Confinement-induced resonance with weak background interaction

Abstract

We studied the scattering problem of two distinguishable atoms with unequal mass, where one atom (atom $\ensuremath{\alpha}$) is trapped in a quasi-one-dimensional (quasi-1D) tube and the other one (atom $\ensuremath{\beta}$) is localized by a 3D harmonic trap. We show that in such a system if atom $\ensuremath{\alpha}$ is much heavier than $\ensuremath{\beta}$, confinement-induced resonance (CIR) can appear when the 3D $s$-wave scattering length ${a}_{s}$ of these two atoms is much smaller than the characteristic lengths (CLs) of the confinements, for either ${a}_{s}>0$ or ${a}_{s}<0$. This is quite different from the usual CIRs which occur only when ${a}_{s}$ is comparable with the CL of confinement. Moreover, the CIRs we find are broad enough to serve as a tool for the control of effective interatomic interaction. We further show the mechanism of these CIRs via the Born-Oppenheimer approximation. Our results can be used for the realization of strongly interacting systems with ultracold atoms with weak 3D background interaction (i.e., small ${a}_{s}$), e.g., the realization of ultracold gases with strong spin-dependent interaction at zero magnetic fields.