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arXiv:0812.5076 · Physical Review A

Rabi oscillations of matter-wave solitons in optical lattices

Yu. V. Bludov, V. V. Konotop, Mario Salerno

Published Aug 27, 2009• 22 citations
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Abstract

Interband Rabi oscillations of gap-soliton matter waves induced by time-dependent periodic forces in combined linear and nonlinear optical lattices are demonstrated. It is shown that under suitable conditions, these oscillations can become long lived. By switching off the external force at proper time, it is possible to create either pure (stationary macroscopically populated) gap-soliton states or linear combination of two gap solitons with appreciably long lifetime.

DOI
10.1103/physreva.80.023623

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Interband Rabi oscillations of gap-soliton matter waves induced by time-dependent periodic forces in combined linear and nonlinear optical lattices are demonstrated. It is shown that under suitable conditions, these oscillations can become long lived. By switching off the external force at proper time, it is possible to create either pure (stationary macroscopically populated) gap-soliton states or linear combination of two gap solitons with appreciably long lifetime.
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We report the possibility of steering gap solitons in Bose-Einstein condensates loaded in optical lattices by means of time-dependent nonlinearities, which allow one to control in a nondestructive manner both Bloch oscillations and Landau-Zener tunneling (i.e., Rabi oscillations) across band gaps. As an example we show how to move a matter-wave soliton in real and in reciprocal space from a lower to higher bands, avoiding dynamical instabilities. This opens the possibility of experimental access to gap solitons of higher bands and forcing of soliton motion through a lattice via the Feshbach resonance technique.
We introduce a new method to achieve long-lived Bloch oscillations and dynamical localization of matter wave gap solitons in optical lattices. The method is based on the time-dependent modulations of the nonlinearity which can be experimentally implemented by means of the Feshbach resonance technique. In particular, we show that the width of the wavepacket is preserved if the time modulations of the nonlinearity are taken proportional to the curvature of the linear band spectrum which for most typical experimental settings are well approximated by harmonic time modulations of proper frequencies.
The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the xxx direction and a nonlinear optical lattice (NOL) in the yyy 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.
It is shown that by a proper design of the nonlinearity it is possible to obtain linear superposition of matter waves in optical lattices. In particular, the possibility to create non-stationary states of Bose-Einstein condensates which are linear superposition of stationary nonlinear matter waves is demonstrated. This is achieved by means of spatial variation of the interatomic interaction which suppresses the nonlinear overlapping terms, which otherwise would destroy the superposition, and at the same time retaining all the nonlinearity necessary for each component state to exist. The superposition state is shown to be long lived and can be split into constituent parts by accelerating the lattice.
We overview our recent theoretical studies on nonlinear atom optics of the Bose-Einstein condensates (BECs) loaded into optical lattices. In particular, we describe the band-gap spectrum and nonlinear localization of BECs in one- and two-dimensional optical lattices. We discuss the structure and stability properties of spatially localized states (matter-wave solitons) in 1D lattices, as well as trivial and vortex-like bound states of 2D gap solitons. To highlight similarities between the behavior of coherent light and matter waves in periodic potentials, we draw useful parallels with the physics of coherent light waves in nonlinear photonic crystals and optically-induced photonic lattices.