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.

中文翻译：

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准 3+0 维超冷气体中弱裸相互作用的约束诱导共振

约束诱导共振 (CIR) 是控制超冷原子之间相互作用的有用工具。在大多数情况下，当限制的特征长度 atrap 与自由三维 (3D) 空间中两个原子的散射长度相似时，就会发生 CIR。如果存在可以在弱裸相互作用下发生的 CIR，即在 $a_{\rm{trap}}\gg a_s$ 条件下，那么它可以在更多系统中实现，即使没有磁性 Feshbach 的帮助共振，会非常有用。Massignan 和 Castin 之前的一项研究 (Phys Rev A 74:013616, 2006) 表明，在准 (3+0)D 系统中实现这样的 CIR 是可能的，其中一个超冷原子正在移动3D 空间和另一个空间由 3D 谐波陷阱定位。在这项工作中，我们仔细研究了该系统中 CIR 的特性。我们表明具有 $a_{\rm{trap}}\gg a_s$ 的 CIR 确实可以发生，并且这种类型的 CIR 的数量随着移动原子和局部原子之间的质量比而增加。然而，当 $a_{\rm{trap}}\gg a_s$ 时，CIR 变得非常窄，因此在实际实验中很难控制。