Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons

TL;DR

This paper derives the effective one-dimensional scattering amplitude and interaction potential for atoms in elongated traps, demonstrating conditions for realizing a Tonks gas of impenetrable bosons experimentally.

Contribution

It provides a theoretical framework for understanding atomic scattering in elongated traps and proposes experimental parameters for realizing a Tonks gas.

Findings

Low-energy scattering degenerates to total reflection

Effective 1D interaction potential derived

Experimental parameters estimated for alkali atoms

Abstract

We calculate, within the pseudopotential approximation, a one-dimensional scattering amplitude and effective one-dimensional interaction potential for atoms confined transversally by an atom waveguide or highly elongated ``cigar''-shaped atomic trap. We show that in the low-energy scattering regime, the scattering process degenerates to a total reflection suggesting an experimental realization of a famous model in theoretical physics - a one-dimensional gas of impenetrable bosons (``Tonks'' gas). We give an estimate for suitable experimental parameters for alkali atoms confined in waveguides.