Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice

TL;DR

This paper demonstrates the geometry-dependent skin effect in a 2D non-Hermitian optical lattice, showing anisotropic Bloch oscillations and revealing how system geometry influences eigenstate localization.

Contribution

It introduces the concept of geometry-dependent skin effect in a 2D optical lattice with atom loss, linking it to anisotropic bulk dynamics and Bloch oscillation behavior.

Findings

GDSE depends on system geometry and boundary conditions

Anisotropic Bloch oscillations reveal complex energy spectra

Intrinsic anisotropic bulk dynamics are demonstrated

Abstract

The interplay between the non-Hermiticity and dimensionality gives rise to exotic characteristics in higher dimensions, with one representative phenomenon known as the geometry-dependent skin effect (GDSE), which refers to that the localization of extensive eigenstates depends on the system's geometry under open boundary conditions. In this paper, we demonstrate the emergence of GDSE in a two-dimensional $sp$ optical ladder lattice with on-site atom loss, which can be manifested by anisotropic dynamics of Bloch oscillations in the bulk of the system. By applying a static force in different directions, the wave-packet dynamics retrieve the complex energy spectra with either nonzero or zero spectral winding number, indicating the presence or absence of skin accumulation in the corresponding directions, respectively. Our results reveal that the GDSE has an intrinsic anisotropic bulk dynamics independent of boundary conditions, and offer its realization and detection in quantum systems.