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Mathematics and Computers in Simulation

Excited Bose–Einstein condensates: Quadrupole oscillations and dark solitons

Vassos Achilleos, Theodoros P. Horikis, Georgios Theocharis, P. G. Kevrekidis, D. J. Frantzeskakis

Published Aug 3, 2010• 0 citations
Publisher
DOI
10.1016/j.matcom.2010.07.019

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Collective modes of the ground and excited states of Bose–Einstein condensates are studied by numerical solution of the time-dependent Gross–Pitaevskii equation in three spatial dimensions. Scissors modes are studied by quadrupole excitation of the ground and excited states of 23 Na condensates in a fully anisotropic magnetic trap. The frequencies of the collective modes for the ground state condensates are found to be in good agreement with previous linear response theory. New results are presented for the frequencies of the collective modes for excited state condensates which exhibit solitary density depressions. A key to the proper characterization of the wide variety of dark-soliton states in atomic condensates is the experimental observation of collective modes.
We present two families of analytical solutions of the one-dimensional nonlinear Schr\"odinger equation, which describe the dynamics of bright and dark solitons in Bose-Einstein condensates (BECs) with the time-dependent interatomic interaction in an expulsive parabolic and complex potential. We also demonstrate that the lifetime of both a bright soliton and a dark soliton in BECs can be extended by reducing both the ratio of the axial oscillation frequency to radial oscillation frequency and the loss of atoms. It is interesting that a train of bright solitons may be excited with a strong enough background. An experimental protocol is further designed for observing this phenomenon.
The evolution characteristics of a Bose-Einstein condensate dark soliton with three-body interactions are investigated by the variational approach.The effects of a harmonic trapping potential on the motion of the dark soliton are discussed. It is shown that the dark soliton will oscillate in the harmonic potential. The trapping strength and the sign of three-body interactions affect the evolution of the dark soliton and change the oscillation characteristics of the Bose-Einstein condensate system.