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arXiv:2106.05297 · Physical Review Research

Quantum non-Hermitian topological sensors

Florian Koch, Jan Carl Budich

Published Feb 11, 2022• 114 citations
arXivHTMLPDF

Abstract

We investigate in the framework of quantum noise theory how the striking boundary sensitivity recently discovered in the context of non-Hermitian (NH) topological phases may be harnessed to devise novel quantum sensors. Specifically, we study a quantum-optical setting of coupled modes arranged in an array with broken ring geometry that would realize a NH topological phase in the classical limit. Using methods from quantum-information theory of Gaussian states, we show that a small coupling induced between the ends of the broken ring may be detected with a precision that increases exponentially in the number of coupled modes, e.g., by heterodyne detection of two output modes. While this robust effect only relies on reaching a NH topological regime, we identify a resonance phenomenon without direct classical counterpart that provides an experimental knob for drastically enhancing the aforementioned exponential growth. Our findings pave the way towards designing quantum NH topological sensors that may observe with high precision any physical observable that couples to the boundary conditions of the device.

DOI
10.1103/physrevresearch.4.013113

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We investigate in the framework of quantum noise theory how the striking boundary sensitivity recently discovered in the context of non-Hermitian (NH) topological phases may be harnessed to devise novel quantum sensors. Specifically, we study a quantum-optical setting of coupled modes arranged in an array with broken ring geometry that would realize a NH topological phase in the classical limit. Using methods from quantum-information theory of Gaussian states, we show that a small coupling induced between the ends of the broken ring may be detected with a precision that increases exponentially in the number of coupled modes, e.g., by heterodyne detection of two output modes. While this robust effect only relies on reaching a NH topological regime, we identify a resonance phenomenon without direct classical counterpart that provides an experimental knob for drastically enhancing the aforementioned exponential growth. Our findings pave the way towards designing quantum NH topological sensors that may observe with high precision any physical observable that couples to the boundary conditions of the device.
High-precision sensors are of fundamental importance in modern society and technology. Although there are various schemes for the construction of sensors relying on different physical mechanisms, obtaining sensors with higher levels of sensitivity and stronger robustness has always been expected. In particular, non-Hermitian quantum sensors have recently attracted substantial attention due to their unique properties. So far, 2 types of non-Hermitian sensors based on exceptional points and topological zero modes have been realized. Here, high-order exceptional bound states with robust properties are constructed for the first time. Based on these states, we propose theoretically and demonstrate experimentally another new type of non-Hermitian quantum sensors. Such sensors not only are robust against disorders but also have unprecedented sensitivity. Their sensing performance can display the improvement of many orders of magnitude over the previous non-Hermitian sensors. Furthermore, we design and fabricate such sensors based on circuit networks. Taking weak magnetic field detection as an example, we also experimentally demonstrate their sensing capabilities. Our work opens up new avenues for the development of highly sensitive sensors, which have a wide range of applications in various fields.
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.
Non-Hermitian systems have emerged as a powerful paradigm for ultrasensitive sensing, leveraging unique spectral and dynamical properties unmatched in Hermitian physics. While recent theoretical bounds suggest these protocols offer no metrological advantage over Hermitian ones in the ideal shot-noise-limited regime when rigorously accounting for the success probability of non-unitary evolution, their practical utility in realistic experimental conditions has not yet been systematically explored. In this work, we shift the focus toward practical laboratory performance and demonstrate that non-Hermitian sensing protocols can significantly outperform their Hermitian counterparts in the presence of pervasive classical technical noises. This performance gain mainly stems from a strongly enhanced susceptibility that amplifies the signal response, effectively overcoming the precision floor imposed by technical imperfections. By numerically evaluating the Fisher information under technical noise, we further substantiate the regimes where non-Hermitian platforms yield definitive practical gains. Our results reconcile the ongoing debate between fundamental limits and experimental observations, offering a concrete avenue for building high-precision, noise-resilient sensors.
Abstract Non-Hermitian (NH) physics predicts open quantum system dynamics with unique topological features such as exceptional points and the NH skin effect. We show that this new paradigm of topological systems can serve as probes for bulk Hamiltonian parameters with quantum-enhanced sensitivity reaching Heisenberg scaling. Such enhancement occurs close to a spectral topological phase transition, where the entire spectrum undergoes a delocalization transition. We provide an explanation for this enhanced sensitivity based on the closing of point gap, which is a genuinely NH energy gap with no Hermitian counterpart. This establishes a direct connection between energy-gap closing and quantum enhancement in the NH realm. Our findings are demonstrated through several paradigmatic NH topological models in various dimensions and potential experimental implementations.
Considering non-Hermitian systems implemented by utilizing enlarged quantum systems, we determine the fundamental limits for the sensitivity of non-Hermitian sensors from the perspective of quantum information. We prove that non-Hermitian sensors do not outperform their Hermitian counterparts (directly couple to the parameter) in the performance of sensitivity, due to the invariance of the quantum information about the parameter. By scrutinizing two concrete non-Hermitian sensing proposals, which are implemented using full quantum systems, we demonstrate that the sensitivity of these sensors is in agreement with our predictions. Our theory offers a comprehensive and model-independent framework for understanding the fundamental limits of non-Hermitian quantum sensors and builds the bridge over the gap between non-Hermitian physics and quantum metrology.
Non-Hermitian topological systems have attracted a lot of research activities in recent times, both theoretically and experimentally, due to their unique physical properties and association with open quantum systems. We show that modular structures, where specific couplings at regular intervals take distinct values, enrich the unique topological attributes of these systems such as the non-Hermitian skin effect and the breakdown of conventional bulk-boundary correspondence. These systems also possess the capability of displaying criticality-enhanced sensitivity for precision metrology. We establish how the modular structure enhances their sensing performance near spectral topological phase transitions and show that the enhancement can be achieved in multi-parameter estimation scenarios as well.