Stability of Bose-Einstein condensates in a Kronig-Penney potential

TL;DR

This paper analytically investigates the stability of Bose-Einstein condensates in a one-dimensional Kronig-Penney potential, revealing conditions for Landau and dynamical instabilities and the emergence of swallow-tail energy loops.

Contribution

It provides an analytical calculation of condensate and Bogoliubov bands in a Kronig-Penney potential and links stability instabilities to transmission properties of excitations.

Findings

Landau and dynamical instabilities occur beyond critical quasimomenta.

Instabilities coincide with forbidden low-energy excitation transmission.

Swallow-tail energy loops appear at high mean-field energies.

Abstract

We study the stability of Bose-Einstein condensates with superfluid currents in a one-dimensional periodic potential. By using the Kronig-Penney model, the condensate and Bogoliubov bands are analytically calculated and the stability of condensates in a periodic potential is discussed. The Landau and dynamical instabilities occur in a Kronig-Penney potential when the quasimomentum of the condensate exceeds certain critical values as in a sinusoidal potential. It is found that the onsets of the Landau and dynamical instabilities coincide with the point where the perfect transmission of low energy excitations through each potential barrier is forbidden. The Landau instability is caused by the excitations with small $q$ and the dynamical instability is caused by the excitations with $q=\pi/a$ at their onsets, where $q$ is the quasimomentum of excitation and $a$ is the lattice constant. A swallow-tail energy loop appears at the edge of the first condensate band when the mean-field energy is sufficiently larger than the strength of the periodic potential. We find that the upper portion of the swallow-tail is always dynamically unstable, but the second Bogoliubov band has a phonon spectrum reflecting the positive effective mass.