Gradient-based optimal control of the non-Hermitian skin effect in optomechanical arrays
Abstract
In single-port non-Hermitian sensors the Petermann factor offsets susceptibility gains, imposing a strict resource bound on metrological precision. We test whether a multi-port geometry can evade this bound: a double-chain optomechanical ladder with opposing non-reciprocal hoppings spatially separates signal amplification from quantum-noise drainage, and gradient-based differentiable optimal control (DOC) maximizes the resource-normalized Fisher information Fnorm subject to a Hurwitz-stability constraint. Across system sizes N∈{num6,…,num16} the optimizer returns Fnorm>0 in every case, with two coexisting solution classes whose selection is initialization-dependent: deep-stability configurations achieve Fnorm∈numrange0.9370.987 with attenuated transmission, while marginal-stability configurations deliver directional gain Gfwd∈qtyrange13.515.5dB with isolation Iso∈qtyrange4064dB. A multi-restart ensemble reveals these classes are the endpoints of a precision--gain frontier. All solutions remain Hurwitz-stable under \qty{5}{\percent} disorder (\qty{87.5}{\percent} recovery), and the deep-stability advantage survives realistic preamplifier noise at Fnormeff≈num0.3--num0.5. Mapped onto circuit-QED parameters, the architecture enables sub-attonewton force sensing and broadband axion searches across the \qtyrange{1}{10}{\giga\hertz} band.
Related
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BibTeX
@misc{deuyekbe2026gradientbased,
title = {{Gradient-based optimal control of the non-Hermitian skin effect in optomechanical arrays}},
author = {Juste Deuyekbe and Philippe Djorwé and A. -H. Abdel-Aty and A. Elrashidi and Nsangou Mama and Serge Guy Nana Engo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04492},
eprint = {2609.04492},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04492},
}
RIS
TY - UNPB
TI - Gradient-based optimal control of the non-Hermitian skin effect in optomechanical arrays
AU - Juste Deuyekbe
AU - Philippe Djorwé
AU - A. -H. Abdel-Aty
AU - A. Elrashidi
AU - Nsangou Mama
AU - Serge Guy Nana Engo
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04492
UR - https://arxiv.org/abs/2609.04492
AB - In single-port non-Hermitian sensors the Petermann factor offsets susceptibility gains, imposing a strict resource bound on metrological precision. We test whether a multi-port geometry can evade this bound: a double-chain optomechanical ladder with opposing non-reciprocal hoppings spatially separates signal amplification from quantum-noise drainage, and gradient-based differentiable optimal control (DOC) maximizes the resource-normalized Fisher information Fnorm subject to a Hurwitz-stability constraint. Across system sizes N∈{num6,…,num16} the optimizer returns Fnorm>0 in every case, with two coexisting solution classes whose selection is initialization-dependent: deep-stability configurations achieve Fnorm∈numrange0.9370.987 with attenuated transmission, while marginal-stability configurations deliver directional gain Gfwd∈qtyrange13.515.5dB with isolation Iso∈qtyrange4064dB. A multi-restart ensemble reveals these classes are the endpoints of a precision--gain frontier. All solutions remain Hurwitz-stable under \qty{5}{\percent} disorder (\qty{87.5}{\percent} recovery), and the deep-stability advantage survives realistic preamplifier noise at Fnormeff≈num0.3--num0.5. Mapped onto circuit-QED parameters, the architecture enables sub-attonewton force sensing and broadband axion searches across the \qtyrange{1}{10}{\giga\hertz} band.
ER -