Nonlinear Schrodinger equations with a multiple-well potential and a Stark-type perturbation

TL;DR

This paper demonstrates that a Bose-Einstein condensate in a lattice with a Stark perturbation can be modeled by a finite-dimensional discrete nonlinear Schrödinger equation, revealing oscillatory behavior influenced by initial conditions and nonlinearity.

Contribution

It provides a reduction of the Gross-Pitaevskii equation to a discrete nonlinear Schrödinger model and explores the oscillation dynamics of the condensate's center of mass.

Findings

Oscillating behavior of the BEC's center of mass depends on initial wavefunction shape.

Oscillation period is affected by the nonlinear interaction strength.

The results raise questions about using oscillation measurements to determine gravitational constants.

Abstract

A Bose-Einstein condensate (BEC) confined in a one-dimensional lattice under the effect of an external homogeneous field is described by the Gross-Pitaevskii equation. Here we prove that such an equation can be reduced, in the semiclassical limit and in the case of a lattice with a finite number of wells, to a finite-dimensional discrete nonlinear Schrodinger equation. Then, by means of numerical experiments we show that the BEC's center of mass exhibits an oscillating behavior with modulated amplitude; in particular, we show that the oscillating period actually depends on the shape of the initial wavefunction of the condensate as well as on the strength of the nonlinear term. This fact opens a question concerning the validity of a method proposed for the determination of the gravitational constant by means of the measurement of the oscillating period.