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Chinese Physics Letters

Dark Lump Excitations in Bose—Einstein Condensates

Guoxiang Huang, 朱善华

Published Jan 1, 2002• 0 citations
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Abstract

We investigate the dynamics of two-dimensional matter-wave pulses in a Bose-Einstein condensate with diskshaped traps.For the case of repulsive atom-atom interactions,a Kadomtsev-Petviashvili equation with positive dipersion is derived using the method of multiple scales.The results show that it is possible to excite dark lump-like two-dimensional nonlinear excitations in the Bose-Einstein condensate.

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Journal of Physics A Mathematical and General•Nov 4, 2004•15 citations
We investigate the dynamics of two-dimensional matter-wave pulses in a Bose-Einstein condensate with diskshaped traps.For the case of repulsive atom-atom interactions,a Kadomtsev-Petviashvili equation with positive dipersion is derived using the method of multiple scales.The results show that it is possible to excite dark lump-like two-dimensional nonlinear excitations in the Bose-Einstein condensate.
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 study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases. A Kadomtsev—Petviashvili I (KPI) solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen—Cooper—Schrieffer (BCS) regime, Bose—Einstein condensate (BEC) regime, and unitarity regime. One-lump solution as well as one-line soliton solutions for the KPI equation are obtained, and two-line soliton solutions with the same amplitude are also studied in the limited cases. The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.
We study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases.A Kadomtsev-Petviashvili I(KPI) solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen-Cooper-Schrieffer(BCS) regime,Bose-Einstein condensate(BEC) regime,and unitarity regime.Onelump solution as well as one-line soliton solutions for the KPI equation are obtained,and two-line soliton solutions with the same amplitude are also studied in the limited cases.The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.
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.
The dynamics of the ring dark soliton in a Bose–Einstein condensate (BEC) with thin disc-shaped potential is investigated analytically and numerically. Analytical investigation shows that the ring dark soliton in the radial non-symmetric cylindrical BEC is governed by a cylindrical Kadomtsev–Petviashvili equation, while the ring dark soliton in the radial symmetric cylindrical BEC is governed by a cylindrical Korteweg–de Vries equation. The reduction to the cylindrical KP or KdV equation may be useful to understand the dynamics of a ring dark soliton. The numerical results show that the evolution properties and the snaking of a ring dark soliton are modified significantly by the trapping.