THEORY OF NONLINEAR MATTER WAVES IN OPTICAL LATTICES

By V. Brazhnyi, Vladimir V. Konotop. 2004

344 citations recorded by the source corpus.

We consider several effects of the matter wave dynamics which can be observed in Bose–Einstein condensates embedded into optical lattices. For low-density condensates, we derive approximate evolution equations, the form of which depends on relation among the main spatial scales of the system. Reduction of the Gross–Pitaevskii equation to a lattice model (the tight-binding approximation) is also presented. Within the framework of the obtained models, we consider modulational instability of the condensate, solitary and periodic matter waves, paying special attention to different limits of the solutions, i.e. to smooth movable gap solitons and to strongly localized discrete modes. We also discuss how the Feshbach resonance, a linear force and lattice defects affect the nonlinear matter waves.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b3516ffa3c0ff4a3f43ec661acedbde4d91e928e

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

(INVITED) Vortex solitons: Old results and new perspectives (2019, background): “Note that the defocusing nonlinearity may create gap solitons in the presence of the lattice potential [5, 7, 176].”
Dynamics of Bose-Einstein condensates in optical lattices (2006, background): “Some examples for this can be found in the review by Brazhnyi and Konotop 2004 .”
Solitons in nonlinear lattices (2010, methodology): “…g q , and g The description of the GSs in the present form makes sense if, as usual, the approximation yields m as the GSs are supported by the interplay of the repulsive nonlinearity, , and the negative effective mass (see reviews by Brazhnyi and Konotop, 2004, and Morsch and Oberthaler, 2006).”
Nonlinear waves in PT -symmetric systems (2016, positive): “In full analogy with the conservative case (Brazhnyi and Konotop, 2004; Pelinovsky, 2011; Yang, 2010), exponentially decaying soliton solutions (alias gap solitons) exist when µ lies inside bandgaps of the underlying linear system.”