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arXiv:2503.01211 · Science Advances

Adaptive cold-atom magnetometry mitigating the trade-off between sensitivity and dynamic range

Zhu Ma, Chengyin Han, Zhi Tan, Hao-Ning He, Shenzhen Shi, Xin Kang, Jiatao Wu, Jiahao Huang, Bo Lü, Chaohong Lee

Published Feb 28, 2025• 19 citations
arXivHTMLPDF

Abstract

Cold-atom magnetometers can achieve an exceptional combination of superior sensitivity and high spatial resolution. One key challenge that these quantum sensors face is improving the sensitivity within a given timeframe while preserving a high dynamic range. Here, we experimentally demonstrate an adaptive entanglement-free cold-atom magnetometry with both superior sensitivity and high dynamic range. Using a tailored adaptive Bayesian quantum estimation algorithm designed for Ramsey interferometry using coherent population trapping (CPT), cold-atom magnetometry facilitates adaptive high-precision detection of a dc magnetic field with high dynamic range. Through implementing a sequence of correlated CPT-Ramsey interferometry, the sensitivity significantly surpasses the standard quantum limit with respect to total interrogation time. We yield a sensitivity of 6.8 ± 0.1 picotesla per square root of hertz over a range of 145.6 nanotesla, exceeding the conventional frequentist protocol by 3.3 ± 0.1 decibels. Our study opens avenues for the next generation of adaptive cold-atom quantum sensors, wherein real-time measurement history is leveraged to improve their performance.

DOI
10.1126/sciadv.adt3938

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Cold-atom magnetometers can achieve an exceptional combination of superior sensitivity and high spatial resolution. One key challenge that these quantum sensors face is improving the sensitivity within a given timeframe while preserving a high dynamic range. Here, we experimentally demonstrate an adaptive entanglement-free cold-atom magnetometry with both superior sensitivity and high dynamic range. Using a tailored adaptive Bayesian quantum estimation algorithm designed for Ramsey interferometry using coherent population trapping (CPT), cold-atom magnetometry facilitates adaptive high-precision detection of a dc magnetic field with high dynamic range. Through implementing a sequence of correlated CPT-Ramsey interferometry, the sensitivity significantly surpasses the standard quantum limit with respect to total interrogation time. We yield a sensitivity of 6.8 ± 0.1 picotesla per square root of hertz over a range of 145.6 nanotesla, exceeding the conventional frequentist protocol by 3.3 ± 0.1 decibels. Our study opens avenues for the next generation of adaptive cold-atom quantum sensors, wherein real-time measurement history is leveraged to improve their performance.
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.
Precision sensing, and in particular high precision magnetometry, is a central goal of research into quantum technologies. For magnetometers, often trade-offs exist between sensitivity, spatial resolution, and frequency range. The precision, and thus the sensitivity of magnetometry, scales as 1/sqrt[T_{2}] with the phase coherence time T_{2} of the sensing system playing the role of a key determinant. Adapting a dynamical decoupling scheme that allows for extending T_{2} by orders of magnitude and merging it with a magnetic sensing protocol, we achieve a measurement sensitivity even for high frequency fields close to the standard quantum limit. Using a single atomic ion as a sensor, we experimentally attain a sensitivity of 4.6 pT/sqrt[Hz] for an alternating-current magnetic field near 14 MHz. Based on the principle demonstrated here, this unprecedented sensitivity combined with spatial resolution in the nanometer range and tunability from direct current to the gigahertz range could be used for magnetic imaging in as of yet inaccessible parameter regimes.
The utilization of Ramsey interferometry via coherent population trapping (CPT), which enables the optical interrogation of microwave transitions without the reliance on microwave cavities, plays a crucial role in the advancement of compact and low-power quantum sensors. Particularly, high-resolution CPT-Ramsey spectroscopy of alkali-metal atoms has found extensive application in constructing miniaturized quantum sensors like atomic magnetometers and atomic clocks. Due to their well-defined environment and extended coherence time, cold atoms offer enhanced sensitivity and precision in CPT-Ramsey interferometry. This review comprehensively examines CPT-Ramsey interferometry with cold atoms, encompassing both conventional and multi-pulse techniques, and explores their potential applications in practical quantum sensors.
Atomic clocks are crucial for fundamental science and practical technology, but their sensitivity is often constrained by the standard quantum limit. With a cold-atom coherent-population-trapping clock, the authors design and experimentally demonstrate an adaptive Bayesian quantum frequency estimation protocol that approaches the Heisenberg scaling with respect to total interrogation time. This atomic clock also yields improved fractional frequency stability and enhanced robustness against technical noises. This work provides a high-precision approach to atomic clock locking, and holds promising applications in various interferometry-based quantum sensors.
Atomic gravimeters are the most accurate sensors for measuring gravity, yet a significant challenge lies in achieving high precision while also maintaining high dynamic range and robustness. Here, we develop a protocol for achieving robust high-precision atomic gravimetry based upon adaptive Bayesian quantum estimation. Our protocol incorporates a sequence of interferometry measurements taken with short to long interrogation times and offers several crucial advantages. Firstly, it enables a high dynamic range without the need to scan multiple fringes for pre-estimation, making it more efficient than the conventional frequentist method. Secondly, it improves robustness against noises, allowing for a significant improvement in measurement precision in noisy environments. The enhancement can be more than 5 times for a transportable gravimeter [] and up to an order of magnitude for a state-of-the-art fountain gravimeter []. Notably, by optimizing the interferometry sequence, our approach can improve the scaling of the measurement precision ( Δ g est ) versus the total interrogation time ( T ̃ ) to Δ g est ∝ T ̃ − 2 or even better, in contrast to the conventional one Δ g est ∝ T ̃ − 0.5 . Our approach offers superior precision, increased dynamic range, and enhanced robustness, making it highly promising for a range of practical sensing applications.
Quantum magnetometry based on adaptive phase estimation allows for Heisenberg precision while avoiding creation and maintenance of complex entangled states. However, the absolute sensitivity is limited by the nonoptimal use of quantum resources provided by multiple-qubit devices and algorithmic realizations of the protocol. Here, addressing both issues, we advance the time-ascending phase estimation protocol by numerical improvements of Bayesian learning, i.e., sequential updating of the field distribution, and optimal exploitation of resources provided by unentangled qubits with limited coherence. Such algorithmic improvements are used to evaluate the absolute sensitivity both on a simulator and by pulsed-transmon experiments conducted on the IBMQ platform, where we take advantage of high coherence time. In addition, we compare the proficiency of separable and entangled states for magnetometry and show that, in practice, separable states provide superior performance. Flux-sensing emulation experiments demonstrate that a sensitivity of $(0.17--1.74)\ensuremath{\mu}{\mathrm{\ensuremath{\Phi}}}_{0}\phantom{\rule{4pt}{0ex}}{(\sqrt{\mathrm{Hz}})}^{\ensuremath{-}1}$ (where ${\mathrm{\ensuremath{\Phi}}}_{0}$ is the flux quantum) for a single-qubit magnetometer and $(0.06--0.65)\ensuremath{\mu}{\mathrm{\ensuremath{\Phi}}}_{0}\phantom{\rule{4pt}{0ex}}{(\sqrt{\mathrm{Hz}})}^{\ensuremath{-}1}$ for a five-qubit magnetometer can be achieved for slowly oscillating 1−−10kHz1--10\phantom{\rule{4pt}{0ex}}\mathrm{kHz}1−−10kHz magnetic fields, which is comparable to more established experimental platforms for magnetometry.