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Nonlinear lattice dynamics of Bose–Einstein condensates
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View: Figures


Image of FIG. 1.
FIG. 1.

Comparison of the lattice reconstructed solution in the tight-binding (dashed line) and the 3-band (dashed–dotted line) approximation with the numerical solution of the GP equation (14) (solid line). The comparison is performed for and different chemical potentials: (left panels) and (right panels). The bottom panels show the same features as the top ones using semi-log plots. Additionally, in both the left and right bottom panels, there is a dotted line showing the result of the dynamical evolution (at ), of the tight-binding approximation in the corresponding cases (i.e., for the left panel and for the right one.) In the left panel, the dynamical evolution practically coincides with the exact solution. In the right panel, the tight-binding initial condition tries to deform itself (from the dashed to dotted profile) to “approach” the shape of the exact solution (solid line).

Image of FIG. 2.
FIG. 2.

(Color online). A quasi-1D condensate (solid line) in a deep periodic optical-lattice potential (dashed line). The condensate is effectively described as a chain of coupled solitons whose positions follow a Toda lattice with on-site potentials [Eq. (31) ]. Using the oscillating ansatz (32) , where the soliton is forced to oscillate with amplitude , one can further reduce the dynamics to a second-order recurrence relationship between neighboring amplitudes [Eq. (33) ].

Image of FIG. 3.
FIG. 3.

(Color online). Homoclinic connection of the origin (top-left panel), giving rise to a spatially localized profile (top-right panel). Bottom: the localized state in the original BEC model (14) generated by the prescribed amplitude configuration. The shaded base, depicting , highlights the areas in which the atomic density varies the most. Observe that the solution decays as one moves away from the center . (As the solution is symmetric with respect to , only its right-hand side is shown.)


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nonlinear lattice dynamics of Bose–Einstein condensates