Above-Barrier Reflection of Cold Atoms by Resonant Laser Light within the Gross-Pitaevskii Approximation

TL;DR

This paper analytically investigates how nonlinearity affects above-barrier reflection of cold atoms by resonant laser light within the Gross-Pitaevskii framework, deriving correction formulas and comparing with numerical results.

Contribution

It introduces a perturbative correction for reflection coefficients accounting for weak nonlinearity in the Gross-Pitaevskii approximation.

Findings

Nonlinearity increases reflection near the barrier height.

Derived correction formulas for reflection coefficients.

Results agree with numerical simulations.

Abstract

Above-barrier reflection of cold alkali atoms by resonant laser light was considered analytically within the Gross-Pitaevskii approximation. Correction for the reflection coefficient because of a weak nonlinearity of the stationary Schroedinger equation has been derived using multiscale analysis as a form of perturbation theory. The nonlinearity adds spatial harmonics to linear incident and reflecting waves. It was shown that the role of nonlinearity increases when the kinetic energy of an atom is nearly to the height of the potential barrier. Results are compared to the known numerical derivations for wave functions of the Gross-Pitaevskii equation with the step potential.