Multidimensional semi-gap solitons in a periodic potential

Baizakov, B. B.; Malomed, Boris A.; Salerno, Mario

doi:10.1140/epjd/e2006-00004-8

Cited by 15 publications

(18 citation statements)

References 48 publications

(65 reference statements)

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“…These effects can be understood as the result of density-dependent inelastic collisions in which the system becomes effectively three-dimensional [18][19][20] . Similar effects have been observed in nonlin-ear optics 21 .…”

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confidence: 99%

Collisions of matter-wave solitons

et al. 2014

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Solitons are localised wave disturbances that propagate without changing shape, a result of a nonlinear interaction which compensates for wave packet dispersion. Individual solitons may collide, but a defining feature is that they pass through one another and emerge from the collision unaltered in shape, amplitude, or velocity, but with a new trajectory reflecting a discontinuous jump. This remarkable property is mathematically a consequence of the underlying integrability of the one-dimensional (1D) equations, such as the nonlinear Schrödinger equation, that describe solitons in a variety of wave contexts, including matter-waves 1, 2 . Here we explore the nature of soliton collisions using Bose-Einstein condensates of atoms with attractive interactions confined to a quasi-one-dimensional waveguide. We show by real-time imaging that a collision between solitons is a complex event that differs markedly depending on the relative phase between the solitons. By controlling the strength of the nonlinearity we shed new light on these fundamental features of soliton collisional dynamics, and explore the implications of collisions in the proximity of the crossover between one and three dimensions 1 arXiv:1407.5087v2 [cond-mat.quant-gas]

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confidence: 99%

Collisions of matter-wave solitons

et al. 2014

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“…Here α j is the scalar polarizability of the level |j , Q(x, t) t represents the time average in an oscillation cycle for the quantity Q(x, t), and therefore we have E L (x) = (E 0 / √ 2) cos(x/R ⊥ ). The aim of introducing the far-detuned optical field is to stabilize the LBs [17,20].…”

Section: Theoretical Modelmentioning

confidence: 99%

“…We now determine the SG deflection angles of each LB components. From the solution (20) we get the propagating velocity of the jth LB component at time t…”

Section: Shown Inmentioning

confidence: 99%

Stern–Gerlach effect of multi-component ultraslow optical solitons via electromagnetically induced transparency

Chen

Huang

2013

J. Opt. Soc. Am. B

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We propose a scheme to exhibit a Stern-Gerlach effect of n-component (n > 2) high-dimensional ultraslow optical solitons in a coherent atomic system with (n + 1)-pod level configuration via electromagnetically induced transparency (EIT). Based on Maxwell-Bloch equations, we derive coupled (3+1)-dimensional nonlinear Schrödinger equations governing the spatial-temporal evolution of n probe-field envelopes. We show that under EIT condition significant deflections of the n components of coupled ultraslow optical solitons can be achieved by using a Stern-Gerlach gradient magnetic field. The stability of the ultraslow optical solitons can be realized by an optical lattice potential contributed from a far-detuned laser field. *

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“…Both the experimental and theoretical results reveal that solitons can be created in lattice potentials, if they do not exist in the uniform space [this is the case of gap solitons (GSs) supported by the self-defocusing nonlinearity, see original works [13][14][15][16] and reviews [7,17]], and solitons may be stabilized, if they are unstable without the lattice (multidimensional solitons in the case of self-focusing, as shown in Refs. [18][19][20][21][22][23][24][25], see also reviews [1,3,4]). The stability of GSs has been studied in detail too-chiefly, close to edges of the corresponding bandgaps-in one [27][28][29] and two [30] dimensions alike.…”

Section: Introductionmentioning

confidence: 99%

Symbiotic two-component gap solitons

2012

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Abstract:We consider a two-component one-dimensional model of gap solitons (GSs), which is based on two nonlinear Schrödinger equations, coupled by repulsive XPM (cross-phase-modulation) terms, in the absence of the SPM (self-phase-modulation) nonlinearity. The equations include a periodic potential acting on both components, thus giving rise to GSs of the "symbiotic" type, which exist solely due to the repulsive interaction between the two components. The model may be implemented for "holographic solitons" in optics, and in binary bosonic or fermionic gases trapped in the optical lattice. Fundamental symbiotic GSs are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. Symmetric solitons are destabilized, including their entire family in the second bandgap, by symmetry-breaking perturbations above a critical value of the total power. Asymmetric solitons of intra-gap and inter-gap types are studied too, with the propagation constants of the two components falling into the same or different bandgaps, respectively. The increase of the asymmetry between the components leads to shrinkage of the stability areas of the GSs. Inter-gap GSs are stable only in a strongly asymmetric form, in which the first-bandgap component is a dominating one. Intra-gap solitons are unstable in the second bandgap. Unstable two-component GSs are transformed into persistent breathers. In addition to systematic numerical considerations, analytical results are obtained by means of an extended ("tailed") Thomas-Fermi approximation (TFA).

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Multidimensional semi-gap solitons in a periodic potential

Cited by 15 publications

References 48 publications

Collisions of matter-wave solitons

Collisions of matter-wave solitons

Stern–Gerlach effect of multi-component ultraslow optical solitons via electromagnetically induced transparency

Symbiotic two-component gap solitons

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