Two-dimensional nonlocal vortices, multipole solitons, and rotating multisolitons in dipolar Bose-Einstein condensates

Lashkin, Volodymyr M.

doi:10.1103/physreva.75.043607

Cited by 64 publications

(40 citation statements)

References 20 publications

(29 reference statements)

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“…The modulation instability (MI) is a general characteristic of wave propagation in nonlinear dispersive media and has been studied in diverse fields as fluid dynamics [1], nonlinear optics [2], plasma physics [3], matter waves [4], etc. It is associated with a process in which weak perturbations to the steady state increase exponentially as a result of interplay between the nonlinearity and the group-velocity dispersion.…”

Section: Introductionmentioning

confidence: 99%

Modulation Instability of Two-Dimensional Dipolar Bose-Einstein Condensate in a Deep Optical Lattice

et al. 2009

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We study the stability of the continuous waves in the pancake shaped dipolar Bose-Einstein condensate trapped in the strong optical lattice potential with the coexisting local (the short-range s-wave) interaction and nonlocal (the dipole-dipole) interactions between the condensate atoms. The system is modeled by two two-dimensional discrete models derived from the Gross-Pitaevskii equation accounting the dipole-dipole interactions: discrete nonlinear Schrödinger equation with cubic nonlinearity and nonpolynomial Schrödinger equation. The corresponding dispersion relations are calculated analytically and the regions of the modulation instability in the parametric space are summarized into the stability diagrams.

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Section: Introductionmentioning

confidence: 99%

Modulation Instability of Two-Dimensional Dipolar Bose-Einstein Condensate in a Deep Optical Lattice

et al. 2009

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“…A quasi-2D isotropic configuration implies that the local moments are polarized perpendicular to the pancake's plane, in which case the DDI is repulsive. In that case, the creation of (bright) 2D solitons may be possible if the sign of the DDI is effectively reversed by means of a rapidly oscillating magnetic field [14]; in the same setting, stable isotropic solitons with embedded vorticity were predicted too [15], and various 2D localized structures may be stabilized by trapping potentials acting in the plane [16]. The very fact of the existence of multidimensional solitons in the dipolar BEC can be proven in a rigorous mathematical form [17].…”

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confidence: 99%

Creating two-dimensional bright solitons in dipolar Bose-Einstein condensates

Köberle

Zajec²,

Malomed³

2012

Phys. Rev. A

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We propose a realistic experimental setup for creating quasi-two-dimensional (2D) bright solitons in dipolar Bose-Einstein condensates (BECs), the existence of which was proposed in Phys. Rev. Lett. 100, 090406 (2008). A challenging feature of the expected solitons is their strong inherent anisotropy, due to the necessary in-plane orientation of the local moments in the dipolar gas. This may be the first chance of making multidimensional matter-wave solitons, as well as solitons featuring the anistropy due to their intrinsic dynamics. Our analysis is based on the extended GrossPitaevskii equation, which includes three-body losses and noise in the scattering length, induced by fluctuations of currents inducing the necessary magnetic fields, which are factors crucial to the adequate description of experimental conditions. By means of systematic 3D simulations, we find a ramping scenario for the change of the scattering length and trap frequencies which results in the creation of robust solitons, that readily withstand the concomitant excitation of the condensate. [4]. The making of magnetic-and electric-dipolar BEC may also be expected, respectively, in erbium [5] and in molecular gases [6]. An updated review of this rapidly progressing field was given in Ref. [7].One of the promising possibilities, which has been, thus far, investigated only theoretically, is the creation of bright solitons in dipolar condensates. This can be easily predicted in various one-dimensional (1D) settings, using, in particular, periodic potentials induced by optical lattices as the stabilizing factor [8]. In the limit of a very deep lattice, the BEC wave function becomes nearly discrete, which makes it possible to predict stable 2D dipolar solitons [9] and vortices [10], as well as 3D solitons [11], in the (quasi-)discrete form.As concerns solitons, the most challenging issue is the creation of such stable matter-wave modes in quasi-2D (pancake-shaped) condensates, as well as their counterparts in the form of spatiotemporal solitons in optics. In spite of intensive theoretical discussions [12], no experimental results in this area have been reported thus far, the most essential obstacle being the inherent instability of 2D solitons to the collapse, driven by the self-focusing cubic nonlinearity (very recently, it was proposed to create stable bright solitons by means of self-defocusing nonlinearity, which is possible in a rather exotic situation with the strength of the nonlinearity growing at r → ∞ faster than r D , where D is the spatial dimension [13]).The dipolar condensates suggest new challenges and possibilities for achieving this fundamental purpose, by making use of the competition between local interactions and long-range dipole-dipole interactions (DDIs). A quasi-2D isotropic configuration implies that the local moments are polarized perpendicular to the pancake's plane, in which case the DDI is repulsive. In that case, the creation of (bright) 2D solitons may be possible if the sign of the DDI is effectively reversed by me...

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“…In contrast to the linear vortex phase, the phase of the azimuthon is a staircaselike nonlinear function of the polar angle. Various kinds of azimuthons have been shown to be stable in media with a nonlocal nonlinear response [7,8,9,10,11].The aim of this Brief Report is to present nonrotating multisoliton (in particular, dipole and quadrupole) and rotating multisoliton (azimuthon) structures in the 2D BEC with attraction and study their stability by a linear stability analysis. We show that, in the presence of a confining potential, stable azimuthons also exist for a medium with a local cubic attractive nonlinearity.…”

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confidence: 99%

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confidence: 99%

Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates

Lashkin

2008

Phys. Rev. A

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We present spatially localized nonrotating and rotating (azimuthon) multisolitons in the twodimensional (2D) ("pancake-shaped configuration") Bose-Einstein condensate (BEC) with attractive interaction. By means of a linear stability analysis, we investigate the stability of these structures and show that rotating dipole solitons are stable provided that the number of atoms is small enough. The results were confirmed by direct numerical simulations of the 2D Gross-Pitaevskii equation.PACS numbers: 03.75. Lm, 05.30.Jp, 05.45.Yv Localized coherent structures, such as fundamental solitons, vortices, nonrotating and rotating multisolitons are universal objects which appear in many nonlinear physical systems [1], and, in particular, in Bose-Einstein condensates (BEC's). Stability of these nonlinear structures is one of the most important questions because of its direct connection with the possibility of experimental observation of solitons and vortices.Detailed investigations of the stability of localized vortices in an effectively two-dimensional (2D) trapped BEC with a negative scattering length (attractive interaction) were performed in Ref.[2] and later extended to the three-dimensional case [3] (see also Ref. [4]). While vortex solitons in attractive BEC are strongly unstable in free space, the presence of the trapping potential results in existence of stable vortices provided that the number of particles does not exceed a threshold value [2,4,5].Recently, a novel class of 2D spatially localized vortices with a spatially modulated phase, the so called azimuthons, was introduced in Ref. [6]. Azimuthons represent intermediate states between the radially symmetric vortices and rotating soliton clusters. In contrast to the linear vortex phase, the phase of the azimuthon is a staircaselike nonlinear function of the polar angle. Various kinds of azimuthons have been shown to be stable in media with a nonlocal nonlinear response [7,8,9,10,11].The aim of this Brief Report is to present nonrotating multisoliton (in particular, dipole and quadrupole) and rotating multisoliton (azimuthon) structures in the 2D BEC with attraction and study their stability by a linear stability analysis. We show that, in the presence of a confining potential, stable azimuthons also exist for a medium with a local cubic attractive nonlinearity. Results of the linear stability analysis were confirmed by direct numerical simulations of the azimuthon dynamics.We consider a condensate which is loaded in an axisymmetric with respect to the (x, y) plane harmonic trap, and tightly confined in the z direction. The dynamics of the condensate is described by the Gross-Pitaevskii equation * Electronic address: vlashkin@kinr.kiev.uawhere Ψ(r, t) is the condensate wave function, a ≷ 0 is the s-wave scattering length. We assume that the axial confinement frequency Ω z is much larger than the radial one Ω r (the pancake configuration). Then, the 3D equation (1) can be reduced to an effective GPE in two dimensions [2] (for a detailed discussion of the appl...

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Two-dimensional nonlocal vortices, multipole solitons, and rotating multisolitons in dipolar Bose-Einstein condensates

Cited by 64 publications

References 20 publications

Modulation Instability of Two-Dimensional Dipolar Bose-Einstein Condensate in a Deep Optical Lattice

Modulation Instability of Two-Dimensional Dipolar Bose-Einstein Condensate in a Deep Optical Lattice

Creating two-dimensional bright solitons in dipolar Bose-Einstein condensates

Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates

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