Landau and dynamical instabilities of Bose-Einstein condensates with superfluid flow in a Kronig-Penney potential

TL;DR

This paper analytically investigates the stability of superfluid flow in Bose-Einstein condensates within a one-dimensional Kronig-Penney potential, revealing conditions for Landau and dynamical instabilities and their relation to excitation transmission and effective mass.

Contribution

It provides an analytical solution to the Bogoliubov equations in a Kronig-Penney potential and links instability onset to excitation transmission and band structure features.

Findings

Landau instability occurs when superfluid velocity exceeds a critical value.

Dynamical instability is linked to negative effective mass in the band.

Upper side of the swallowtail band is dynamically unstable despite positive effective mass.

Abstract

We study the elementary excitations of Bose-Einstein condensates in a one-dimensional periodic potential and discuss the stability of superfluid flow based on the Kronig-Penney model. We analytically solve the Bogoliubov equations and calculate the excitation spectrum. The Landau and dynamical instabilities occur in the first condensate band when the superfluid velocity exceeds certain critical values, which agrees with the result of condensates in a sinusoidal potential. It is found that the onset of the Landau instability coincides with the point where the perfect transmission of low-energy excitations is forbidden, while the dynamical instability occurs when the effective mass is negative. It is well known that the condensate band has a peculiar structure called swallowtail when the periodic potential is shallow compared to the mean field energy. We find that the upper side of the swallowtail is dynamically unstable although the excitations have the linear dispersion reflecting the positive effective mass.