Temporal evolution of attractive Bose-Einstein condensate in a quasi 1D cigar-shape trap modeled through the semiclassical limit of the focusing Nonlinear Schroedinger Equation

TL;DR

This paper explores the evolution of attractive Bose-Einstein condensates in a quasi-1D trap using the semiclassical limit of the focusing nonlinear Schrödinger equation, revealing ordered structures amidst modulation instability.

Contribution

It applies semiclassical analysis of the focusing NLS to describe phenomena in attractive BECs, highlighting ordered structures and proposing new observables.

Findings

Ordered structures in semiclassical NLS solutions

Bright soliton phenomena in BEC dynamics

Potential new observables for BEC evolution

Abstract

One-dimensional (1D) Nonlinear Schroedinger Equaation (NLS) provides a good approximation to attractive Bose-Einshtein condensate (BEC) in a quasi 1D cigar-shaped optical trap in certain regimes. 1D NLS is an integrable equation that can be solved through the inverse scattering method. Our observation is that in many cases the parameters of the BEC correspond to the semiclassical (zero dispersion) limit of the focusing NLS. Hence, recent results about the strong asymptotics of the semiclassical limit solutions can be used to describe some interesting phenomena of the attractive 1D BEC. In general, the semiclassical limit of the focusing NLS exibits very strong modulation instability. However, in the case of an analytical initial data, the NLS evolution does displays some ordered structure, that can describe, for example, the bright soliton phenomenon. We discuss some general features of the semiclassical NLS evolution and propose some new observables.