Non-Hermitian Anomalous Scaling Engineering

TL;DR

This paper experimentally demonstrates and controls anomalous scaling in non-Hermitian photonic lattices, revealing new phenomena and enabling nonlinear non-Hermitian physics exploration.

Contribution

It introduces the first experimental platform for linear and nonlinear anomalous scaling engineering in non-Hermitian systems.

Findings

Direct observation of scaling-driven spectral reshaping and eigenstate localization.

Scaling can induce a non-Hermitian topological phase transition with protected edge modes.

Weak nonlinearity affects the speed of anomalous scaling, while strong nonlinearity suppresses it.

Abstract

Non-Hermitian systems exhibit anomalous scaling, a striking departure from conventional bulk laws, rooted in the non-Hermitian skin effect (NHSE). Here, we experimentally uncover this scaling and demonstrate its active control in a temporal photonic lattice. By tracking the real-time evolution of all eigenstates as system size varies, we directly observe scaling-driven spectral reshaping and eigenstate localization, revealing phenomena absent in Hermitian or NHSE-free lattices. In a Su-Schrieffer-Heeger lattice, scaling alone can trigger a non-Hermitian topological phase transition, with edge modes remaining protected. Crucially, Kerr interactions open the frontier of nonlinear non-Hermitian physics: weak nonlinearity accelerates or decelerates anomalous scaling, while strong nonlinearity suppresses it entirely. These results establish the first experimental platform for linear and nonlinear anomalous scaling engineering, paving the way for compact non-Hermitian devices and exploration of nonlinear and many-body non-Hermitian phenomena.