Generalized nonpolynomial Schrodinger equations for matter waves under anisotropic transverse confinement

TL;DR

This paper derives a 1D generalized nonpolynomial Schrödinger equation from the 3D Gross-Pitaevskii equation to accurately describe Bose-Einstein condensates under anisotropic transverse confinement and periodic potentials.

Contribution

It introduces a generalized 1D equation accounting for anisotropic transverse confinement and maps the 3D GPE with optical lattices to a discrete form, extending previous models.

Findings

Derivation of a 1D generalized nonpolynomial Schrödinger equation from 3D GPE.

Reduction to known equations in isotropic cases.

Mapping of 3D GPE with optical lattices to a discrete 1D form.

Abstract

Starting from the three-dimensional Gross-Pitaevskii equation we derive a 1D generalized nonpolynomial Schrodinger equation, which describes the dynamics of Bose-Einstein condensates under the action of a generic potential in the longitudinal axial direction and of an anisotropic harmonic potential in the transverse radial direction. This equation reduces to the familiar 1D nonpolynomial Schrodinger equation [Phys. Rev. A 65, 043614 (2002)] in the case of isotropic transverse harmonic confinement. In addition, we show that if the longitudinal potential models a periodic optical lattice the 3D GPE can be mapped into a 1D generalized discrete nonpolynomial Schrodinger equation.