Localized-Interaction-Induced Quantum Reflection and Filtering of Bosonic Matter in a One-Dimensional Lattice Guide

We study the dynamics of quantum bosonic waves confined in a one-dimensional tilted optical lattice. The bosons are under the action of an effective spatially localized nonlinear two-body potential barrier set in the central part of the lattice. This version of the Bose-Hubbard model can be realized in atomic Bose-Einstein condensates, by means of localized Feshbach resonance, and in quantum optics, using an arrayed waveguide with selectively doped guiding cores. Our numerical analysis demonstrates that the central barrier induces anomalous quantum reflection of incident wave packets acting solely on bosonic components with multiple onsite occupancies. From the other side single-occupancy components can pass the barrier thus allowing one to distill them in the central interacting zone. As a consequence, in this region one finds a state in which the multiple occupancy is forbidden, i.e., a Tonks-Girardeau gas. Our results demonstrate that this regime can be obtained dynamically, using relatively weak interactions, irrespective of their sign.