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arXiv:cond-mat/0306624 · Journal of Physics B Atomic Molecular and Optical Physics

Adiabatic compression of soliton matter waves

F. Kh. Abdullaev, Mario Salerno

Published Jun 19, 2003• 57 citations
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Abstract

The evolution of atomic solitary waves in Bose–Einstein condensate under adiabatic changes of the atomic scattering length is investigated. Variations of amplitude, width, and velocity of the soliton are found for both spatial and time adiabatic variations. The possibility of using these variations to compress solitons up to very high local matter densities is shown both in the absence and in the presence of a parabolic confining potential.

DOI
10.1088/0953-4075/36/13/314

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The evolution of atomic solitary waves in Bose–Einstein condensate under adiabatic changes of the atomic scattering length is investigated. Variations of amplitude, width, and velocity of the soliton are found for both spatial and time adiabatic variations. The possibility of using these variations to compress solitons up to very high local matter densities is shown both in the absence and in the presence of a parabolic confining potential.
An analytical study on the dynamics of bright solitons of Bose–Einstein condensates (BEC) with a time-varying atomic scattering length in a time-varying expulsive parabolic potential is presented. Exact solutions of the one-dimensional Gross–Pitaevskii equation are obtained. The results show that the bright soliton (including the higher-order bright soliton) can be compressed into a desired width and amplitude in a controllable manner by changing the scattering length and external potential. Furthermore, it is shown numerically that the present method is also efficient for the two-dimensional BEC's compression.
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We investigate dynamical effects of a bright soliton in Bose–Einstein condensed (BEC) systems with local and smooth space variations of the two-body atomic scattering length. It includes a discussion about the possible observation of a new type of standing nonlinear atomic matter wave in cigar-type traps. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. By considering an analytical time-dependent variational approach and also full numerical simulation of one-dimensional and three-dimensional Gross–Pitaevskii equations, we study processes such as trapping, reflection and transmission of the bright matter soliton due to the impurity. We also derive conditions for the collapse of the bright solitary wave, considering a quasi-one-dimensional BEC with attractive local inhomogeneity.