Non-Hermitian skin effect and self-acceleration

TL;DR

This paper reveals that non-Hermitian systems exhibit early-time wave packet self-acceleration, a new dynamical signature of the non-Hermitian skin effect, which is proportional to the spectrum's enclosed area and observable in synthetic systems.

Contribution

It introduces early-time wave packet self-acceleration as a novel dynamical signature of the non-Hermitian skin effect in lattice models.

Findings

Self-acceleration occurs in single-band lattice models with single-site excitation.

The acceleration is proportional to the area enclosed by the energy spectrum.

Early-time self-acceleration can be observed in synthetic non-Hermitian systems.

Abstract

Non-Hermitian systems exhibit nontrivial band topology and a strong sensitivity of the energy spectrum on the boundary conditions. Remarkably, a macroscopic number of bulk states get squeezed toward the lattice edges under open boundary conditions, an effect dubbed the non-Hermitian skin effect (NHSE). A well-established dynamical signature of the NHSE in real space is the directional bulk flow (or persistent current) for arbitrary initial excitation of the system, which is observed at long times. Here we unravel a different dynamical signature of the NHSE in real space that manifests itself in the {\em early-time} dynamics of the system, namely self-acceleration of the wave function. Self-acceleration is demonstrated to occur rather generally in single--band lattice models probed by single-site excitation, where the acceleration turns out to be proportional to the area enclosed by the energy spectrum of the Bloch Hamiltonian under periodic boundary conditions. The observation of wave packet self-acceleration at early times is a clear signature of the NHSE and should be experimentally accessible using synthetic non-Hermitian matter, for example in discrete-time photonic quantum walks.