Energy-Resolved Eigenmode Spectroscopy of 1-D and 2-D Non-Hermitian Skin Effects

TL;DR

This paper demonstrates energy-resolved eigenmode spectroscopy of non-Hermitian skin effects in 1D and 2D lattices using a frequency synthetic dimension in an electro-optic resonator, revealing boundary-localized states and directional transport.

Contribution

It introduces a novel spectroscopic method to directly probe non-Hermitian skin modes and constructs 2D frequency lattices with tunable edge states and transport.

Findings

Revealed boundary-localized skin states across the spectrum.

Demonstrated eigenenergy-dependent displacement of modes from the edge.

Observed tunable directional transport and edge localization in 2D synthetic lattices.

Abstract

Non-Hermitian lattices can host the non-Hermitian skin effect, a boundary-induced collapse of all bulk eigenstates into exponentially localized edge modes. This effect underlies anomalous bulk-boundary correspondence and remarkable enhancements in non-Hermitian sensing, yet direct energy-resolved access to the eigenmodes of non-Hermitian lattices has remained limited. Here we report band- and energy-resolved eigenmode spectroscopy of skin modes in a frequency synthetic dimension. By introducing strong frequency-domain boundaries in an electro-optically modulated ring resonator, we realize finite non-Hermitian lattices and use laser detuning as a spectroscopic axis for the eigenenergies of the effective Hamiltonian. Site-resolved heterodyne measurements then reconstruct the spatial profile of each mode, revealing boundary-localized skin states throughout the spectrum and their eigenenergy-dependent displacement from the edge. Beyond 1D, the same frequency-boundary architecture, upon incorporating long-range couplings between finite lattices, produces genuine 2D frequency lattices rather than the hitherto-realized folded 1D systems on twisted tubes. In these lattices we observe tunable directional transport and edge localization in two synthetic dimensions. Our results introduce eigenmode spectroscopy as a direct probe of non-Hermitian physics and establish strongly bounded frequency lattices as a flexible platform for Hamiltonian engineering.