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Chinese Physics

Head-on collision of ring dark solitons in Bose–Einstein condensates

Xue Ju-Kui, Peng Ping

Published May 31, 2006• 13 citations
Publisher

Abstract

The ring dark solitons and their head-on collisions in a Bose–Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincare–Lighthill–Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r−1/3 law and depend on the initial soliton amplitude and radius.

DOI
10.1088/1009-1963/15/6/005

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The ring dark solitons and their head-on collisions in a Bose–Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincare–Lighthill–Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r−1/3 law and depend on the initial soliton amplitude and radius.
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.
Interactions of solitary waves in a cylindrically confined Bose-Einstein condensate are investigated by simulating their head-on collisions. Slow vortex rings and fast solitons are found to collide elastically contrary to the situation in the three-dimensional homogeneous Bose gas. Strongly inelastic collisions are absent for low density condensates but occur at higher densities for intermediate velocities. The scattering behavior is rationalized by use of dispersion diagrams. During inelastic collisions, spherical shell-like structures of low density are formed and they eventually decay into depletion droplets with solitary-wave features. The relation to similar shells observed in a recent experiment by Ginsberg et al. [Phys. Rev. Lett. 94, 040403 (2005)] is discussed.
Abstract The collision between two chiral solitons in a Bose-Einstein Condensate (BEC) under density-dependent gauge potential is studied. By means of Poincaré-Lighthill-Kuo (PLK) perturbation method, the different kinds of colliding chiral soliton pairs self-consistently excited upon the background of the system are obtained analytically. The coupling of the current nonlinearity induced by the gauge potential and mean-field atomic interaction results in rich collision dynamics of chiral soliton pairs. When the atomic interaction is repulsive, head-on collisions of dark-dark and dark-bright solitons are observed. However, when the atomic interaction is attractive, unidirectional chiral dark soliton pairs are excited, and overtaking collision between two chiral dark solitons takes place. The phase shifts following the collision of soliton pairs are derived analytically and confirmed numerically. Interestingly, due to the contribution of the density-dependent gauge potential, the phase shifts of the two interacting chiral solitons are different from each other. This is distinct from the case without the density-dependent gauge potential, where the phase shifts of the two colliding ordinary solitons are the same. Thus, phase shifts of interacting chiral soliton pairs can be used to identify the chiral properties of solitons in BEC under density-dependent gauge potential. Furthermore, both elastic and inelastic collisions of chiral solitons in the system are presented numerically. The phase diagram for occurrence of elastic and inelastic collisions of chiral soliton is obtained, which strongly depends on the strength of density-dependent gauge potential.
The successive dynamical evolution of a Bose-Einstein condensate confined in a cylindrical well is numerically studied in the framework of the time-dependent Gross-Pitaevskii equation. Interference in the nonlinear matter wave leads to concentric density rings. The phase distribution exhibits a discontinuous sequence of plateaulike belts. Abrupt jumps in the phase between adjacent belts imply large radial superfluid velocity at the borderline. This, however, does not mean large particle current because the corresponding superfluid density is nearly zero. The density zeros along with the large gradient are identified as ring dark solitons, which have a brief lifetime before evolving into other soliton states.