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Chinese Physics Letters

Soliton Solutions in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in an Expulsive Parabolic Potential

张解放, 杨琴

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

We present both the bright and dark solitons of Bose-Einstein condensates with a time-dependent atomic scattering length in an expulsive parabolic potential. As a discussed example, we select the experimental parameter, i.e. the Feshbach-managed nonlinear coefficient reading a(t) = go exp(λt), and obtain the results which can be recovered in the literature [Phys. Rev. Lett. 94 (2005) 050402].

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We present both the bright and dark solitons of Bose-Einstein condensates with a time-dependent atomic scattering length in an expulsive parabolic potential. As a discussed example, we select the experimental parameter, i.e. the Feshbach-managed nonlinear coefficient reading a(t) = go exp(λt), and obtain the results which can be recovered in the literature [Phys. Rev. Lett. 94 (2005) 050402].
Both dark and bright solitons are constructed exactly for a Bose–Einstein condensation with a time-dependent scattering length in an expulsive parabolic potential. It is shown analytically how the size of the cloud and the sharp peak of the condensate changes via the Feshbach resonance. It is also found that the atom loss due to three-body recombination can be controlled with the help of Feshbach resonance. The exact calculation is performed to compare the rate of the atom loss between the system with time-dependent scattering length in an expulsive parabolic potential and the system with constant scattering length.
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.
We analyze the dynamics of a bright soliton in Bose–Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential. Under a safe range of parameters in which the Gross–Pitaevskii (GP) equation is effective in one dimension, our results show that, the dynamics of the bright soliton can be classed into two phases, depending on the value of the scattering length. Meanwhile, there exists a critical value of the absolute value of the atomic scattering length, below which, the dynamics of the bright soliton is very regular. Those phenomena can be useful for developing concrete applications of the nonlinear matter waves. We also obtain the orbital equation of the bright soliton and get some interesting data which may be useful for the experimental observation of the bright soliton and the application of the atom laser with manipulated intensity.