Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry

TL;DR

This paper investigates the rotational behavior and excitation spectrum of a two-component Bose-Einstein condensate in a ring trap, revealing simple dispersion relations and the role of collective excitations.

Contribution

It introduces a combined mean-field and many-body diagonalization approach to analyze excitation spectra in asymmetric two-component Bose gases in ring potentials.

Findings

Angular momentum can be carried by single-particle or collective excitations.

The dispersion relation simplifies under typical conditions.

Collective excitations determine the dispersion relation in certain regimes.

Abstract

We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or "collective" excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.