Dark-soliton states of Bose-Einstein condensates in anisotropic traps

Feder, David L.; Pindzola, M. S.; Collins, L. A.; Schneider, Barry I.; Clark, Charles W.

doi:10.1103/physreva.62.053606

Cited by 213 publications

(217 citation statements)

References 46 publications

(75 reference statements)

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“…Using α = 1.6 and γ = 0.02, our simulations show that L x blows up after 15 ms of excitation. At this point, the condensate forms wavy patterns which develop to dark solitary waves which subsequently decay into several vortex pairs via the snake instability [29]. A more complex dynamics takes place after the first events of vortex formation, consisting in the generation of an undetermined number of vortices which characterizes the emergence of the turbulent regime.…”

Section: Numerical Calculations Formentioning

confidence: 99%

Route to turbulence in a trapped Bose-Einstein condensate

Seman¹,

Henn²,

Shiozaki³

et al. 2011

Laser Phys. Lett.

116

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We have studied a Bose-Einstein condensate of 87 Rb atoms under an oscillatory excitation. For a fixed frequency of excitation, we have explored how the values of amplitude and time of excitation must be combined in order to produce quantum turbulence in the condensate. Depending on the combination of these parameters different behaviors are observed in the sample. For the lowest values of time and amplitude of excitation, we observe a bending of the main axis of the cloud. Increasing the amplitude of excitation we observe an increasing number of vortices. The vortex state can evolve into the turbulent regime if the parameters of excitation are driven up to a certain set of combinations. If the value of the parameters of these combinations is exceeded, all vorticity disappears and the condensate enters into a different regime which we have identified as the granular phase. Our results are summarized in a diagram of amplitude versus time of excitation in which the different structures can be identified. We also present numerical simulations of the Gross-Pitaevskii equation which support our observations.

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Section: Numerical Calculations Formentioning

confidence: 99%

Route to turbulence in a trapped Bose-Einstein condensate

Seman¹,

Henn²,

Shiozaki³

et al. 2011

Laser Phys. Lett.

116

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“…In particular, it has been found that in elongated harmonic traps a DS oscillates with frequency Ω/ √ 2, where Ω is the axial trap frequency. Thermal [11] and dynamical [12] instabilities, mainly referring to rectilinear DSs, have been investigated. On the other hand, generalizations of the rectilinear solitons, such as ring-shaped DSs, have recently been proposed [13].…”

Section: Introductionmentioning

confidence: 99%

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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“…The dynamics of dark solitons (DSs) in the presence of the external magnetic trap has been extensively studied [4], including thermal [5] and dynamical [6] instabilities. More recently, apart from the rectilinear DSs, ring-shaped counterparts were predicted in BECs [7].…”

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confidence: 99%

Stability of dark solitons in a Bose-Einstein condensate trapped in an optical lattice

et al. 2003

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Phys. Rev. A 68 035602 (2003)We investigate the stability of dark solitons (DSs) in an effectively one-dimensional Bose-Einstein condensate in the presence of the magnetic parabolic trap and an optical lattice (OL). The analysis is based on both the full Gross-Pitaevskii equation and its tight-binding approximation counterpart (discrete nonlinear Schrödinger equation). We find that DSs are subject to weak instabilities with an onset of instability mainly governed by the period and amplitude of the OL. The instability, if present, sets in at large times and it is characterized by quasi-periodic oscillations of the DS about the minimum of the parabolic trap. Apart from the mean-field description via the GrossPitaevskii (GP) equation [8][9][10][11][12][13], a BEC trapped in a strong OL may be described, in the tight-binding limit, by the discrete nonlinear Schrödinger (DNLS) equation [16]. This approximation is not always accurate, but its applicability can be systematically examined [17]. In cases where such a reduction is possible (e.g., when the chemical potential is much lower than the height of the potential barriers induced by the OL), the DNLS model is particularly relevant and has been successfully applied in many instances (for a recent review on DNLS see, e.g., [18] and references therein).In this paper, we study DSs in repulsive BECs (i.e., positive-scattering-length collisions) in the presence of OLs. We use both the continuous-GP and DNLS equations. In particular, we assume a cigar-shaped BEC, which can be described by the following normalized quasi-one-dimensional GP equation [1,19,20],Here, u(x, t) is the mean-field wave function, while the terms in the square brackets represent the external magnetic trap and the OL potential, respectively, with the strengths k and V 0 , while λ is the wavelength of the interference pattern created by the laser beams.To study the dynamics of a DS in the framework of Eq. (1), we consider an initial condition similar to an ansatz proposed for the description of DSs in BECs in Ref.[21]where u TF = max(0, µ − kx 2 ) is the Thomas-Fermi (TF) expression for the background wave-function distribution [1] (µ is the chemical potential) and x 0 is the initial location of the DS's center. In most cases, we set x 0 = 0, i.e., the dark soliton is placed at the bottom of the magnetic trap.In the tight-binding limit, Eq. (1) reduces to the following DNLS equation [16],where the dot denotes time derivative, n is the latticesite index, and C is the so-called coupling constant (see e.g., Refs. [16,17] for exact expressions and relevant estimates). An initial condition for a DS in the case of Eq. (3) can be given by a straightforward discretization of the continuum ansatz (2). Typically, simulations were run for a lattice with 200 sites, and free boundary conditions were used for both the continuum and discrete models. In fact, it has been verified that the results are insensitive to the choice of boundary conditions. Note that DSs in discrete lattices (in the absence of a parabolic tr...

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Dark-soliton states of Bose-Einstein condensates in anisotropic traps

Cited by 213 publications

References 46 publications

Route to turbulence in a trapped Bose-Einstein condensate

Route to turbulence in a trapped Bose-Einstein condensate

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

Stability of dark solitons in a Bose-Einstein condensate trapped in an optical lattice

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