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arXiv:0808.3831 · Physical Review A

Controlling soliton interactions in Bose-Einstein condensates by synchronizing the Feshbach resonance and harmonic trap

Xiao-Fei Zhang, Qin Yang, Jie-Fang Zhang, Xiaohang Chen, W. M. Liu

Published Feb 11, 2008• 100 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.77.023613

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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.
We consider the one-dimensional nonlinear Schrödinger equations that describe the dynamics of a Bose–Einstein Condensates with time-dependent scattering length in a complex potential. Our results show that as long as the integrable relation is satisfied, exact solutions of the one-dimensional nonlinear Schrödinger equation can be found in a general closed form, and interactions between two solitons are modulated in a complex potential. We find that the changes of the scattering length and trapping potential can be effectively used to control the interaction between two bright soliton.
We present three families of exact matter-wave soliton solutions for an effective one-dimension two-component Bose—Einstein condensates (BECs) with tunable interactions, harmonic potential and gain or loss term. We investigate the dynamics of bright-bright solitons, bright-dark solitons and dark-dark solitons for the time-dependent expulsive harmonic trap potential, periodically modulated harmonic trap potential, and kinklike modulated harmonic trap potential. Through the Feshbach resonance, these dynamics can be realized in experiments by suitable control of time-dependent trap parameters, atomic interactions, and interaction with thermal cloud.
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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.
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