Matter-wave dark solitons in optical lattices

Louis, Pearl J. Y.; Ostrovskaya, Elena A.; Kivshar, Yuri S.

doi:10.1088/1464-4266/6/5/020

Cited by 32 publications

(20 citation statements)

References 38 publications

(51 reference statements)

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“…Comparison of discrete dark solitons properties in lattices with saturable and Kerr nonlinearities was performed by Fitrakis, Kevrekidis, Susanto, and Frantzeskakis [2007]. Dark matter-wave solitons in optical lattices were discussed by Louis, Ostrovskaya, and Kivshar [2004]. The properties of dark solitons in dynamical lattices with cubic-quintic nonlinearity have been addressed recently by Maluckov, Hadzievski, and Malomed [2007].…”

Section: Fundamental Solitonsmentioning

confidence: 99%

Soliton Shape and Mobility Control in Optical Lattices

2009

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We present a progress overview focused on the recent theoretical and experimental advances in the area of soliton manipulation in optical lattices. Optical lattices offer the possibility to engineer and to control the diffraction of light beams in media with periodicallymodulated optical properties, to manage the corresponding reflection and transmission bands, and to form specially designed defects. Consequently, they afford the existence of a rich variety of new families of nonlinear stationary waves and solitons, lead to new rich dynamical phenomena, and offer novel conceptual opportunities for all-optical shaping, switching and routing of optical signals encoded in soliton formats. In this overview, we consider reconfigurable optically-induced lattices as well as waveguide arrays made in suitable nonlinear materials. We address both, one-dimensional and multi-dimensional geometries.We specially target the new possibilities made possible by optical lattices induced by a variety of existing non-diffracting light patterns, we address nonlinear lattices and soliton arrays, and we briefly explore the unique features exhibited by light propagation in defect modes and in random lattices, an area of current topical interest and of potential crossdisciplinary impact.

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Section: Fundamental Solitonsmentioning

confidence: 99%

Soliton Shape and Mobility Control in Optical Lattices

2009

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“…The experimental control over the OL has led to the realization of numerous interesting phenomena including Bloch oscillations [18,22], Landau-Zener tunneling [16] (in the additional presence of a linear external potential), and classical [23] and quantum [21] superfluidinsulator transitions. With respect to the above, the dissipative dynamics of the DSs (including detailed quantitative measurements of the sound emitted by the soliton) in a quasi one-dimensional (1D) BEC confined through a harmonic trap and an OL, as well as the structure and the mobility properties of DSs in single and double-periodic OLs have recently been considered in [24,25], respectively. On the other hand, the stability of DSs in the combined harmonic trapping and OL potential, in both the discrete and the continuum mean-field model framework, has recently been studied [26].…”

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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“…Since then, to get the explicit solutions of some special cases of VCNLSEs with concrete coefficients, there are several typical transformations involving dependent variables and independent variables, such as lens type transformations [19][20][21][22], similarity transformations [9-12, 15, 23-25], and some others [26][27][28][29][30][31]. However, for the extensively studied potentials in BEC and nonlinear optical systems, i.e., optical-lattice and super-lattice potentials (or periodic potentials) [32][33][34][35][36][37][38][39][40][41] and multiwell potentials [39][40][42][43][44][45][46][47][48][49][50], to our best knowledge, the exact and analytical solutions of the VCNLSEs, such as solitons, have not been reported in the literatures except stationary solutions and numerical solutions. To show dynamical properties of the solitons in one-dimensional BEC and nonlinear optical systems under the control of the two kinds of the external potentials above mentioned, we shall develop a new method to design corresponding integrable VCNLSEs, and then get its soliton solutions.…”

Section: Introductionmentioning

confidence: 99%

Designable Integrability of the Variable Coefficient Nonlinear Schrödinger Equations

2010

Stud Appl Math

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The designable integrability (DI) [51] of the variable coefficient nonlinear Schrödinger equations (VCNLSEs) is first introduced by construction of an explicit transformation, which maps VCNLSE to the usual nonlinear Schrödinger equations (NLSEs). One novel feature of VCNLSE with DI is that its coefficients can be designed artificially and analytically by using transformation. A special example between nonautonomous NLSEs and NLSEs is given here. Further, the optical super-lattice potentials (or periodic potentials) and multiwell potentials are designed, which are two kinds of important potential in Bose-Einstein condensation and nonlinear optical systems. There are two interesting features of the soliton of the VCNLSEs indicated by the analytic and exact formula. Specifically, its profile is variable and its trajectory is not a straight line when it evolves with time t.

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Matter-wave dark solitons in optical lattices

Cited by 32 publications

References 38 publications

Soliton Shape and Mobility Control in Optical Lattices

Soliton Shape and Mobility Control in Optical Lattices

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

Designable Integrability of the Variable Coefficient Nonlinear Schrödinger Equations

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