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arXiv:0912.1432 · Physical Review A

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

Deng‐Shan Wang, Xinghua Hu, Jiangping Hu, Wu‐Ming Liu

Published Feb 25, 2010• 144 citations
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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.

DOI
10.1103/physreva.81.025604

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We investigate the profiles and stability of the localized nonlinear matter waves in a Bose–Einstein condensate with spatially inhomogeneous two- and three-body interactions in various external potentials both analytically and numerically. Several families of localized stationary solutions of the one-dimensional mean-field Gross–Pitaevskii equation with cubic–quintic nonlinearities are obtained by similarity transformation. It is shown that the whole Bose–Einstein condensate can have an infinite number of localized nonlinear matter waves determined by certain non-negative integers. The linear and dynamical stabilities of the localized stationary solutions are studied numerically, and some stable localized nonlinear matter waves are found. We demonstrate that the attractive inhomogeneous two- and three-body interactions support linearly and dynamically stable localized nonlinear matter waves, but attractive two-body interaction along with repulsive three-body interaction destroys the linear stability. Moreover, an anharmonic potential is proposed to stabilize the localized nonlinear matter waves in the Bose–Einstein condensate with spatially inhomogeneous interactions.
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