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arXiv:cond-mat/0206184 · Physical Review Letters

Bright Soliton Trains of Trapped Bose-Einstein Condensates

Usama Al Khawaja, Henk T. C. Stoof, Randall G. Hulet, Kevin E. Strecker, Guthrie B. Partridge

Published Oct 29, 2002• 219 citations
arXivHTMLPDF

Abstract

We variationally determine the dynamics of bright soliton trains composed of harmonically trapped Bose-Einstein condensates with attractive interatomic interactions. In particular, we obtain the interaction potential between two solitons. We also discuss the formation of soliton trains due to the quantum mechanical phase fluctuations of a one-dimensional condensate.

DOI
10.1103/physrevlett.89.200404

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We variationally determine the dynamics of bright soliton trains composed of harmonically trapped Bose-Einstein condensates with attractive interatomic interactions. In particular, we obtain the interaction potential between two solitons. We also discuss the formation of soliton trains due to the quantum mechanical phase fluctuations of a one-dimensional condensate.
The dynamics of a bright—bright vector soliton in cigar-shaped Bose—Einstein condensate trapping in a harmonic potential is studied. The interaction between bright solitons in different species with small separation is derived. Unlike the interaction between solitons of the same species, it is independent of the phase difference between the solitons, and may be of attraction or repulsion. In the former case, each soliton will oscillate about and pass through each other around the mass center of the system, which will also oscillate harmonically due to harmonic trapping potential.
We model the formation of bright atomic solitons due to collapse of Bose-Einstein condensates with attractive interactions reported by S. L. Cornish et al., [Phys. Rev. Lett. 96 170401 (2006)] in a realistic three dimensional situation. We show that mean-field theory does not adequately explain the experiment, while the inclusion of quantum fluctuations gives rise to bright soliton formation at the appropriate time scales. The solitons are produced either in-phase or out-of-phase and their number increases with the strength of the attractive interaction.
The dynamics of a bright-bright vector soliton in a cigar-shaped Bose-Einstein condensate trapping in a harmonic potential is studied.The interaction between bright solitons in different species with small separation is derived.Unlike the interaction between solitons of the same species,it is independent of the phase difference between solitons.It may be of attraction or repulsion.In the former case,each soliton will oscillate about and pass through each other around the mass-center of the system,which will also oscillate harmonically due to the harmonic trapping potential.
The dynamics of a bright-bright vector soliton in a cigar-shaped Bose-Einstein condensate trapping in a harmonic potential is studied. The interaction between bright solitons in different species with small separation is derived. Unlike the interaction between solitons of the same species, it is independent of the phase difference between solitons. It may be of attraction or repulsion. In the former case, each soliton will oscillate about and pass through each other around the mass-center of the system, which will also oscillate harmonically due to the harmonic trapping potential.
We demonstrate fast control of the interatomic interactions in a Bose-Einstein condensate by coherently coupling two atomic states with intra- and interstate scattering lengths of opposite signs. We measure the elastic and inelastic scattering properties of the system and find good agreement with a theoretical model describing the interactions between dressed states. In the attractive regime, we observe the formation of bright solitons formed by dressed-state atoms. Finally, we study the response of the system to an interaction quench from repulsive to attractive values, and observe how the resulting modulational instability develops into a bright soliton train.
We review recent experimental and theoretical work on the creation of bright matter wave solitons in Bose–Einstein condensates. In two recent experiments, solitons are formed from Bose–Einstein condensates of 7 Li by utilizing a Feshbach resonance to switch from repulsive to attractive interactions. The solitons are made to propagate in a one-dimensional potential formed by a focused laser beam. For repulsive interactions, the wavepacket undergoes dispersive wavepacket spreading, while for attractive interactions, localized solitons are formed. In our experiment, a multi-soliton train containing up to ten solitons is observed to propagate without spreading for a duration of 2 s. Adjacent solitons are found to interact repulsively, in agreement with a calculation based on the nonlinear Schrödinger equation assuming that the soliton train is formed with an alternating phase structure. The origin of this phase structure is not entirely clear.