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arXiv:physics/0408030 · Physical Review Letters

Soliton Eigenvalue Control in Optical Lattices

Yaroslav V. Kartashov, L.-C. Crasovan, Anna S. Zelenina, Victor A. Vysloukh, Anna Sanpera, Maciej Lewenstein, Lluís Torner

Published Sep 27, 2004• 32 citations
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Abstract

We address the dynamics of higher-order solitons in optical lattices, and predict their self-splitting into the set of their single-soliton constituents. The splitting is induced by the potential introduced by the lattice, together with the imprinting of a phase tilt onto the initial multisoliton states. The phenomenon allows the controllable generation of several coherent solitons linked via their Zakharov-Shabat eigenvalues. Application of the scheme to the generation of correlated matter waves in Bose-Einstein condensates is discussed.

DOI
10.1103/physrevlett.93.143902

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We address the dynamics of higher-order solitons in optical lattices, and predict their self-splitting into the set of their single-soliton constituents. The splitting is induced by the potential introduced by the lattice, together with the imprinting of a phase tilt onto the initial multisoliton states. The phenomenon allows the controllable generation of several coherent solitons linked via their Zakharov-Shabat eigenvalues. Application of the scheme to the generation of correlated matter waves in Bose-Einstein condensates is discussed.
We discuss a method for creating bright matter solitons by loading a Bose-Einstein condensate of atoms in a driven tilted optical lattice. It is shown that one can realize the self-focusing regime for the wave-packet dynamics by properly adjusting the phase of the driving field with respect to the phase of Bloch oscillations. If atom-atom interactions are larger than some critical value gmin{g}_{\mathrm{min}}gmin​, this self-focusing regime is followed by the formation of bright solitons. Increasing the interactions above another critical value gmax{g}_{\mathrm{max}}gmax​ makes this process unstable. Instead of soliton formation one now meets the phenomenon of incoherent self-trapping. In this regime a fraction of atoms is trapped in incoherent localized wave packets, while the remaining atoms spread ballistically.
As a coherent matter wave,the Bose-Einstein condensate(BEC) provides a playground for the investigation of the macroscopic quantum phenomenon.The nonlinear optical lattice,which is consisted of two counter-propagating laser beams,is a powerful and widely used tool for the controlling of the dynamics of the coherent matter wave.In view of the potential applications of BEC,two or more independently grown condensates provide extra controllable degrees of freedom and can be used in many areas,such as quantum metrology and quantum computation.In this paper,a multi-mode description is introduced to characterize the multi-component coherent matter wave.To determine the evolution property of the multi-mode matter wave in a nonlinear optical lattice,we solve the multi-mode coupled nonlinear equations.A set of analytical bright soliton solutions are constructed with a similarity transformation.
We consider coupled matter-wave bright solitons in spatial coherence spin–orbit coupled Bose–Einstein condensates (SOC-BECs) in optical and Rabi-coupling lattice (RL) potentials and find an effective potential for separation of coupled matter-wave solitons. We show that the Rabi lattice significantly affects the potential near the region of overlap between the solitons. We study the effects of Rabi lattice on the dynamics of solitons for different initial overlaps and show that the dynamics is controlled by the interplay between the Rabi lattice and inter-component interaction. We investigate that, by tuning the Rabi lattice strength, one can realize localize, periodic and splitting dynamics of the total density profile of the coupled solitons.