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arXiv:2412.13249 · Physical Review Research

Quantum sensing with driven-dissipative Su-Schrieffer-Heeger lattices

Oscar Arandes, Emil J. Bergholtz

Published Mar 24, 2025• 7 citations
arXivHTMLPDF

Abstract

The remarkable sensitivity of non-Hermitian systems has been extensively studied and stimulated ideas about developing new types of sensors. In this paper, we examine a chain of parametrically driven coupled resonators governed by the squeezed Su-Schrieffer-Heeger model. We emphasize the qualitative difference in sensor performance between configurations depending on bulk topology and boundary modes, specifically for detecting both on-site and non-Hermitian skin effect perturbations. Our analysis goes beyond the scenario of infinitesimal perturbations, extending to arbitrary perturbation strengths beyond the linear response regime. We stress the importance of optimizing the system's parameters to achieve quantum enhancement while avoiding fine-tuned regimes that could limit the practical applicability of this system for real-world quantum sensing.

DOI
10.1103/physrevresearch.7.013309

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The remarkable sensitivity of non-Hermitian systems has been extensively studied and stimulated ideas about developing new types of sensors. In this paper, we examine a chain of parametrically driven coupled resonators governed by the squeezed Su-Schrieffer-Heeger model. We emphasize the qualitative difference in sensor performance between configurations depending on bulk topology and boundary modes, specifically for detecting both on-site and non-Hermitian skin effect perturbations. Our analysis goes beyond the scenario of infinitesimal perturbations, extending to arbitrary perturbation strengths beyond the linear response regime. We stress the importance of optimizing the system's parameters to achieve quantum enhancement while avoiding fine-tuned regimes that could limit the practical applicability of this system for real-world quantum sensing.
Non-Hermitian systems have been employed to construct a high-sensitivity sensor. To evaluate the performance of the sensors, the quantum Fisher information per photon, or equivalently signal-to-noise ratio per photon, is provided as a “true” sensing criterion, which avoids the trivial contribution from the photon numbers. The specific properties of non-Hermitian systems, e.g., exceptional points and skin effect, have been connected to the true exponentially enhanced sensing performance. To date, the relation between the non-Hermitian topological phase and the true sensing performance has not been reported clearly. Here, we construct the high-sensitivity sensor based on the non-Hermitian Su–Schrieffer–Heeger lattice and establish the relationship between the exponentially enhanced sensing and the non-Hermitian topologically nontrivial phase. The saturation of sensing with the size emerges in the sense of one perturbation. Such a limitation can be surpassed through the change of incident positions of driving fields, and the exponentially enhanced sensing reappears.
Distinct non-Hermitian dynamics has demonstrated its advantages in improving measurement precision over traditional sensing protocols. Multimode non-Hermitian lattice dynamics can provide exponentially enhanced quantum sensing where the quantum Fisher information (QFI) per photon increases exponentially with the lattice size. However, it has also been shown that the quintessential non-Hermitian skin effect does not provide any true advantage. In this paper, we demonstrate the importance of optimizing the phase of the coherent drive and the position of the injection and detection in multimode non-Hermitian quantum sensing. The QFI per photon can be exponentially enhanced or exponentially reduced depending on the parameters of the drive and detection. Specifically, it is demonstrated that for large amplification, by choosing appropriate coherent drive parameters, the non-Hermitian skin effect can provide exponentially enhanced quantum sensing. Moreover, in the regime beyond linear response, the skin effect can also provide a clear advantage as compared to the local perturbation and the proposed protocol is robust in tuning the amplification factor.
The covariant quantum Fisher information (CQFI) has recently been established as the ultimate precision benchmark for pseudo-Hermitian sensors [Phys. Rev. Lett. 136, 080802 (2026)], yet existing analyses are limited to single-mode systems. Here we extend the CQFI formalism to multi-mode non-Hermitian Su-Schrieffer-Heeger lattices and reveal tunable topological enhancement enabled by the non-Hermitian skin effect (NHSE). Under open boundary conditions, the NHSE deforms the conventional Brillouin zone into a generalized Brillouin zone of radius r = exp(\k{appa}), where \k{appa} denotes the non-Bloch decay rate. While the total CQFI scales linearly with system size N, its prefactor depends critically on \k{appa}, yielding an enhancement factor E(N) = F_OBC / F_PBC that exceeds 30 for N ~ 30, substantially outperforming periodic-boundary sensors. The enhancement is robust against moderate local disorder and supports multi-parameter estimation, with the joint Cramér-Rao bound reduced by up to 15 orders of magnitude. These findings establish a spatial-domain mechanism for quantum metrology that complements time-domain strategies and is experimentally accessible using topoelectrical circuits, photonic lattices, and superconducting circuits with current technology.
Non-Hermitian systems have been extensively studied in quantum metrology due to their unique properties, such as the skin effects, exceptional points, and the non-reciprocity. It has been demonstrated that although non-Hermitian systems may achieve ultra-high precision of quantum sensing, the measurement precision greatly depends on the position of the coherent drive in the regime of linear response. In this paper, we further investigate how the position of the coherent drive impacts the precision of non-Hermitian sensing in the regime beyond linear response. It is found that in contrast to the linear case, the best possible quantum Fisher information per photon of the sensor does not depend on the position of the coherent drive in the nonlinear perturbation regime.
Abstract Non-Hermitian systems exhibit markedly different phenomena than their conventional Hermitian counterparts. Several such features, such as the non-Hermitian skin effect, are only present in spatially extended systems. Potential applications of these effects in many-mode systems however remains largely unexplored. Here, we study how unique features of non-Hermitian lattice systems can be harnessed to improve Hamiltonian parameter estimation in a fully quantum setting. While the quintessential non-Hermitian skin effect does not provide any distinct advantage, alternate effects yield dramatic enhancements. We show that certain asymmetric non-Hermitian tight-binding models with a Z2{{\mathbb{Z}}}_{2}Z2​ Z 2 symmetry yield a pronounced sensing advantage: the quantum Fisher information per photon increases exponentially with system size. We find that these advantages persist in regimes where non-Markovian and non-perturbative effects become important. Our setup is directly compatible with a variety of quantum optical and superconducting circuit platforms, and already yields strong enhancements with as few as three lattice sites.
Non-Hermitian systems exhibit markedly different phenomena than their conventional Hermitian counterparts. Several such features, such as the non-Hermitian skin effect, are only present in spatially extended systems. Potential applications of these effects in many-mode systems however remains largely unexplored. Here, we study how unique features of non-Hermitian lattice systems can be harnessed to improve Hamiltonian parameter estimation in a fully quantum setting. While the quintessential non-Hermitian skin effect does not provide any distinct advantage, alternate effects yield dramatic enhancements. We show that certain asymmetric non-Hermitian tight-binding models with a [Formula: see text] symmetry yield a pronounced sensing advantage: the quantum Fisher information per photon increases exponentially with system size. We find that these advantages persist in regimes where non-Markovian and non-perturbative effects become important. Our setup is directly compatible with a variety of quantum optical and superconducting circuit platforms, and already yields strong enhancements with as few as three lattice sites.