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Chinese Physics Letters

（2＋1）—Dimensional Envelope Solitons in a Disk—Shaped Bose—Einstein Condensate

HUANGGuo-Xiang, Guoxiang Huang

Published Jan 1, 2003• 0 citations
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Abstract

We show that, due to the nonlinear coupling between a wavepacket superposed by short-wavelength collective modes and a long-wavelength mean field generated by the self-interaction of the wavepacket, the (2+1)-dimensional envelope solitons decaying in all spatial directions, i.e., dromions, are possible nonlinear excitations in a disk-shaped Bose-Einstein condensate with a repulsive interatomic interaction.

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We show that, due to the nonlinear coupling between a wavepacket superposed by short-wavelength collective modes and a long-wavelength mean field generated by the self-interaction of the wavepacket, the (2+1)-dimensional envelope solitons decaying in all spatial directions, i.e., dromions, are possible nonlinear excitations in a disk-shaped Bose-Einstein condensate with a repulsive interatomic interaction.

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We show that, due to the nonlinear coupling between a wavepacket superposed by short-wavelength collective modes and a long-wavelength mean field generated by the self-interaction of the wavepacket, the (2+1)-dimensional envelope solitons decaying in all spatial directions, i.e., dromions, are possible nonlinear excitations in a disk-shaped Bose-Einstein condensate with a repulsive interatomic interaction.
We study nonlinear modulation of collective excitations in disk-shaped Bose-Einstein condensates with a repulsive interatomic interaction. Using a method of multiple scales we show that the nonlinear evolution of a wave packet, formed by the superposition of short-wavelength excitations, and a long-wavelength mean field, generated by the self-interaction of the wave packet, are governed by Davey-Stewartson (DS) equations. Consequently, two-dimensional soliton (dromion) solutions can develop and propagate. We further derive a set of DS equations with variable coefficients for the situation where a slowly varying trapping potential in transverse directions has been taken into consideration. Finally, the dromion solutions and their stability are investigated by numerical simulations.
A three-wave resonant interaction of collective modes and related soliton excitations in a disk-shaped Bose–Einstein condensate are investigated. The phase-matching conditions for the resonant interaction are satisfied by suitably choosing the wavevectors and the frequencies of the collective modes. A set of nonlinearly coupled envelope equations describing the spatio-temporal evolution of the three-wave resonant interaction are derived by using a method of multiple-scales, and some explicit (2+1)-dimensional three-wave soliton solutions are also presented and discussed.
We consider, both analytically and numerically, the evolution of two-dimensional (2D) nonlinear matter-wave pulses in a Bose-Einstein condensate with a disk-shaped trap and repulsive atom-atom interactions. Due to the strong confinement in the axial direction the sound speed of the system is c=(1/21/4)c0,{c=(1/2}^{1/4}{)c}_{0},c=(1/21/4)c0​, where c0{c}_{0}c0​ is the corresponding value without the trap. From the 3D order-parameter equation of the condensate, we derive a soliton-bearing Kadomtsev-Petriashvili equation with positive dispersion. When the trapping potential is weak in two transverse directions, a low-depth plane dark soliton can propagate in the condensate with a changing profile but preserving its structure down to the boundary of the condensate. We show that high-depth plane dark solitons are unstable to long-wavelength transverse disturbances. The instability appears as a longitudinal modulation of the soliton amplitude decaying into vortices. We also show how a dark lumplike 2D nonlinear excitation can be excited in the system. Furthermore, a dark lump decaying algebraically in two spatial directions can propagate rather stable in the condensate, but disappears near the boundary of the condensate where two vortices are nucleated. The vortices move in opposite directions along the boundary and when meeting merge creating a new lump. Finally, we also provide results for head-on and oblique collisions of two lumps in the system.
We investigate, both analytically and numerically, the nonlinear dynamics of (2+1)-dimensional [(2+1)D] matter waves excited in a disk-shaped dipolar Bose-Einstein condensate (BEC) when quantum fluctuations described by the Lee-Huang-Yang (LHY) correction are taken into consideration. By using a method of multiple scales, we derive Davey-Stewartson I equations that govern the nonlinear evolution of matter-wave envelopes. We demonstrate that the system supports (2+1)D matter-wave dromions, which are superpositions of a short-wavelength excitation and a long-wavelength mean flow. We found that the stability of the matter-wave dromions can be enhanced by the LHY correction. We also found that such dromions display interesting behaviors of collision, reflection, and transmission when they interact with each other and are scattered by obstacles. The results reported here are useful not only for improving the understanding on the physical property of the quantum fluctuations in BECs, but also for possible experimental findings of new nonlinear localized excitations in systems with long-ranged interactions.
For two-component disk-shaped Bose–Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a Kadomtsev–Petviashvili-I equation at the lowest order from the original coupled Gross–Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev–Petviashvili-I equation are given, therefore, the wave functions of both atomic gases are obtained as well. The instability of a soliton under higher-order long wavelength disturbance has been investigated. It is found that the instability depends on the angle between two directions of both soliton and disturbance.