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arXiv:2605.15863

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

Wenwen Liu, Zhang Shuang

quant-phphysics.opticsSubmitted May 15, 2026• Announced May 18, 2026• Revised Aug 10, 2026 (v2)
v1 · May 15, 2026v2 · Aug 10, 2026
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Abstract

Programmable mode selection is essential for integrated photonic networks, yet selectively isolating individual modes without delicate balancing of gain and loss remains challenging. Here we introduce a gauge-engineering method in non-Hermitian 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 emerges naturally, separated from the remaining modes by a large, tunable energy gap. By introducing synthetic gauge fields through phase-compensated non-reciprocal hopping, any desired pure decay mode can be promoted to the dominant position while its amplitude profile is preserved, which can be naturally interpreted by spectral graph theory. The approach further 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.

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Programmable mode selection is essential for integrated photonic networks, yet selectively isolating individual modes without delicate balancing of gain and loss remains challenging. Here we introduce a gauge-engineering method in non-Hermitian 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 emerges naturally, separated from the remaining modes by a large, tunable energy gap. By introducing synthetic gauge fields through phase-compensated non-reciprocal hopping, any desired pure decay mode can be promoted to the dominant position while its amplitude profile is preserved, which can be naturally interpreted by spectral graph theory. The approach further 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.
Non-Hermitian physics has unveiled a realm of exotic phenomena absent in Hermitian systems, with the non-Hermitian skin effect (NHSE) showcasing boundary-localized eigenstates driven by non-reciprocal interactions. Here, we introduce a new class of non-Hermitian systems exhibiting pure decay modes-eigenstates with pure, smooth exponential decay, devoid of the oscillatory wave patterns typical of traditional NHSE. Modeled as directed graphs with nonreciprocal hopping, these systems reveal quantized decay charges, defined as the sum of decay constants along edges at each node, offering a novel topological invariant. We derive universal conditions for these modes, enabling versatile configurations from one-dimensional rings, directed graphs with complicated connectivity, to higher-dimensional lattices. Experimental validation using microwave resonant circuits confirms the predicted pure decay profiles. This discovery paves the way for potential applications in photonics, signal processing, and beyond, harnessing the unique topological properties of non-Hermitian networks.
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Non-Hermitian physics traditionally relies on active gain--loss modulation or non-reciprocal couplings, which often introduce significant complexity, compromise stability, and offer very limited scalability in conservative systems. Here we propose an attenuation-gauge duality paradigm in which non-Hermitian topology emerges within fully passive, conservative systems through coupling to a structured reservoir. We derive that a spatially varying reservoir can establish an attenuation-gauge duality, where the spatial variation manifests as an emergent imaginary gauge field in the effective dynamics. It drives the boundary accumulation of skin modes while preserving energy conservation, analogous to Feshbach projection in quantum open systems. We validate this universal wave paradigm via macroscopic mechanical metamaterials, demonstrating that the direction of the skin effect can be reversed by tuning a single passive coupling parametert⊥t_\perpt⊥​, driven by a topological phase transition characterized by the spectral winding number. This framework also allows for a nonlinear extension, where amplitude-dependent coupling can induce intrinsic topological transitions.
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.
Programmable preparation of entangled quantum states is a central requirement for scalable quantum information processing, quantum networking and photonic quantum computing. Topological photonic platforms offer an attractive route towards robust quantum-state generation by encoding information in symmetry- protected optical modes, yet the generated entangled states are typically dictated by the lattice geometry and therefore lack programmability. Here we demonstrate programmable preparation of topological entangled states by inverse engineering the nonlinear optical pump profile of an integrated photonic lattice. Our approach enables deterministic control over both the dimensionality and modal structure of the generated entangled state while preserving its topological character. We experimentally realize silicon photonic topological superlattices in which the nonlinear generation pathway itself becomes programmable via tailored excitations. The superlattices host a multiband manifold of co localized topological interface modes, while coherently controlled inputs synthesize pump superpositions within this protected basis. We showcase this principle by selectively addressing topological biphoton eigenstates, steering correlations to produce a desired target state in a high-dimensional Hilbert space, and inverse-designing pump states that generate targeted Schmidt dimensionalities. Site-resolved two-photon correlation measurements remain reproducible across nominally identical fabricated devices, demonstrating robustness to realistic nanofabrication-induced disorder. Programmable preparation of topological entangled states establishes a pathway towards exploiting topological photonic modes as application-specific quantum resources, enabling tailored input states for high-dimensional quantum communication, quantum networking and photonic quantum computing.
Non-Abelian gauge fields play a key role in describing the behavior of particles whose motion is coupled to internal degrees of freedom, such as their spin. Here, we experimentally realize a tuneable non-Abelian gauge field in an active mechanical lattice by using pairs of oscillators to encode a local pseudo-spin for each site, with inter-site spin-dependent couplings engineered via real-time measurement and feedback. We experimentally extract Wilson-loop observables in our set-up and hence demonstrate that we can create a genuinely non-Abelian gauge field. We then exploit the controllability of our mechanical lattice to engineer non-reciprocal hoppings to explore non-Hermitian non-Abelian gauge potentials. For a two-dimensional (2D) lattice, we demonstrate that the non-Hermiticity can manifest in direction-dependent Wilson loops for a single plaquette, while for a one-dimensional (1D) system, we show that a non-Abelian gauge potential can switch the localization of non-Hermitian skin modes between opposite ends of a chain. Our work establishes active mechanical lattices as a flexible and programmable platform for probing non-Abelian gauge fields and exploring their interplay with non-Hermitian dynamics.