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Chinese Physics Letters

Fission and Fusion of Two Bright Solitons in a Growing Bose–Einstein Condensate

He Zhang-Ming, Denglong Wang, Weixi Zhang, Fengjiao Wang, Jianwen Ding

Published Sep 1, 2008• 7 citations
Publisher

Abstract

We analytically study the interaction characteristics of two bright solitons in a one-dimensional growing Bose–Einstein condensate with time-dependent periodic atomic scattering length. It is shown that the interaction between two bright solitons can generate fission and fusion in the presence of both time-dependent periodic atomic scattering length and the growing case. Furthermore, we propose experimental protocols to realize these interaction phenomena by varying the scattering length via the Feshbach resonance in the future experiment.

DOI
10.1088/0256-307x/25/9/018

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We analytically study the interaction characteristics of two bright solitons in a one-dimensional growing Bose–Einstein condensate with time-dependent periodic atomic scattering length. It is shown that the interaction between two bright solitons can generate fission and fusion in the presence of both time-dependent periodic atomic scattering length and the growing case. Furthermore, we propose experimental protocols to realize these interaction phenomena by varying the scattering length via the Feshbach resonance in the future experiment.
We present how to control interactions between solitons, either bright or dark, in Bose-Einstein condensates by synchronizing Feshbach resonance and harmonic trap. Our results show that as long as the scattering length is to be modulated in time via a changing magnetic field near the Feshbach resonance, and the harmonic trapping frequencies are also modulated in time, exact solutions of the one-dimensional nonlinear Schr\"odinger equation can be found in a general closed form, and interactions between two solitons are modulated in detail in currently experimental conditions. We also propose experimental protocols to observe the phenomena such as fusion, fission, warp, oscillation, elastic collision in future experiments.
By using Darboux transformation, this paper studies analytically the nonlinear dynamics of a one-dimensional growing Bose–Einstein condensate (BEC). It is shown that the growing model has an important effect on the amplitude of the soliton in the condensates. In the absence of the growing model, there exhibits the stable alternate bright solitons in the condensates. In the presence of the growing model, the obtained results show that the amplitude of the bright soliton decreases (increases) for the BEC growing coefficient Ω < 0 (Ω > 0). Furthermore, we propose experimental protocols to manipulate the amplitude of the bright soliton by varying the scattering length via the Feshbach resonance in the future experiment.
Considering the periodically driving linear potential, we study the interactions between two solitons in Bose-Einstein condensate (BEC). By using Darboux transformation, the double bright soliton solution of Gross-Pitaevskii equation is obtained. Then we numerically calculate the properties of interaction between the two bright solitons in BEC, and obtain a critical value of the S-wave scattering length (SL). It is shown that, when the SL is more than the critical value, the attractive interaction and the atom transfer between two bright solitons can be observed. While the SL is less than the critical value, two bright solitons can keep stable and localized. Furthermore, the stable periodic oscillations of two solitons can be observed by slowly changing the potential. These results will be conducive to the BEC soliton experiments.
Abstract By using the Crank–Nicolson method, we investigate numerically the dynamical properties of bright–bright solitons in two species Bose–Einstein condensates (BECs) trapped in an optical lattice. We confirm that the soliton splitting behavior occurs at a critical depth of optical potential. The splitting behavior of solitons and the fusion behavior of condensates can be accurately controlled by adjusting the depth and lattice parameter of optical potential, the initial amplitude and position of solitons, and the interspecies interactions. When the lattice parameter is fixed but the interspecies interaction increased exponentially with the time, each soliton splits into two soltions with different amplitude, and partial fusion of two species BECs can be found. While the interspecies interaction remains unchanged but the lattice parameter increases exponentially with the time, interestingly, the bright solitons with zero initial velocity can pass through each other and accomplish a transmission collision. Furthermore, for the case of both the interspecies interaction and lattice parameter increased exponentially with the time, a head-on collision of the bright solitons in two species BECs occurred. After the collision, each soliton splits into two soltions with equal amplitude. Meanwhile, the complete fusion of two species BECs can be observed. The relevant results can provide help for the precise manipulation of BECs experiments.
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.