Formation of soliton trains in Bose-Einstein condensates as a nonlinear Fresnel diffraction of matter waves

TL;DR

This paper presents an analytical framework for understanding how soliton trains form in elongated Bose-Einstein condensates, modeling it as a nonlinear Fresnel diffraction of matter waves, supported by simulations and experiments.

Contribution

It provides a complete analytical solution for soliton train formation in BECs with sharp density boundaries using Whitham theory, linking it to nonlinear wave diffraction.

Findings

Analytical solution matches numerical simulations.

Soliton train formation resembles nonlinear Fresnel diffraction.

Experimental data confirms theoretical predictions.

Abstract

The problem of generation of atomic soliton trains in elongated Bose-Einstein condensates is considered in framework of Whitham theory of modulations of nonlinear waves. Complete analytical solution is presented for the case when the initial density distribution has sharp enough boundaries. In this case the process of soliton train formation can be viewed as a nonlinear Fresnel diffraction of matter waves. Theoretical predictions are compared with results of numerical simulations of one- and three-dimensional Gross-Pitaevskii equation and with experimental data on formation of Bose-Einstein bright solitons in cigar-shaped traps.