Bloch oscillations in tight-binding lattices with defects

Abstract

Defects in tight-binding lattices generally destroy the onset of Bloch oscillations (BOs) and the periodic self-imaging of the wave packet due to the lack of an equally-spaced Wannier-Stark ladder spectrum. Here it is shown that localized and extended defects in the lattice can be engineered to be transparent for BOs. Such lattices are synthesized from the defect-free lattice by the technique of intertwining operators generally employed in supersymmetric quantum mechanics. The energy spectrum of the synthesized lattices differs from the Wannier-Stark ladder of the defect-free lattice because of the missing of pairs of resonances in the ladder, thus ensuring the persistence of BOs.