Experimental Observation of Oscillating and Interacting Matter Wave Dark Solitons

Weller, Andreas; Ronzheimer, Jens Philipp; Groß, Christian; Estève, Jérôme; Oberthaler, Markus K.; Frantzeskakis, D. J.; Theocharis, G.; Kevrekidis, P. G.

doi:10.1103/physrevlett.101.130401

Cited by 302 publications

(425 citation statements)

References 36 publications

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“…One can thus straightforwardly generalize the above equation for N -interacting DB-soliton states, similar to the case of multiple dark solitons in one-component BECs [13,14,38]. Importantly, the presence of the trap allows for the existence of stationary DB-soliton molecules not only for out-of-phase bright solitons (as in the homogeneous case) but also for in-phase bright solitons.…”

Section: Multiple Dark-bright Solitons In the Trapmentioning

confidence: 99%

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Multiple dark-bright solitons in atomic Bose-Einstein condensates

et al. 2011

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Motivated by recent experimental results, we present a systematic theoretical analysis of dark-bright-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component Bose-Einstein condensates. We study analytically the interactions between two dark-bright solitons in a homogeneous condensate and then extend our considerations to the presence of the trap. We illustrate the existence of robust stationary dark-bright-soliton "molecules," composed of two or more solitons, which are formed due to the competition of the interaction forces between the dark-and bright-soliton components and the trap force. Our analysis is based on an effective equation of motion, derived for the distance between two dark-bright solitons. This equation provides equilibrium positions and characteristic oscillation frequencies of the solitons, which are found to be in good agreement with the eigenfrequencies of the anomalous modes of the system.

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Section: Multiple Dark-bright Solitons In the Trapmentioning

confidence: 99%

“…The latter works have finally realized oscillating, and even interacting, robust dark solitons in atomic BECs. This has been achieved by means of various techniques, including phase-imprinting and density engineering [10][11][12], matter-wave interference [13,14], and dragging localized defects through the BECs [15].…”

Section: Introductionmentioning

confidence: 99%

Multiple dark-bright solitons in atomic Bose-Einstein condensates

et al. 2011

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“…[541][542][543] on various higher dimensional aspects of BECs in random potentials and transitions associated with Anderson localization (we thank Dr. B. Shapiro for bringing these works to our attention) and the intense experimental activity on the oscillations and interactions of dark and darkbright solitons in Refs. [544,545].…”

Section: Beyond Mean-field Descriptionmentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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Abstract. The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.PACS numbers: 03.75. Kk, 03.75.Lm, 05.45 • EP: Ermakov-Pinney (Equation)• GP: Gross-Pitaevskii (Equation)• KdV: Korteweg-de Vries (Equation)• LS: Lyapunov-Schmidt (Technique)• MT: Magnetic Trap• NLS: Nonlinear Schrödinger (Equation)• NPSE: Non-polynomial Schrödinger Equation IntroductionThe phenomenon of Bose-Einstein condensation is a quantum phase transition originally predicted by Bose [1] and Einstein [2,3] in 1924. In particular, it was shown that below a critical transition temperature T c , a finite fraction of particles of a boson gas (i.e., whose particles obey the Bose statistics) condenses into the same quantum state, known as the Bose-Einstein condensate (BEC). Although BoseEinstein condensation is known to be a fundamental phenomenon, connected, e.g., to superfluidity in liquid helium and superconductivity in metals (see, e.g., Ref.[4]), BECs were experimentally realized 70 years after their theoretical prediction: this major achievement took place in 1995, when different species of dilute alkali vapors confined in a magnetic trap (MT) were cooled down to extremely low temperatures [5][6][7], and has already been recognized through the 2001 Nobel prize in Physics [8,9]. This first unambiguous manifestation of a macroscopic quantum state in a manybody system sparked an explosion of activity, as reflected by the publication of several thousand papers related to BECs since then. Nowadays there exist more than fifty experimental BEC groups around the world, while an enormous amount of theoretical work has followed and driven the experimental efforts, with an impressive impact on many branches of Physics.From a theoretical standpoint, and for experimentally relevant conditions, the static and dynamical properties of a BEC can be described by means of an effective mean-field equation known as the Gross-Pitaevskii (GP) equation [10,11]. This is a variant of the famous nonlinear Schrödinger (NLS) equation [12] (incorporating an external potential used to confine th...

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“…While these were designed to measure the speed of sound, these studies very early on elicited somewhat controversial [11] theoretical suggestions that dark solitons had been created in the process [3,[12][13][14][15]. Similar experiments have led to the observation of a variety of defects [1,[16][17][18], while other studies engineered localized excitations through phase imprinting [4][5][6][19][20][21]. The theory associated with these experiments has suggested that solitons, or vortices or vortex rings (in some combination or sequentially) are created in the process [4,[6][7][8][22][23][24][25].…”

Section: Introductionmentioning

confidence: 98%

Generic equilibration dynamics of planar defects in trapped atomic superfluids

et al. 2015

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We investigate equilibration processes shortly after sudden perturbations are applied to ultracold trapped superfluids. We show the similarity of phase imprinting and localized density depletion perturbations, both of which initially are found to produce "phase walls". These planar defects are associated with a sharp gradient in the phase. Importantly they relax following a quite general sequence. Our studies, based on simulations of the complex time-dependent Ginzburg-Landau equation, address the challenge posed by these experiments: how a superfluid eventually eliminates a spatially extended planar defect. The processes involved are necessarily more complex than equilibration involving simpler line vortices. An essential mechanism for relaxation involves repeated formation and loss of vortex rings near the trap edge.

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Experimental Observation of Oscillating and Interacting Matter Wave Dark Solitons

Cited by 302 publications

References 36 publications

Multiple dark-bright solitons in atomic Bose-Einstein condensates

Multiple dark-bright solitons in atomic Bose-Einstein condensates

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Generic equilibration dynamics of planar defects in trapped atomic superfluids

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