Soliton-Sound Interactions in Quasi-One-Dimensional Bose-Einstein Condensates

Parker, N. G.; Proukakis, N. P.; Leadbeater, M.; Adams, Charles S.

doi:10.1103/physrevlett.90.220401

Cited by 84 publications

(158 citation statements)

References 21 publications

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“…The case of manipulation of dark solitons by periodic potentials is more subtle because dark solitons subject to tight confinements are prone to weak radiation loss, as shown numerically in Refs. [454][455][456][457] and analytically in Ref. [263].…”

Section: Periodic Potentialsmentioning

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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Section: Periodic Potentialsmentioning

confidence: 99%

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

2008

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“…These small-amplitude oscillations last up to t ≈ 770; after that, the soliton has gained the kinetic energy necessary to escape from the well and move to a neighboring one. There, it is again trapped due to a reabsorption of the radiation waves: this effect [14] causes the soliton to become deeper, which results in loss of its kinetic energy, and a subsequent stabilization of its motion. The soliton oscillates in that well from t = 825 up to t = 980.…”

Section: Intermediate Optical Lattice Periodmentioning

confidence: 99%

“…Note that, at t = 1000, the soliton is still oscillating in the potential well of the OL where it was initially placed. For even larger times (not shown here), it is natural to expect that it will escape from the well and will further increase (decrease) the amplitude (frequency) of the oscillation (see also a discussion in the next sections, as well as [14,24] for a detailed description of the effect of radiation). (8), respectively.…”

Section: The Long-period Optical Latticementioning

confidence: 99%

“…6 (left)], thus continuously losing its energy [37] (see also discussion in Ref. [14]). This energy loss renders the soliton shallower.…”

Section: Intermediate Optical Lattice Periodmentioning

confidence: 99%

“…On the other hand, generalizations of the rectilinear solitons, such as ring-shaped DSs, have recently been proposed [13]. Systematic studies of the sound emitted by the DS due to inhomogeneities, as well as soliton-sound interactions have also been performed [14]. Furthermore, it has been shown that another dissipative effect, the so-called quantum depletion of DSs [15], reduces the dark soliton lifetime as atoms fill up the dark soliton notch.…”

Section: Introductionmentioning

confidence: 99%

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Dark soliton dynamics in spatially inhomogeneous media: Application to Bose–Einstein condensates

Theocharis

Frantzeskakis

Kevrekidis

et al. 2005

Mathematics and Computers in Simulation

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We study the dynamics of dark solitons in spatially inhomogeneous media with applications to cigar-shaped Bose-Einstein condensates trapped in a harmonic magnetic potential and a periodic potential representing an optical lattice. We distinguish and systematically investigate the cases with the optical lattice period being smaller, larger, or comparable to the width of the dark soliton. Analytical results, based on perturbation techniques, for the motion of the dark soliton are obtained and compared to direct numerical simulations. Radiation effects are also considered. Finally, we demonstrate that a moving optical lattice may capture and drag a dark soliton.

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Manipulations of Coherent Matter-Waves

Kevrekidis¹,

Frantzeskakis²,

Carretero-González³

Emergent Nonlinear Phenomena in Bose-Einstein Condensates

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Soliton-Sound Interactions in Quasi-One-Dimensional Bose-Einstein Condensates

Cited by 84 publications

References 21 publications

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

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

Dark soliton dynamics in spatially inhomogeneous media: Application to Bose–Einstein condensates

Manipulations of Coherent Matter-Waves

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