Gauge-Engineered Tunable Mode Selection in Non-Hermitian Directed-Graph Networks

TL;DR

This paper presents a gauge-engineering approach in directed-graph networks that allows for tunable, robust mode selection and control without gain or loss, advancing quantum and wave system applications.

Contribution

It introduces a novel gauge-engineering method to selectively promote pure decay modes in non-Hermitian directed-graph networks, enabling customizable mode control.

Findings

A single dominant mode with a large energy gap naturally emerges in fully connected networks.

Synthetic gauge fields can promote any desired decay mode to dominance while preserving its profile.

The method extends to multi-mode distributions in higher-dimensional networks.

Abstract

Non-Hermitian physics enables novel control over open quantum and wave systems, but selectively isolating individual modes without delicate balancing of gain and loss remains challenging. Here we introduce a gauge-engineering method in directed-graph networks that support geometry-protected pure decay modes-eigenstates exhibiting smooth exponential amplitude decay along directed paths. In fully connected configurations, a single dominant mode naturally emerges with a large, tunable energy gap from the rest. By adding synthetic gauge fields via phase-compensated non-reciprocal hopping, we can promote any desired pure decay mode to the dominant position, while preserving its amplitude profile. The approach extends to simultaneous selection of paired modes in half-connected graphs and customizable multi-mode distributions in higher dimensions via orthogonal folding. Our method enables robust, loss/gain-free control over mode profiles, advancing applications in single-mode lasers, sensors, and quantum processing.