Quantized Quasi-Two Dimensional Bose-Einstein Condensates with Spatially Modulated Nonlinearity

TL;DR

This paper explores exact localized nonlinear matter waves in quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity, revealing their quantum properties and proposing an experimental observation method.

Contribution

It provides mathematically exact solutions for localized nonlinear waves in BECs with spatially varying nonlinearity, detailing their quantum and topological properties.

Findings

Existence of arbitrary localized nonlinear matter waves with discrete energies

Wave functions' parity depends on quantum number n

Number of density packets depends on quantum numbers n and l

Abstract

We investigate the localized nonlinear matter waves of the quasi-two dimensional Bose-Einstein condensates with spatially modulated nonlinearity in harmonic potential. It is shown that the whole Bose-Einstein condensates, similar to the linear harmonic oscillator, can have an arbitrary number of localized nonlinear matter waves with discrete energies, which are mathematically exact orthogonal solutions of the Gross-Pitaevskii equation. Their novel properties are determined by the principle quantum number n and secondary quantum number l: the parity of the matter wave functions and the corresponding energy levels depend only on n, and the numbers of density packets for each quantum state depend on both n and l which describe the topological properties of the atom packets. We also give an experimental protocol to observe these novel phenomena in future experiments.