Confinement-induced Resonances in Quasi-one-dimensional Traps with Transverse Anisotropy

TL;DR

This paper investigates atom-atom scattering in anisotropic quasi-one-dimensional traps, demonstrating the existence of a single confinement-induced resonance and challenging recent experimental observations of resonance splitting.

Contribution

It provides a theoretical analysis showing only one confinement-induced resonance in anisotropic traps, contrasting with experimental reports of multiple resonances.

Findings

Only one confinement-induced resonance exists in anisotropic traps.

Theoretical results are inconsistent with recent experimental resonance splitting.

Formal two-channel model confirms the single resonance phenomenon.

Abstract

We study atom-atom scattering in quasi-one-dimensional geometries with transverse anisotropy. By assuming an s-wave pseudo-potential of contact interaction, we show that the system would exhibit a single confinement-induced resonance, where the scattering process degenerates to a total reflection as a one-dimensional gas of impenetrable bosons. For a general form of interaction, we present a formal calculation based on the two-channel model and conclude the existence of only one confinement-induced resonance. Our findings are inconsistent with a recent experiment by Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)], where a splitting of confinement-induced resonances has been observed in an anisotropic quasi-one-dimensional quantum gas of Cs atoms.