Analytical solutions for two heteronuclear atoms in a ring trap

TL;DR

This paper derives analytical solutions for two heteronuclear atoms in a ring trap with short-range interactions, revealing unique features distinct from identical atoms and connecting to the Lieb-Liniger model.

Contribution

It provides the first analytical solutions for heteronuclear atoms in a ring trap, extending the Bethe-ansatz approach to systems with different atomic masses.

Findings

Eigen-energies expressed via coupled equations

Distinct features from identical atom systems

Reduction to Lieb-Liniger solution for equal masses

Abstract

We consider two heteronuclear atoms interacting with a short-range $\delta$ potential and confined in a ring trap. By taking the Bethe-ansatz-type wavefunction and considering the periodic boundary condition properly, we derive analytical solutions for the heteronuclear system. The eigen-energies represented in terms of quasi-momentums can then be determined by solving a set of coupled equations. We present a number of results, which display different features from the case of identical atoms. Our result can be reduced to the well-known Lieb-Liniger solution when two interacting atoms have the same masses.