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Confinement induced resonance (CIR) is a useful tool for the control of theinteraction between ultracold atoms. In most cases the CIR occurs when thecharacteristic length atrap of the confinement is similar as the scatteringlength as of the two atoms in the free three-dimensional (3D) space. If thereis 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, evenwithout the help of a magnetic Feshbach resonance, and would be very useful. Ina previous research by Massignan and Castin (Phys Rev A 74:013616, 2006), itwas 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 localizedby a 3D harmonic trap. In this work we carefully investigate the properties ofthe CIRs in this system. We show that the CIR with $a_{\rm{trap}}\gg a_s$ canreally occur, and the number of the CIRs of this type increases with the massratio between the moving and localized atoms. However, when $a_{\rm{trap}}\gga_s$ the CIR becomes extremely narrow, and thus are difficult to be controlledin realistic experiments.

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