Non-Hermitian invisibility in tight-binding lattices

TL;DR

This paper demonstrates that in tight-binding lattices, a broad class of time-dependent non-Hermitian potentials can be made fully invisible due to the lattice's finite energy bandwidth, enabling new wave control methods.

Contribution

It introduces a method to synthesize invisible non-Hermitian potentials in Hermitian tight-binding lattices exploiting their finite energy bandwidth.

Findings

Wide class of non-Hermitian potentials can be made invisible in lattices.

Invisibility is achieved through the finite energy bandwidth of the lattice.

Method applies to arbitrary spatial shapes of potentials.

Abstract

A flexible control of wave scattering in complex media is of relevance in different areas of classical and quantum physics. Recently, a great interest has been devoted to scattering engineering in non-Hermitian systems, with the prediction and demonstration of new classes of non-Hermitian potentials with unique scattering properties, such as transparent and invisibile potentials or one-way reflectionless potentials. Such potentials have been found for both continuous and discrete (lattice) systems. However, wave scattering in lattice systems displays some distinct features arising from the discrete (rather than continuous) translational invariance of the system, characterized by a finite band of allowed energies and a finite speed of wave propagation on the lattice. Such distinct features can be exploited to realize invisibility on a lattice with methods that fail when applied to continuous systems. Here we show that a wide class of time-dependent non-Hermitian scattering potentials or defects with arbitrary spatial shape can be synthesized in an Hermitian single-band tight-binding lattice, which are fully invisible owing to the limited energy bandwidth of the lattice.