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npj Quantum Information

Fundamental quantum limits of magnetic nearfield measurements

Chen Mechel, Jonathan Nemirovsky, Eliahu Cohen, Ido E. Kaminer

Published Feb 21, 2023• 3 citations
Publisher

Abstract

Abstract Major advances in the precision of magnetic measurements bring us closer to quantum detection of individual spins at the single-atom level. On the quest for reducing both classical and quantum measurement noise, it is intriguing to look forward and search for precision limits arising from the fundamental quantum nature of the measurement process itself. Here, we present the limits of magnetic quantum measurements arising from quantum information considerations, and apply these limits to a concrete example of magnetic force microscopy (MFM). We show how such microscopes have a fundamental limit on their precision arising from the theory of imperfect quantum cloning, manifested by the entanglement between the measured system and the measurement probe. We show that counterintuitively, increasing the probe complexity decreases both the measurement noise and back action, and a judicious design of the magnetic interaction reveals optimal schemes already at spin-1 probes.

DOI
10.1038/s41534-022-00674-5

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Abstract Major advances in the precision of magnetic measurements bring us closer to quantum detection of individual spins at the single-atom level. On the quest for reducing both classical and quantum measurement noise, it is intriguing to look forward and search for precision limits arising from the fundamental quantum nature of the measurement process itself. Here, we present the limits of magnetic quantum measurements arising from quantum information considerations, and apply these limits to a concrete example of magnetic force microscopy (MFM). We show how such microscopes have a fundamental limit on their precision arising from the theory of imperfect quantum cloning, manifested by the entanglement between the measured system and the measurement probe. We show that counterintuitively, increasing the probe complexity decreases both the measurement noise and back action, and a judicious design of the magnetic interaction reveals optimal schemes already at spin-1 probes.
Abstract Recent advances in transmission electron microscopy (TEM) have opened the path toward spin resonance spectroscopy with single-spin sensitivity. To assess this potential, we investigate the quantum precision limits for sensing magnetic moments with free-electron probes. Using a scattering model where an electron wavepacket interacts with a localized spin, we study two metrological tasks: estimating the magnitude of the magnetic moment and discriminating the presence of a spin. The sensitivity for a given measurement setting is generally determined by the classical Fisher information, which we benchmark against the quantum bound optimized over all measurements. We find that conventional TEM imaging can saturate the quantum bound when backaction of the probe electron onto the spin state is negligible. We also find that, when backaction is relevant, one could do better by realizing a measurement of the electron's orbital angular momentum state. These results establish the quantum limits of spin sensing in TEM and guide the development of future experiments probing individual electron spins or nanoscale ensembles of nuclear spins.
Quantum metrology uses quantum features such as entanglement and squeezing to improve the sensitivity of quantum-limited measurements. Long established as a valuable technique in optical measurements such as gravitational-wave detection, quantum metrology is increasingly being applied to atomic instruments such as matter-wave interferometers, atomic clocks, and atomic magnetometers. Several of these new applications involve dual optical/atomic quantum systems, presenting both new challenges and new opportunities. Here we describe an optical magnetometry system that achieves both shot-noise-limited and projection-noise-limited performance, allowing study of optical magnetometry in a fully-quantum regime [1]. By near-resonant Faraday rotation probing, we demonstrate measurement-based spin squeezing in a magnetically-sensitive atomic ensemble [2-4]. The versatility of this system allows us also to design metrologically-relevant optical nonlinearities, and to perform quantum-noise-limited measurements with interacting photons. As a first interaction-based measurement [5], we implement a non-linear metrology scheme proposed by Boixo et al. with the surprising feature of precision scaling better than the 1/N “Heisenberg limit” [6].
Precision measurement plays a vital role in metrology. To achieve the ultimate precision predicted by quantum theory, one can leverage quantum entanglement—correlations between particles of light or matter that cannot be explained in classical physics. The use of quantum entanglement in probing an object enhances measurement precision by a factor of √N beyond what is attainable with classical resources, where precision is typically limited by Poisson noise. Here, N represents the number of entangled particles. To date, most research efforts have focused on understanding and characterizing non-classical correlations between two particles. For instance, in 2022, optical clocks were synchronized using quantum entanglement, achieving frequency uncertainties of √2 lower than what is possible with non-entangled clocks. However, despite rapid advancements in single-particle sensing technologies, the generation and characterization of quantum correlation involving three or more particles remain an ongoing challenge. The absence of rigorous measurement standards for multi-particle entanglement, coupled with the lack of photon-number-resolving (PNR) detection capabilities, can lead to faulty measurements and reduced metrological accuracy and precision. It is therefore essential to establish robust methodologies and standards for the creation and validation of multi-particle entanglement to enable quantum-limited precision measurements. These developments will provide significant impacts in various fields, including optical astronomy, frequency standards, microscopy, and secure communication. The integration of entanglement-assisted sensors with PNR detection will enhance imaging resolution in applications such as astronomy and biological sample analysis. Additionally, standardized metrological frameworks for quantum entanglement and hardware evaluation will enhance the security level of quantum communication by mitigating vulnerabilities associated with inconsistencies arising from the use of dissimilar characterization methodologies. These fundamental research efforts will have far-reaching implications, not only improving the quality of quantum measurements but also guiding national metrology institutes in developing standardized quantum measurement protocols.
State-of-the-art linear sensors of force, motion, and magnetic fields have reached the sensitivity where the quantum noise of the meter is significant or even dominant. In particular, the sensitivity of the best optomechanical devices has reached the standard quantum limit (SQL), which directly follows from the Heisenberg uncertainty relation and corresponds to balancing the measurement imprecision and the perturbation of the probe by the quantum back-action of the meter. The SQL is not truly fundamental and several methods for its overcoming have been proposed and demonstrated. At the same time, two quantum sensitivity constraints which are more fundamental are known. The first limit arises from the finiteness of the probing strength (in the case of optical interferometers---of the circulating optical power) and is known as the energetic quantum limit or, in a more general context, as the quantum Cram\'er-Rao bound (QCRB). The second limit arises from the dissipative dynamics of the probe, which prevents full efficacy of the quantum back-action evasion techniques developed for overcoming the SQL. No particular name has been assigned to this limit; we propose the term dissipative quantum limit (DQL) for it. Here we develop a unified theory of these two fundamental limits by deriving the general sensitivity constraint for stationary, linear systems from which they follow as particular cases. Our analysis reveals a phase transition occurring at the boundary between the QCRB-dominated and the DQL regimes, manifested by the discontinuous derivatives of the optimal spectral densities of the meter quantum noise. This leads to the counterintuitive (but favorable) finding that quantum-limited sensitivity can be achieved with meter noise cross-correlations having a nonzero imaginary component, a feature arising in lossy meter systems. Finally, we show that the DQL originates from the nonautocommutativity of the internal thermal noise of the probe and that it can be overcome in nonstationary measurements.
Recently, there have been significant developments in entanglement-based quantum metrology. However, entanglement is fragile against experimental imperfections, and quantum sensing to beat the standard quantum limit in scaling has not yet been achieved in realistic systems. Here, we show that it is possible to overcome such restrictions so that one can sense a magnetic field with an accuracy beyond the standard quantum limit even under the effect of decoherence, by using a realistic entangled state that can be easily created even with current technology. Our scheme could pave the way for the realizations of practical entanglement-based magnetic field sensors.