The precise measurement of a magnetic field is one of the most fundamental and important tasks in quantum metrology. Although extensive studies on quantum magnetometry have been carried out over past decades, the ultimate precision that can be achieved for the estimation of all three components of a magnetic field with entangled probe states under the parallel scheme remains unknown. Here we present the ultimate lower bound for the sum of arbitrarily weighted variances in the estimation of all three components of a magnetic field under the parallel scheme and show that this lower bound can be achieved for sufficiently large N. The optimal entangled probe state that achieves the ultimate precision is also explicitly constructed. The obtained precision sets the ultimate limit for the multi-parameter quantum magnetometry under the parallel scheme, which is of fundamental interest and importance in quantum metrology. Our approach also provides a way to characterize the tradeoff among the precisions of multiple parameters that arise from the constraints on the probe states.
We address the estimation of the magnetic field B acting on an ensemble of atoms with total spin J subjected to collective transverse noise. By preparing an initial spin coherent state, for any measurement performed after the evolution, the mean-square error of the estimate is known to scale as $1/J$, i.e. no quantum enhancement is obtained. Here, we consider the possibility of continuously monitoring the atomic environment, and conclusively show that strategies based on time-continuous non-demolition measurements followed by a final strong measurement may achieve Heisenberg-limited scaling $1…
Solid-state qubits hold the promise to achieve unmatched combination of sensitivity and spatial resolution. To achieve their potential, the qubits need however to be shielded from the deleterious effects of the environment. While dynamical decoupling techniques can improve the coherence time, they impose a compromise between sensitivity and bandwidth, since to higher decoupling power correspond higher frequencies of the field to be measured. Moreover, the performance of pulse sequences is ultimately limited by control bounds and errors. Here we analyze a versatile alternative based on continuo…
Master equation-based model for infrared-based magnetometry with nitrogen-vacancy centers in diamond cavities: a path to sub-picotesla sensitivity at sub-millimeter scales
Quantum metrology of electric and magnetic dipole moments: ultimate limits and optimal regimes
Università di Modena e Reggio Emilia（摩德纳与雷焦艾米利亚大学）；CNR-Istituto di Nanoscienze（国家研究委员会纳米科学研究所）；Università degli Studi di Milano（米兰大学）；INFN, Sezione di Milano（意大利国家核物理研究所米兰分部）
We address metrological protocols for the estimation of the intensity and the orientation of a magnetic field, and show that quantum-enhanced precision may be achieved by probing the field with an arbitrary spin at thermal equilibrium. We derive a general expression for the ultimate achievable precision, as given by the quantum Fisher information, and express this quantity in terms of common thermodynamic quantities. We also seek for the optimal observable, and show that it corresponds to the spin projection along a suitable direction, defined by a universal function of the spin temperature. F…
Approaching the Limit in Multiparameter AC Magnetometry with Quantum Control
Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院电子研究实验室）；Department of Nuclear Science and Engineering, Massachusetts Institute of Technology（麻省理工学院核科学与工程系）；Pritzker School of Molecular Engineering, The University of Chicago（芝加哥大学普里茨克分子工程学院）；Department of Electrical and Electronic Engineering, Institute of Science Tokyo（东京科学大学电气与电子工程系）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）；Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong（香港科技大学机械与自动化工程系）；Department of Physics, The University of Tokyo（东京大学物理系）
A photon-magnon hybrid system can be realised by coupling the electron spin resonance of a magnetic material to a microwave cavity mode. The quasiparticles associated with the system dynamics are the cavity magnon polaritons, which arise from the mixing of strongly coupled magnons and photons. We illustrate how these particles can be used to probe the magnetisation of a sample with a remarkable sensitivity, devising suitable spin-magnetometers which ultimately can be used to directly assess oscillating magnetic fields. Specifically, the capability of cavity magnon polaritons of converting magn…
Entanglement-enhanced AC magnetometry in the presence of Markovian noises
The University of Tokyo（东京大学）；High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；Tohoku University（东北大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）；Massachusetts Institute of Technology（麻省理工学院）
We present an implementation of all-diamond scanning probes for scanning nitrogen-vacancy (NV) magnetometry fabricated from (111)-oriented diamond material. The realized scanning probe tips on average contain single NV spins, a quarter of which have their spin quantization axis aligned parallel to the tip direction. Such tips enable single-axis vector magnetic field imaging with nanoscale resolution, where the measurement axis is oriented normal to the scan plane. We discuss how these tips bring multiple practical advantages for NV magnetometry, in particular regarding quantitative analysis of…
Continuously monitored atomic spin-ensembles allow, in principle, for real-time sensing of external magnetic fields beyond classical limits. Within the linear-Gaussian regime, thanks to the phenomenon of measurement-induced spin-squeezing, they attain a quantum-enhanced scaling of sensitivity both as a function of time, $t$, and the number of atoms involved, $N$. In our work, we rigorously study how such conclusions based on Kalman filtering methods change when inevitable imperfections are taken into account: in the form of collective noise, as well as stochastic fluctuations of the field in t…
The confluence of quantum physics and biology is driving a new generation of quantum-based sensing and imaging technology capable of harnessing the power of quantum effects to provide tools to understand the fundamental processes of life. One of the most promising systems in this area is the nitrogen-vacancy centre in diamond - a natural spin qubit which remarkably has all the right attributes for nanoscale sensing in ambient biological conditions. Typically the nitrogen-vacancy qubits are fixed in tightly controlled/isolated experimental conditions. In this work quantum control principles of …
We demonstrate a vector magnetometer that simultaneously measures all Cartesian components of a dynamic magnetic field using an ensemble of nitrogen-vacancy (NV) centers in a single-crystal diamond. Optical NV-diamond measurements provide high-sensitivity, broadband magnetometry under ambient or extreme physical conditions; and the fixed crystallographic axes inherent to this solid-state system enable vector sensing free from heading errors. In the present device, multi-channel lock-in detection extracts the magnetic-field-dependent spin resonance shifts of NVs oriented along all four tetrahed…
Nitrogen-vacancy (NV) quantum magnetometers offer exceptional sensitivity and long-term stability. However, their use to date in distributed sensing applications, including remote detection of ferrous metals, geophysics, and biosensing, has been limited due to the need to combine optical, RF, and magnetic excitations into a single system. Existing approaches have yielded localized devices but not distributed capabilities. In this study, we report on a continuous system-in-a-fiber architecture that enables distributed magnetic sensing over extended lengths. Key to this realization is a thermall…
Quantum metrology offers an enhanced performance in experiments such as gravitational wave-detection, magnetometry or atomic clocks frequency calibration. The enhancement, however, requires a delicate tuning of relevant quantum features such as entanglement or squeezing. For any practical application the inevitable impact of decoherence needs to be taken into account in order to correctly quantify the ultimate attainable gain in precision. We compare the applicability and the effectiveness of various methods of calculating the ultimate precision bounds resulting from the presence of decoherenc…
The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving $N$ probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections -- with global control operations, …
High-resolution wide-field magnetic imaging with sparse sampling using nitrogen-vacancy centers
College of Physics and Optoelectronic Engineering, Taiyuan University of Technology（太原理工大学物理与光电工程学院）；Shanxi Key Laboratory of Precision Measurement Physics, Taiyuan University of Technology（太原理工大学精密测量物理学山西省重点实验室）；Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, and Shanxi Province, Taiyuan University of Technology（太原理工大学先进换能器与智能控制系统教育部和山西省重点实验室）
A realization of the force-induced remnant magnetization spectroscopy (FIRMS) technique of specific biomolecular binding is presented where detection is accomplished with wide-field optical and diamond-based magnetometry using an ensemble of nitrogen-vacancy (NV) color centers. The technique may be adapted for massively parallel screening of arrays of nanoscale samples.
The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a broad class of parameters, like atomic frequencies in spectroscopy or external magnetic field in magnetometry, can be overcome when using quantum probes. Environmental noise, however, generally alters the ultimate precision that can be achieved in the estimation of an unknown parameter. This tutorial reviews recent theoretical work aimed at obtaining general pre…
Quantum Metrology calculates the ultimate precision of all estimation strategies, measuring what is their root mean-square error (RMSE) and their Fisher information. Here, instead, we ask how many bits of the parameter we can recover, namely we derive an information-theoretic quantum metrology. In this setting we redefine "Heisenberg bound" and "standard quantum limit" (the usual benchmarks in quantum estimation theory), and show that the former can be attained only by sequential strategies or parallel strategies that employ entanglement among probes, whereas parallel-separable strategies are …
One of the main quests in quantum metrology is to attain the ultimate precision limit with given resources, where the resources are not only of the number of queries, but more importantly of the allowed strategies. With the same number of queries, the restrictions on the strategies constrain the achievable precision. In this work, we establish a systematic framework to identify the ultimate precision limit of different families of strategies, including the parallel, the sequential, and the indefinite-causal-order strategies, and provide an efficient algorithm that determines an optimal strateg…
We challenge the current thinking and approach to the design of photonic integrated circuits (PICs) for applications in communications, quantum information and sensing. The standard PICs are based on directional couplers, that provide a wide range of functionalities but do not fully respond to the major technological challenges: massive parallelisation of transmission channels, low-energy dissipation and small footprint. We propose a new concept for design of PICs with the ultimate downscaling capability, the absence of geometric loss and a high-fidelity throughput. This is achieved by a perio…
Optimal Strategies for Multi-parameter Quantum Metrology
The Chinese University of Hong Kong（香港中文大学）；The University of Hong Kong（香港大学）；The Hong Kong Institute of Quantum Information Science and Technology（香港量子信息科学与技术研究所）
Quantization together with quantum dynamics can be simultaneously formulated as the problem of finding an appropriate flat connection on a Hilbert bundle over a contact manifold. Contact geometry treats time, generalized positions and momenta as points on an underlying phase-spacetime and reduces classical mechanics to contact topology. Contact quantization describes quantum dynamics in terms of parallel transport for a flat connection; the ultimate goal being to also handle quantum systems in terms of contact topology. Our main result is a proof of local, formal gauge equivalence for a broad …
Planar scanning probe microscopy enables vector magnetic field imaging at the nanoscale
University of Rostock（罗斯托克大学）；Fraunhofer Institute for Applied Solid State Physics（弗劳恩霍夫应用固态物理研究所）；Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften（瓦尔特-迈斯纳研究所，巴伐利亚科学院）；Technical University of Munich（慕尼黑工业大学）
