Bright solitons in ultracold atoms

TL;DR

This paper reviews the experimental and theoretical understanding of bright solitons in Bose-Einstein condensates of alkali-metal atoms, focusing on derivations of the governing equations and comparison with experimental results.

Contribution

It derives the 3D and reduced 1D equations for bright solitons and compares theoretical predictions with experimental data.

Findings

Derivation of 3D Gross-Pitaevskii equation from many-body interactions.

Reduction to 1D GPE and NPSE for confined condensates.

Comparison of theoretical soliton solutions with experimental observations.

Abstract

We review old and recent experimental and theoretical results on bright solitons in Bose-Einstein condensates made of alkali-metal atoms and under external optical confinement. First we deduce the three-dimensional Gross-Pitaevskii equation (3D GPE) from the Dirac-Frenkel action of interacting identical bosons within a time-dependent Hartree approximation. Then we discuss the dimensional reduction of the GPE from 3D to 1D, deriving the 1D GPE and also the 1D nonpolynomial Schr\"odinger equation (1D NPSE). Finally, we analyze the bright solition solutions of both 1D GPE and 1D NPSE and compare these theoretical predictions with the available experimental data.