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arXiv:0907.3720 · Journal of Physics B Atomic Molecular and Optical Physics

Long-lived matter wave Bloch oscillations and dynamical localization by time-dependent nonlinearity management

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

Published May 8, 2009• 17 citations
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Abstract

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.

DOI
10.1088/0953-4075/42/10/105302

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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 dynamics of matter waves in linear and nonlinear optical lattices subject to a spatially uniform linear force is studied both analytically and numerically. It is shown that by properly designing the spatial dependence of the scattering length it is possible to induce long-living Bloch oscillations of gap-soliton matter waves in optical lattices. This occurs when the effective nonlinearity and the effective mass of the soliton have opposite signs for all values of the crystal momentum in the Brillouin zone. The results apply to all systems modeled by the periodic nonlinear Schrödinger equation, including propagation of light in photonic and photorefractive crystals with tilted band structures.
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 study the Bloch oscillations (BOs) of two-component Bose-Einstein condensates (BECs) trapped in spin-dependent optical lattices. Based on the derived equations of motion of the wave packet in the basis of localized wave functions of the lattice sites, the damping effect induced by the intercomponent and intracomponent interactions to the BOs is explored analytically and numerically. We also show that such damping of the BOs can be suppressed entirely if all the atom-atom interactions are modulated synchronously and harmonically in time with suitable frequency via the Feshbach resonance. When the intercomponent and the intracomponent interactions have inverse signs, we find that the long-living BOs and even the revival of the BOs can be achieved via only statically modulating the configuration of optical lattices. The results provide a valuable guidance for achieving long-living BOs in the two-component BEC system by the Feshbach resonances and manipulating the configuration of the optical lattices.
In the present work this situation is studied analytically and numerically. In particular, we show that this is a way of managing the dynamics of matter waves - making them accelerating, oscillating, etc. In a general case, to describe the effect of the modulation, we compute dependence of the gap structure, of the group velocity of the Bloch wave, and of the effective mass of the soliton on spatial variable. The effective mass approach appears to be a useful analytical tool in this case, as well. The main physical interest of this situation consists of the fact that now the defect affects a matter soliton by interacting with its carrier wave and gives origin to various resonant effects
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.