A system of two interacting atoms confined in 1D harmonic trap and perturbed by an absorbing boundary potential is studied using the Lippmann-Schwinger formalism. The atom atom interaction potential was considered as a nonlocal separable model. The perturbed absorbing boundary potential was also assumed in the form of Scarf II complex absorbing potential. The model is used for the study of 1D optical lattices that support the trapping of a pair atom within a unit cell. Moreover, it allows to describe the scattering particles in a tight smooth trapping surface and to analyze the bound and resonance states. The analytical expressions for wavefunctions and transition matrix as well as the absorption probabilities are calculated. A demonstration of how the complex absorbing potential affecting the bound states and resonances of particles confined in a harmonic trap is described.