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Acta Physica Sinica

Soliton dynamical behavior of the condensates trapped in a square-well potential

Bo Zhang, Denglong Wang, She Yan-Chao, Weixi Zhang

Published Jan 1, 2013• 1 citation
Publisher

Abstract

Using multiple-scale method, we study analytically the soliton dynamical behaviors of the Bose-Einstein condensates trapped in a square-well potential. It is found that the square-well potential has important effects on the soliton dynamics. When the soliton goes into the square-well potential, its movement is accelerated; while it leaves the square-well potential, the soliton is decelerated. With the increase in depth of the square-well potential, the velocity of the soliton increases, and its amplitude becomes larger and its width decreases. This may serve as a reference effect for controlling the dynamical characteristics of the soliton in experiments.

DOI
10.7498/aps.62.110501

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Using multiple-scale method, we study analytically the soliton dynamical behaviors of the Bose-Einstein condensates trapped in a square-well potential. It is found that the square-well potential has important effects on the soliton dynamics. When the soliton goes into the square-well potential, its movement is accelerated; while it leaves the square-well potential, the soliton is decelerated. With the increase in depth of the square-well potential, the velocity of the soliton increases, and its amplitude becomes larger and its width decreases. This may serve as a reference effect for controlling the dynamical characteristics of the soliton in experiments.
By using multiple-scale method, we analytically study the soliton dynamics of Bose–Einstein condensate (BEC) trapped in a double square well potential. It is shown that dark soliton can be stable, which is generated in BEC trapped in a double square well. The amplitude and the width of dark soliton are related to the initial position of the soliton. Within the double square well, because of the confinement of the potential, the amplitude of the dark soliton is larger, while the width of the dark soliton is smaller. Furthermore, we also find that the amplitude and the width of the soliton are closely related to the depth of the double square well. With the increase of the depth, the amplitude of the dark soliton increases remarkably, while the width of the dark soliton decreases slowly.
We first present an analytical solution of the single and double solitions of Bose—Einstein condensates trapped in a double square well potential using the multiple-scale method. Then, we show by numerical calculation that a dark soliton can be transmitted through the square well potential. With increasing depth of the square well potential, the amplitude of the dark soliton becomes larger, and the soliton propagates faster. In particular, we treat the collision behaviour of the condensates trapped in either equal or different depths of the double square well potential. If we regard the double square well potential as the output source of the solitons, the collision locations (position and time) between two dark solitons can be controlled by its depth.
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.
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By using a multiple-scale method, we analytically study the effect of a localized impurity on the soliton dynamics in the Bose-Einstein condensates. It is shown that a dark soliton can be transmitted through a repulsive (or attractive) impurity, while at the position of the localized impurity the soliton can be quasitrapped by the impurity. Additionally, we find that the strength of the localized impurity has an important effect on the dark soliton dynamics. With increasing strength of the localized impurity, the amplitude of the dark soliton becomes bigger, while its width is narrower, and the soliton propagates slower.
We present an analytical solution of two solitons of Bose—Einstein condensates trapped in a double-barrier potential by using a multiple-scale method. In the linear case, we find that the stable spots of the soliton formation are at the top of the barrier potential and at the region of barrier potential absence. For weak nonlinearity, it is shown that the height of the barrier potential has an important effect on the dark soliton dynamical properties. Especially, in the case of regarding a double-barrier potential as the output source of the solitons, the collision spots between two dark solitons can be controlled by the height of the barrier potential.