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arXiv:cond-mat/0201155 · Physical Review A

Generation and interaction of solitons in Bose-Einstein condensates

Sven Burger, Lincoln D. Carr, Patrik Öhberg, K. Sengstock, Anna Sanpera

Published Apr 1, 2002• 61 citations
arXivHTMLPDF

Abstract

Generation, interaction, and detection of dark solitons in Bose-Einstein condensates are studied. In particular, we focus on the dynamics resulting from phase imprinting and density engineering. We show that solitons slow down significantly when the trap is opened and that soliton phase shifts after binary interactions cannot be observed with present experiments. Finally, motivated by the recent experimental results of Cornish et al. [Phys. Rev Lett. 85, 1795 (2000)], we analyze the stability of dark solitons under changes of the scattering length and thereby demonstrate a new way to detect them. Our theoretical and numerical results compare well with the existing experimental ones and provide guidance for future experiments.

DOI
10.1103/physreva.65.043611

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Generation, interaction, and detection of dark solitons in Bose-Einstein condensates are studied. In particular, we focus on the dynamics resulting from phase imprinting and density engineering. We show that solitons slow down significantly when the trap is opened and that soliton phase shifts after binary interactions cannot be observed with present experiments. Finally, motivated by the recent experimental results of Cornish et al. [Phys. Rev Lett. 85, 1795 (2000)], we analyze the stability of dark solitons under changes of the scattering length and thereby demonstrate a new way to detect them. Our theoretical and numerical results compare well with the existing experimental ones and provide guidance for future experiments.
Abstract: In this thesis we experimentally observe the dynamics of dark solitons in elongated Bose-Einstein condensates (BEC) in the crossover regime between 1D and 3D. Dark solitons are dynamically stable in this regime. This allows the observation of the collisional and oscillational dynamics of two dark solitons in a harmonically confined BEC over several oscillation periods. We can detect the repulsive intersolitonic interaction as an increase of the oscillation frequency of the two solitons strongly depending on their mean distance. Thereby we give the first experimental evidence of the theoretically predicted repulsive interaction between the solitons. We compare our experimental findings to numerical simulations of the Gross-Pitaevskii equation and effective 1D equations. Additionally we develop a model in which the solitons are approximated by repulsively interacting classical particles. This model is based on a soliton interaction potential suggested by [Kiv1995] and can describe the essentials of the soliton dynamics. We observe well agreement between the soliton oscillation frequencies measured in the experiment, the numerical simulations and the results of the particle model. Besides we verify the theoretical prediction that the oscillation frequency of dark solitons in a harmonically confined BEC should be slower than the trap frequency.
The dynamics of a dark soliton in an elongated Bose-Einstein condensate is studied at finite temperatures. In addition to accurately reproducing all stages of the decay of the soliton observed in the experiment of Burger et al. [Phys. Rev. Lett. 83, 5198 (1999)], our numerical simulations reveal the existence of an experimentally accessible parameter regime for which phase-imprinted dark solitons can execute at least one full axial oscillation prior to their decay. The dependence of the decay time scale on temperature and initial soliton depth is analyzed and the role of interatomic collisions quantified.
Summary form only given. Bose-Einstein condensates (BEC) of weakly interacting gases allow for the new regime of nonlinear atom optics. Of special interest are macroscopically excited states like dark solitons or vortices. Solitons, as particle like excitations of matter wave fields, provide a link from condensate physics to fluid mechanics, nonlinear optics and fundamental particle physics. Dark solitons in matter waves are characterized by a local density minimum and, a steep phase gradient of the wavefunction at the position of the minimum. We report on experimental and theoretical investigation of dark solitons in BECs of /sup 87/Rb which are produced by the method of phase imprinting. A highly anisotropic confining potential allows us to be close to the (quasi) 1D situation where dark solitons are expected to be dynamically stable. By monitoring the evolution of the density profile we observe the evolution of density minima travelling at a smaller velocity than the speed of sound. By comparison to analytical and numerical solutions of the 3D Gross-Pitaevskii equation for our experimental conditions we identify these density minima to be moving dark solitons. We have studied in detail the creation and the dynamics of dark solitons as a function of evolution time and imprinted phase.
The dynamics of a dark soliton in an elongated Bose-Einstein condensate is studied at finite temperatures. In addition to accurately reproducing all stages of the decay of the soliton observed in the experiment of Burger [Phys. Rev. Lett. 83, 5198 (1999)], our numerical simulations reveal the existence of an experimentally accessible parameter regime for which phase-imprinted dark solitons can execute at least one full axial oscillation prior to their decay. The dependence of the decay time scale on temperature and initial soliton depth is analyzed and the role of interatomic collisions quantified. © 2007 The American Physical Society.
The creation, interaction, observation and stability of dark solitons in two-component condensates are investigated. As a first scenario, we consider the case of miscible components, analysing the creation of solitons in different components via phase-imprinting, and the soliton-soliton interaction in different situations, which include the formation of a soliton-soliton binary system and free single solitons accompanied by a filling of the other component. The different regimes of interaction are analysed numerically, and compared with a variational calculation. The observability of the solitons and their stability are also analysed. In a second scenario, we study the soliton propagation in the presence of domains, and show that a dark soliton can be transferred from one component to the other at the domain wall when exceeding a critical velocity.
We present experiments investigating different aspects concerning the coherent manipulation of a Bose-Einstein condensate wavefunction with far blue detuned dipole potentials. In a first set of experiments we study a waveguide for matter waves as an important atom optical element allowing to hold and guide the atoms for long observation times. We present a flexible realization of this waveguide based on a tube shaped Laguerre Gaussian laser beam and investigate the dynamics of a Bose condensed ensemble transferred into this guide. In a second set of experiments we study the dynamics of dark solitons created by the manipulation of the phase of the condensate wave function by temporally applied dipole potentials. This method of phase imprinting represents a powerful tool for the design of matter waves and the controlled creation of various excitations. The dynamics of dark solitons in matter waves is investigated in detail by experimentally and numerically studying the temporal evolution of the condensate density as well as by mapping the velocity field of the excited condensate wavefunction. In these measurements we directly detect the flux of the wave function associated with the dark soliton using spatially resolved Bragg scattering. Experiments investigating the creation and interaction of several dark solitons conclude this chapter.