Dynamics of Bright Matter Wave Solitons in a Bose–einstein Condensate

Abdullaev, F. Kh.; Gammal, A.; Камчатнов, А. М.; Tomio, Lauro

doi:10.1142/s0217979205032279

Cited by 165 publications

(98 citation statements)

References 87 publications

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“…The formation of bright solitons, which was previously demonstrated in BEC experimentally [42], and studied in detail theoretically [43,44], requires the presence of self-attraction. However, in models with local interactions it has been recently demonstrated that bright solitons may be supported by the repulsive cubic nonlinearity in the D-dimensional geometry, provided that the nonlinearity strength is modulated in space, growing from the center to periphery at any rate faster than R D , where R is the radial coordinate [45]- [48].…”

Section: Introduction and The Settingmentioning

confidence: 83%

Matter-wave solitons supported by field-induced dipole-dipole repulsion with spatially modulated strength

Liu

Pang

et al. 2013

Phys. Rev. A

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We demonstrate the existence of one and two-dimensional bright solitons in the Bose-Einstein condensate with repulsive dipole-dipole interactions induced by a combination of dc and ac polarizing fields, oriented perpendicular to the plane in which the BEC is trapped, assuming that the strength of the fields grows in the radial (r) direction faster than r 3 . Stable tightly confined 1D and 2D fundamental solitons, twisted solitons in 1D, and solitary vortices in 2D are found in a numerical form. The fundamental solitons remain robust under the action of an expulsive potential, which is induced by the interaction of the dipoles with the polarizing field. The confinement and scaling properties of the soliton families are explained analytically. The Thomas-Fermi approximation is elaborated for fundamental solitons. The mobility of the fundamental solitons is limited to the central area. Stable 1D even and odd solitons are also found in the setting with a double-well modulation function, along with a regime of Josephson oscillations.

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Section: Introduction and The Settingmentioning

confidence: 83%

Matter-wave solitons supported by field-induced dipole-dipole repulsion with spatially modulated strength

Liu

Pang

et al. 2013

Phys. Rev. A

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“…Such solitons have been observed in optics using waveguide arrays, photo-refractive materials, photonic crystal fibers, etc., in both one-dimensional and multidimensional lattices, mostly periodic sinusoidal square lattices [1,2,3,4,5,6,7,8] or single waveguide potentials [9,10,11], but also in discontinuous lattices (surface solitons) [12], radially-symmetric Bessel lattices [13], lattices with triangular or hexagonal symmetry [14,15], lattices with defects [16,17,18,19,20,21,22], with quasicrystal structures [16,23,24,25,26,27,28] or with random potentials [29,30]. Solitons have also been observed in the context of Bose-Einstein Condensates (BEC) [31,32], where lattices have been induced using a variety of techniques.…”

Section: Introductionmentioning

confidence: 99%

Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons

Sivan

Fibich²,

Ilan³

et al. 2008

Phys. Rev. E

103

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We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to a focusing instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows to predict the stability and instability strength.

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“…In particular, OLs support gap solitons in BEC with repulsive interaction between atoms (the general topic of BEC solitons was reviewed in Ref. [2]). Gap solitons in BEC were predicted theoretically [3,4] and then created experimentally in an effectively one-dimensional ("cigar-shaped") trap equipped with the OL in the axial direction.…”

Section: Introduction and The Modelmentioning

confidence: 99%

“…With regard to Eqs. (2), the corresponding tunnel-coupling time, which is t coupl = π/(2κ) in normalized units, translates, for d = 1 µm, into physical coupling time T coupl ∼ 10 µs and 100 µs, for lithium and rubidium, respectively. As for the number of atoms in the solitons, in the AA system is scales, in the normalized units, between N ≃ 2 and N ≃ 15, see Fig.…”

Section: Introduction and The Modelmentioning

confidence: 99%

“…As follows from Eqs. (2) and (3), this corresponds to the actual number of 7 Li atoms per soliton between 10 4 and 10 5 , if experimentally relevant values are assumed, ω ⊥ ≃ 2π × 1 KHz and a s ≃ −0.15 nm (in the experiments without the OL, the number of atoms in the solitons was up to 5, 000 [22]). Similarly, in the RR model the number of 87 Rb atoms in gap solitons is expected to be ∼ 1000 (in the first experiments, it was ≃ 250 [1]).…”

Section: Introduction and The Modelmentioning

confidence: 99%

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Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

Gubeskys

Malomed

2007

Phys. Rev. A

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We study spontaneous symmetry breaking in a system of two parallel quasi-one-dimensional traps (cores), equipped with optical lattices (OLs) and filled with a Bose-Einstein condensate (BEC). The cores are linearly coupled by tunneling (the model may also be interpreted in terms of spatial solitons in parallel planar optical waveguides with a periodic modulation of the refractive index). Analysis of the corresponding system of linearly coupled Gross-Pitaevskii equations (GPEs) reveals that spectral bandgaps of the single GPE split into subgaps. Symmetry breaking in two-component BEC solitons is studied in cases of the attractive (AA) and repulsive (RR) nonlinearity in both traps; the mixed situation, with repulsion in one trap and attraction in the other (RA), is considered too. In all the cases, stable asymmetric solitons are found, bifurcating from symmetric or antisymmetric ones (and destabilizing them), in the AA and RR systems, respectively. In either case, bi-stability is predicted, with a nonbifurcating stable branch, either antisymmetric or symmetric, coexisting with asymmetric ones. Solitons destabilized by the bifurcation tend to rearrange themselves into their stable asymmetric counterparts. In addition to the fundamental solitons, branches of twisted (odd) solitons in the AA system, and twisted bound states of fundamental solitons in both AA and RR systems, are found too. The impact of a phase mismatch, ∆, between the OLs in the two cores is also studied. It is concluded that ∆ = π/2 only mildly deforms the picture, while ∆ = π changes it drastically, replacing the symmetry-breaking bifurcations by pseudo-bifurcations, with the branch of asymmetric solutions asymptotically approaching its symmetric or antisymmetric counterpart (in the AA and RR system, respectively), rather than splitting off from it. Also considered is a related model, for a binary BEC in a single-core trap with the OL, assuming that the two species (representing different spin states of the same atom) are coupled by linear interconversion. In that case, the symmetry-breaking bifurcations in the AA and RR models switch their character, if the inter-species nonlinear interaction becomes stronger than the intra-species nonlinearity.

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Dynamics of Bright Matter Wave Solitons in a Bose–einstein Condensate

Cited by 165 publications

References 87 publications

Matter-wave solitons supported by field-induced dipole-dipole repulsion with spatially modulated strength

Matter-wave solitons supported by field-induced dipole-dipole repulsion with spatially modulated strength

Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons

Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

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