Dynamics and Manipulation for Gap Solitons in Bose-Einstein Condensatesunder Optical Lattice and Harmonic Potentials

By means of an extended variational approach, we study dynamics for gap solitons in a repulsive interaction Bose-Einstein condensate under both a harmonic and an optical lattice confinement. The simplified analytic theory gives the critical strength ratio of harmonic to optical lattice necessary to support multiple stable lattice sites for the condensate. Moreover, we use numerical experiments to guide and manipulate the gap solitons to an arbitrary position via a time-dependent potential. All predictions of the extended variational approach are reasonably close to results of the simulations. In particular,
the variational model helps capture the composition relationship between the variations of chirp and amplitude.