Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice

Abdullaev, F. Kh.; Gammal, A.; Luz, H. L. F. da; Tomio, Lauro

doi:10.1103/physreva.76.043611

Cited by 33 publications

(19 citation statements)

References 46 publications

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“…In the 2D case, it was shown in Ref. [29] that, for conservative systems, an NOL in one direction by itself cannot give stable localized solutions in the case of attractive interactions. This fact also remains true for 2D NOLs both for attractive and repulsive interactions.…”

Section: Introductionmentioning

confidence: 99%

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

et al. 2010

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The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

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Section: Introductionmentioning

confidence: 99%

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

et al. 2010

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“…The standard variational approach for the dissipative system is given by [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] ∂ ∂z…”

Section: Soliton Dynamics In Dissipative Graded Index Kerr Mediamentioning

confidence: 99%

“…[10][11][12][13] In such systems the diffraction term alone is not enough to balance the nonlinear changes in a stable way. [14][15][16] Hence the influence of dissipation can be crucial for the existence of stable multidimensional optical solitons. 17 In a two-dimensional dissipative medium with constant dissipation, the balancing between diffraction, dissipation and nonlinear changes results in the stabilization of spatial solitons.…”

Section: Introductionmentioning

confidence: 99%

Spatial solitons in a medium with lumped amplification and dissipation

Muhsina

Subha

2015

J. Nonlinear Optic. Phys. Mat.

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This work analyzes the dynamics of two-dimensional spatial solitons in dissipative graded index Kerr media, analytically and numerically. The dynamics of two-dimensional spatial solitons has been studied in a medium with lumped amplification. The presence of lumped amplification in the medium results in the formation of soliton like waves called similaritons. The spatial soliton dynamics has been studied in a dissipative medium. In a dissipative graded index Kerr medium, the balancing between the coefficients of constant dissipation and lumped amplification results in the stabilization of the beam. The beam dynamics has also been studied by varying amplification coefficients with propagation distance. Hyperbolic, linear, and exponential amplification profiles are considered. When amplification coefficient varies with propagation distance, the beam gets compressed. The beam compression is higher in the case of exponential amplification profile than that of hyperbolic and linear amplification profiles.

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“…This space-dependent property is seldom considered in optical multimode solitons. However, this property can greatly influence the behavior of coherent matter waves, especially when the waves are trapped in the potentials of the nonlinear optical lattice (NOL); the interaction of the NOL among atoms is spatially modulated via the lattice created by the interference of two laser beams [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Multisoliton complexes of Bose–Einstein condensates in nonlinear optical lattices

Lin

Cai

2013

J. Opt. Soc. Am. B

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We theoretically study the role of the mode structure of a multicomponent Bose-Einstein condensate (BEC) in the potential created by a nonlinear optical lattice. We describe a multisoliton complex (MSC) as a superposition of different fundamental soliton modes in the matter-wave system. Using a similarity transformation, we solve the nonlinear evolution equation of the multimode coupled matter-wave field and construct a set of analytical bright soliton solutions. A perturbation method is used to examine the linear stability of the constructed solitons. Based on these particular solutions, we numerically analyze the mode structure of a MSC. The results show that the periodicity causes a Bloch modulation in the envelopes of the density distribution. When different fundamental modes collide with each other in the nonlinear lattice, the collision-induced shifts, and the space-dependent modulation of external potentials change the density profile of the multimode soliton complex. Therefore, the mode structure, which is absent in a one-mode BEC, provides the possible multiscale modeling of the matter-wave field with extra degrees of freedom.

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Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice

Cited by 33 publications

References 46 publications

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

Spatial solitons in a medium with lumped amplification and dissipation

Multisoliton complexes of Bose–Einstein condensates in nonlinear optical lattices

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