Excitations of the One Dimensional Bose-Einstein Condensates in a Random Potential

TL;DR

This paper studies how excitations in one-dimensional Bose-Einstein condensates become localized in a random potential, revealing a transition in localization behavior at a critical disorder strength.

Contribution

It demonstrates how the localization length exponent varies with disorder strength, identifying a critical point where the system transitions from superfluid to insulator.

Findings

Localization length diverges as 1/ω^α at low frequency

α=2 for weak disorder, decreases with increasing disorder

At critical disorder, α=1 indicating a phase transition

Abstract

We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as $\ell(\omega)\sim 1/\omega^\alpha$. We show that the well known result $\alpha=2$ applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, $\alpha$ starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, $\alpha=1$. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.