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Science Technology and Engineering

Soliton Properties in the Condensation with the Three-body Interactions

Wenli Li

Published Jan 1, 2010• 0 citations
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Abstract

Soliton properties in one-dimensional Bose-Einstein condensation with the three-body interactions are studied analytically.It is shown that the dark soliton in the condensation is still stable propagation under the consideration of the three-body interactions.And the three-body interactions have an important effect on its soliton properties.With the increasing the three-body interactive strength,the amplitude of the soliton keeps unchanged,however,the width of the soliton becomes narrower.

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Soliton properties in one-dimensional Bose-Einstein condensation with the three-body interactions are studied analytically.It is shown that the dark soliton in the condensation is still stable propagation under the consideration of the three-body interactions.And the three-body interactions have an important effect on its soliton properties.With the increasing the three-body interactive strength,the amplitude of the soliton keeps unchanged,however,the width of the soliton becomes narrower.
By using multiple-scale method, we study analytically the soliton characteristics of the two-dimensional condensates with two- and three-body interaction. The results show that a ring dark soliton can be found in the condensates when the two-body interaction is repulsive and three-body interaction is attractive. With the strength of the three-body interaction decreasing, the height of the center peak of the ring dark soliton decreases. When the three-body interaction vanishes, the ring dark soliton becomes a perfect dark soliton. If the two- and the three-body interaction are both repulsive,the width and the amplitude of the dark soliton decrease with the strength of the three-body interaction increasing. Especially, if the strength of the three-body interaction is large, which is on the order of that of the two-body interaction, the condensat collapse takes place.
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.
The stability properties of dark solitons in quasi-one-dimensional Bose-Einstein condensate (BEC) loaded in a Jacobian elliptic sine potential with three-body interactions are investigated theoretically. The solitons are obtained by the Newton-Conjugate Gradient method. A stationary cubic-quintic nonlinear Schrödinger equation is derived to describe the profiles of solitons via the multi-scale technique. It is found that the three-body interaction has distinct effect on the stability properties of solitons. Especially, such a nonlinear system supports the so-called dark solitons (kink or bubble), which can be excited not only in the gap, but also in the band. The bubbles are always linearly and dynamically unstable, and they cannot be excited if the three-body interaction is absent. Both stable and unstable kinks, depending on the physical parameters, can be excited in the BEC system.
By using the multiple-scale method, this paper analytically studies the effect of a barrier potential on the dynamical characteristics of the soliton in Bose–Einstein condensates. It is shown that a stable soliton is exhibited at the top of the barrier potential and the region of the absence of the barrier potential. Meanwhile, it is found that the height of the barrier potential has an important effect on the dark soliton dynamical characteristics in the condensates. With the increase of height of the barrier potential, the amplitude of the dark soliton becomes smaller, its width is narrower, and the soliton propagates more slowly.
For the first time, we find the complex solitons for a quasi-one-dimensional Bose-Einstein condensate with two-and three-body interactions. These localized solutions are characterized by a power law behaviour. Both dark and right solitons can be excited in the experimentally allowed parameter domain, when two-and three-body interactions are,respectively, repulsive and attractive. The dark solitons travel with a constant speed, which is quite different from the Lieb mode, where profiles with different speeds, bounded above by sound velocity, can exist for specified interaction strengths. We also study the properties of these solitons in the presence of harmonic confinement with time-dependent nonlinearity and loss. The modulational instability and the Vakhitov-Kolokolov criterion of stability are also studied.
The evolution characteristics of the Bose-Einstein Condensate(BEC) soliton with three-body interactions are investigated with a variational approach and direct numerical simulations of the Gross-Pitaevskii-Ginzburg equation.It is found that the effects of the three-body interactions on the evolution characteristics of the BEC soliton are larger than the effecs of the two-body interactions.Its effect depends on the sign of the interactions,the number of atoms in the trap,the coefficient of the trap and the initial pulse width of the BECs soliton.