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arXiv:2109.04040 · Physical Review Applied

Exponentially Enhanced Quantum Non-Hermitian Sensing via Optimized Coherent Drive

Liying Bao, Bo Qi, Daoyi Dong

Published Jan 26, 2022• 29 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevapplied.17.014034

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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.
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.
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 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.
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 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.
Exceptional points (EPs) exhibit strongly enhanced spectral responses and are therefore promising candidates for sensing applications. Whether these non-Hermitian degeneracies provide a genuine advantage in the quantum regime has been the subject of ongoing debate. Here, we address this issue within a scattering-matrix formalism for sensing with coherent light, which allows the quantum Fisher information (QFI) to be evaluated directly from experimentally accessible scattering data without introducing additional noise channels beyond those inherent to the scattering process. We analyze both nondegenerate and degenerate scattering-matrix poles, including EPs of arbitrary order, and show that the QFI per incoming photon flux is governed by three key factors: the decay rate of the resonant mode, the strength of the spectral response associated with non-normality, and the adjustment between the scattering states and the information source. For spatially localized perturbations, this implies that the Fisher information is fully determined by the local density of states at the perturbation site. Within this framework, we demonstrate that EPs can enhance the QFI compared to isolated modes or diabolic points with identical decay rates, and that the QFI can be further increased by moving away from the EP toward parameter regimes where non-Hermitian linewidth splitting reduces the decay rate of one mode. We further show that sufficiently small additional internal losses do not alter this overall picture, thereby providing a unified and experimentally relevant perspective on the design of quantum-limited non-Hermitian sensors.