# Confinement-Induced Resonance with Weak Background Interaction

## TL;DR

This paper reveals a new type of confinement-induced resonance (CIR) in a two-atom system with unequal masses, occurring at small scattering lengths and enabling control of interactions in ultracold atomic gases.

## Contribution

It demonstrates the existence of broad CIRs at small scattering lengths in mass-imbalanced systems, differing from traditional CIRs, and explains the mechanism using the Born-Oppenheimer approximation.

## Key findings

- CIR can occur at small scattering lengths when one atom is much heavier.
- These CIRs are broad and tunable for interaction control.
- Potential applications in ultracold gases with weak background interactions.

## Abstract

We studied the scattering problem of two distinguishable atoms with unequal mass, where one atom (atom $\alpha$) is trapped in a quasi-one-dimensional (quasi-1D) tube and the other one (atom $\beta$) is localized by a 3D harmonic trap. We show that in such a system if atom $\alpha$ is much heavier than $\beta$, 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 occurs only when $a_s$ is comparable with the CL of confinement. Moreover, the CIRs we find are broad enough that can serve as a tool for the control of effective inter-atomic 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.