Traces of integrability in scattering of one-dimensional dimers on a barrier

TL;DR

This paper reveals that in one-dimensional dimer scattering, odd incident waves do not produce unbound atoms due to integrability constraints, with potential experimental applications in atom interferometry.

Contribution

It demonstrates a novel integrability-related effect in dimer scattering and proposes experimental methods to observe and utilize this phenomenon.

Findings

Odd incident waves produce no unbound atoms during scattering.

The effect is linked to a specific integrable system with symmetry constraints.

Potential use in atom interferometry without spatial separation.

Abstract

We consider molecules made of two one-dimensional short-range-interacting bosonic atoms. We show that in the process of scattering of these molecules off a narrow barrier, odd incident waves produce \emph{no unbound atoms, even when the incident energy exceeds the dissociation threshold}. This effect is a consequence of a prohibition on chemical reactions acting in a generally unphysical Bethe Ansatz integrable system of a $C_{2}$-type, with which our system shares the spatially odd eigenstates. We suggest several experimental implementations of the effect. We also propose to use the monomer production as an alternative read-out channel in an atom interferometer: unlike in the standard interferometric schemes, no spatial separation of the output channels will be required.