Quantized quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity

Abstract

We investigate the localized nonlinear matter waves of the quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity in the harmonic potential. It is shown that all of the 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 properties are determined by the principal 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 phenomena in future experiments.