Dimensional reduction and localization of a Bose-Einstein condensate in a quasi-1D bichromatic optical lattice

TL;DR

This paper investigates how interactions affect the localization of a Bose-Einstein condensate in a quasi-one-dimensional bichromatic optical lattice, using numerical solutions of the Gross-Pitaevskii equation derived from a dimensional reduction.

Contribution

It derives a reduced 1D Gross-Pitaevskii equation from 3D theory and demonstrates how repulsive interactions suppress localization in a bichromatic optical lattice.

Findings

Localization is suppressed when the scattering length is large.

Derived coupled equations reduce to the 1D GPE under certain conditions.

Numerical analysis confirms the impact of interactions on localization.

Abstract

We analyze the localization of a Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasi-periodic optical-lattice potential by numerically solving the 1D Gross-Pitaevskii equation (1D GPE). We first derive the 1D GPE from the dimensional reduction of the 3D quantum field theory of interacting bosons obtaining two coupled differential equations (for axial wavefuction and space-time dependent transverse width) which reduce to the 1D GPE under strict conditions. Then, by using the 1D GPE we report the suppression of localization in the interacting BEC when the repulsive scattering length between bosonic atoms is sufficiently large.