Confinement Induced Resonance with Weak Bare Interaction in a Quasi 3+0 Dimensional Ultracold Gas

Abstract

Confinement induced resonance (CIR) is a useful tool for the control of the interaction between ultracold atoms. In most cases the CIR occurs when the characteristic length atrap of the confinement is similar as the scattering length as of the two atoms in the free three-dimensional (3D) space. If there is a CIR which can occur with weak bare interaction, i.e., under the condition $a_{\rm{trap}}\gg a_s$, then it can be realized for much more systems, even without the help of a magnetic Feshbach resonance, and would be very useful. In a previous research by Massignan and Castin (Phys Rev A 74:013616, 2006), it was shown that it is possible to realize such a CIR in a quasi-(3+0)D system, where one ultracold atom is moving in the 3D space and another one is localized by a 3D harmonic trap. In this work we carefully investigate the properties of the CIRs in this system. We show that the CIR with $a_{\rm{trap}}\gg a_s$ can really occur, and the number of the CIRs of this type increases with the mass ratio between the moving and localized atoms. However, when $a_{\rm{trap}}\gg a_s$ the CIR becomes extremely narrow, and thus are difficult to be controlled in realistic experiments.