Confinement Induced Resonances in Spherical Shell Traps

Abstract

We have computed exactly the energy spectrum and corresponding wave functions of two bosonic particles, which are confined in a spherically symmetric shell-shaped trap of the radius r0 and interact with each other via a three-dimensional zero-range potential characterized by the s-wave scattering length a0. Confinement induced resonances (CIRs) are found to occur at certain values of r0 and a0 as avoided crossings between the bound (molecular) and trap (non-molecular) states, as well as between two trap states. The found CIRs originate entirely from the strong coupling of the relative and center-of-mass motions of the two particles. By working close to a CIR, that is at a certain shell radius and a given scattering length, these results offer a new way to increase the atom-atom interaction and even to drive the formation of molecules in the shell-shaped atomic gas.