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Dark-soliton dynamics in Bose-Einstein condensates at finite temperature

B. Jackson, Nick P. Proukakis, Carlo Barenghi

Published Dec 31, 2007• 0 citations
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Abstract

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.

DOI
10.25405/ncl.34634592

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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 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.
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.
During the last decade the physics of ultracold quantum gases has matured into a highly active and versatile field of research. Experiments dedicated to the physics of Bose-Einstein condensates have been performed and diverse phenomena, which are distinguished by fundamentally different regimes of interaction, can be investigated. Particularly solitons, characterized as non-spreading wavepackets, are stabilized against dispersion by a suitable non-linear interaction and can propagate in a condensate[1,2]. In the present work the dynamical evolution of long-lived dark solitons has been studied as a paradigm of non-linear physics for the first time. We have been able to observe oscillations of dark solitons in elongated Bose-Einstein condensates and good agreement with the theoretically predicted oscillation frequency of ω/√2 has been obtained [1]. Moreover the results of detailed studies of the collision of two dark solitons distinguished by different depths are presented. This particular feature enables the identification of the individual solitons beyond the actual collision process and as a central result we show shown that these peculiar entities interpenetrate without significantly influencing each other [3]. The theoretical description of solitons as weakly interacting quasi particles is in good agreement with these findings. Continuative studies on vectorial “dark-bright” solitons and their dynamical properties complement the investigations on dark solitons.
The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark-soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long-lived soliton trajectories within each ensemble of numerical realizations [S. P. Cockburn et al., Phys. Rev. Lett. 104, 174101 (2010)]. Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based upon the dissipative Gross-Pitaevskii model (with the same ab initio damping). Probing the regime for which 0.8 ${k}_{B}T<\ensuremath{\mu}<1.6$ kBT{k}_{B}TkB​T, we find average soliton lifetimes to scale with temperature as $\ensuremath{\tau}\ensuremath{\sim}{T}^{\ensuremath{-}4}$, in agreement with predictions previously made for the low-temperature regime ${k}_{B}T\ensuremath{\ll}\ensuremath{\mu}$. The model is also shown to capture the experimentally relevant decrease in the visibility of an oscillating soliton due to the presence of background fluctuations.