Dynamical instability and dispersion management of an attractive condensate in an optical lattice

TL;DR

This paper analyzes the stability of an attractive Bose-Einstein condensate in a moving optical lattice, revealing conditions for dynamical instability and stable regimes, with implications for condensate coherence and density patterns.

Contribution

It provides a linear stability analysis of an attractive condensate in a moving optical lattice, highlighting the stability conditions and dynamical behaviors distinct from repulsive cases.

Findings

System is dynamically unstable at low quasimomenta.

Stability improves near the band edge.

Low interaction instabilities produce oscillating density patterns.

Abstract

We investigate the stability of an attractive Bose-Einstein condensate in a moving 1D optical lattice in the presence of transverse confinement. By means of a Bogoliubov linear stability analysis we find that the system is dynamically unstable for low quasimomenta and becomes stable near the band edge, in a specular fashion with respect to the repulsive case. For low interactions the instability occurs via long wavelength excitations that are not sufficient for spoiling the condensate coherence, producing instead an oscillating density pattern both in real and momentum space. This behaviour is illustrated by simulations for the expansion of the condensate in a moving lattice.