Bloch oscillations in tight-binding lattices with defects

TL;DR

This paper demonstrates how to engineer defects in tight-binding lattices to preserve Bloch oscillations by using supersymmetric quantum mechanics techniques, despite the presence of defects.

Contribution

It introduces a method to create defect-tolerant lattices that maintain Bloch oscillations through spectral engineering using intertwining operators.

Findings

Defects can be made transparent for Bloch oscillations.

Engineered lattices preserve BOs despite missing resonances.

Spectral modifications ensure persistent BOs in defective lattices.

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.