Resonant scattering of matter-wave gap solitons by optical lattice defects

The physical mechanism underlying scattering properties of matter-wave gap solitons (GSs) by linear-optical-lattice defects is investigated. The occurrence of repeated reflection, transmission, and trapping regions for increasing strengths of an optical-lattice defect are shown to be due to resonances with impurity modes inside the defect potential with chemical potentials and numbers of atoms matching corresponding quantities of the incoming GSs. For small amplitude GSs the number of these resonances coincides with the number of bound states existing in the defect potential for the given defect strength. The dependence of the positions and widths of the transmission resonant peaks on incoming velocities is investigated by means of defect-mode analysis and effective-mass theory. The comparisons with direct integrations of the Gross-Pitaevskii equation provide good agreement confirming the correctness of our approach. Multiple resonant transmissions through arrays of optical lattice defects are also investigated and the possibility of using them for very precise GS dynamical filters is also suggested.