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arXiv:2405.14687 · Physical Review Letters

Quantum Thermodynamic Derivation of the Energy Resolution Limit in Magnetometry

Iannis K. Kominis

Published Dec 26, 2024• 10 citations
arXivHTMLPDF

Abstract

It was recently demonstrated that a multitude of realizations of several magnetic sensing technologies satisfy the energy resolution limit, which connects a quantity composed by the variance of the magnetic field estimate, the sensor volume and the measurement time, and having units of action, with ℏ. A first-principles derivation of this limit is still elusive. We here present such a derivation based on quantum thermodynamic arguments. We show that the energy resolution limit is a result of quantum thermodynamic work necessarily associated with quantum measurement and Landauer erasure, the work being exchanged with the magnetic field. We apply these considerations to atomic magnetometers, diamond magnetometers, and SQUIDs, spanning an energy resolution from 10^{0}ℏ to 10^{7}ℏ. This connection between quantum thermodynamics and magnetometry can help advance quantum sensing technologies towards even more sensitive devices.

DOI
10.1103/physrevlett.133.263201

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It was recently demonstrated that a multitude of realizations of several magnetic sensing technologies satisfy the energy resolution limit, which connects a quantity composed by the variance of the magnetic field estimate, the sensor volume and the measurement time, and having units of action, with ℏ. A first-principles derivation of this limit is still elusive. We here present such a derivation based on quantum thermodynamic arguments. We show that the energy resolution limit is a result of quantum thermodynamic work necessarily associated with quantum measurement and Landauer erasure, the work being exchanged with the magnetic field. We apply these considerations to atomic magnetometers, diamond magnetometers, and SQUIDs, spanning an energy resolution from 10^{0}ℏ to 10^{7}ℏ. This connection between quantum thermodynamics and magnetometry can help advance quantum sensing technologies towards even more sensitive devices.
Abstract Quantum sensing provides advanced technologies which significantly improve sensitivity and accuracy for sensing changes of motion, gravity, electric and magnetic field. Therein, quantum sensors for the detection of magnetic fields, so-called quantum magnetometers, are one of the most promising technological realizations. We firstly will provide a brief overview on methods in geophysical exploration benefitting from quantum magnetometers with resolution at the physical and technical limit. We will introduce recent developments on SQUID and OPM based sensors as specific implementations of a quantum magnetometer systems and application examples.
We demonstrate quantum sensing of dc magnetic fields that exceeds the sensitivity of conventional ${T}_{2}^{\ensuremath{\ast}}$-limited dc magnetometry by more than an order of magnitude. We use nitrogen-vacancy centers in a diamond rotating at periods comparable to the spin coherence time, and characterize the dependence of magnetic sensitivity on measurement time and rotation speed. Our method up-converts only the dc field of interest and preserves the quantum coherence of the sensor. These results definitively improve the sensitivity of a quantum magnetometer to dc fields, demonstrating that sensitivity below the ${T}_{2}^{\ensuremath{\ast}}$ limit is possible and can be applied to any diamond magnetometer where ${T}_{2}\ensuremath{\gg}{T}_{2}^{\ensuremath{\ast}}$ to yield an order-of-magnitude sensitivity improvement.
The heat dissipation in quantum metrology represents not only an unavoidable problem towards practical applications of quantum sensing devices but also a fundamental relationship between thermodynamics and quantum metrology. However, a general thermodynamic principle which governs the rule of energy consumption in quantum metrology, similar to Landauer's principle for heat dissipation in computations, has remained elusive. Here, we establish such a physical principle for energy consumption in order to achieve a certain level of measurement precision in quantum metrology, and show that it is intrinsically determined by the erasure of quantum Fisher information. The principle provides a powerful tool to investigate the advantage of quantum resources, not only in measurement precision but also in energy efficiency. It also serves as a bridge between thermodynamics and various fundamental physical concepts related in quantum physics and quantum information theory.
In modern-day quantum metrology, quantum sensors are widely employed to detect weak magnetic fields or nanoscale signals. Quantum devices, exploiting quantum coherence, are inevitably connected to physical constants and can achieve accuracy, repeatability, and precision approaching fundamental limits. As a result, these sensors have shown utility in a wide range of research domains spanning both science and technology. A rapidly emerging quantum sensing platform employs atomic-scale defects in crystals. In particular, magnetometry using nitrogen-vacancy (NV) color centers in diamond has garnered increasing interest. NV systems possess a combination of remarkable properties, optical addressability, long coherence times, and biocompatibility. Sensors based on NV centers excel in spatial resolution and magnetic sensitivity. These diamond-based sensors promise comparable combination of high spatial resolution and magnetic sensitivity without cryogenic operation. The above properties of NV magnetometers promise increasingly integrated quantum measurement technology, as a result, they have been extensively developed with various protocols and find use in numerous applications spanning materials characterization, nuclear magnetic resonance (NMR), condensed matter physics, paleomagnetism, neuroscience and living systems biology, and industrial vector magnetometry. In this chapter, NV centers are explored for magnetic sensing in a number of contexts. In general, we introduce novel regimes for magnetic-field probes with NV ensembles. Specifically, NV centers are developed for sensitive magnetometers for applications where microwaves (MWs) are prohibitively invasive and operations need to be carried out under zero ambient magnetic field. The primary goal of our discussion is to improve the utility of these NV center-based magnetometers.
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