The measurement precision of the static atomic gravimetry is limited by white Gaussian noise in short term, which costs previous works an inevitable integration to reach the precision demanded. Here, we propose a statistical model based on the quantum projection noise and apply the associated Kalman filter with the waveform estimation in static atomic gravimetry. With the white Gaussian noise significantly removed by the Kalman-filter formalism, the measurement noise of the gravimetry is reshaped in short term and shows τ1/2 feature that corresponds to a random walk. During 200 h of static measurement of gravity, the atomic gravimeter using Kalman filter demonstrates a sensitivity as good as 0.6 nms2/s and highlights a precision of 1.7 nms2 at the measuring time of a single sample. The measurement noise achieved is also lower than the quantum projection limit below ∼30 s.
The measurement precision of the static atomic gravimetry is limited by white Gaussian noise in short term, which costs previous works an inevitable integration to reach the precision demanded. Here, we propose a statistical model based on the quantum projection noise and apply the associated Kalman filter with the waveform estimation in static atomic gravimetry. With the white Gaussian noise significantly removed by the Kalman-filter formalism, the measurement noise of the gravimetry is reshaped in short term and shows τ1/2 feature that corresponds to a random walk. During 200 h of static measurement of gravity, the atomic gravimeter using Kalman filter demonstrates a sensitivity as good as 0.6 nms2/s and highlights a precision of 1.7 nms2 at the measuring time of a single sample. The measurement noise achieved is also lower than the quantum projection limit below ∼30 s.
Atomic gravimetry measures the gravitional acceleration of an ensemble of identical neutral atoms through the atom interferometry based on Raman two-photon transition, where the Raman lasers are used as “optical ruler" and the identical neutral atoms play the role of test mass and quantum storage of gravity field information. As the novel gravimetry system suffers no mechanical wear and works at a higher repetition rate, atom gravimetry can reach a much better short-term sensitivity than the classical falling-corner-cube counterpart, and the accuracy is reasonably well. Since the very first in-laboratory device built over 30 years ago, atomic gravimetry has matured to a versatile tool that offers both precise and accurate absolute gravity measurement to fundamental research and metrology, such as testing the weak equivalence principle or linking the mass and weight of the test mass in Watt (Kibble) balance. As the current rapid development of compact cold-atom gravimeters, atomic gravimetry is moving out of the laboratory to be used as a quantum enhancement of classical devices in dynamical measurement, such as geophysics survey, inertial navigation and space mission. We review the roadmap for the development of cold-atom absolute gravimetry, highlight recent advances in the dynamical measurement using compact cold atom gravimeters and discuss the associated technological challenges. In the future, with the maturity of its application in dynamical measurement or civil engineering and the innovation in atom interferometry theory, atomic gravimetry could play a more and more important role in our life.
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.
Atom interferometry offers new perspectives for geophysics and inertial sensing. We present the industrial prototype of a quantum-based instrument: a compact, transportable, differential quantum gravimeter capable of measuring simultaneously the absolute values of both gravitational acceleration g and its vertical gradient ${\mathrm{\ensuremath{\Gamma}}}_{zz}$. While the sensitivity to g is competitive with the best industrial gravimeters, the sensitivity on ${\mathrm{\ensuremath{\Gamma}}}_{zz}$ reaches the limit set by quantum projection noise---leading to a long-term stability of 0.1E ($1\phantom{\rule{0.28em}{0ex}}\mathrm{E}=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{0.28em}{0ex}}{\mathrm{s}}^{\ensuremath{-}2}$). This dual-purpose instrument constitutes the industrial integration of cold atom sensors for practical applications. It paves the way for different applications in geophysics, civil engineering, and gravity-aided navigation, where accurate mapping of the gravitational field plays an important role.
Sensing a magnetic field with an atomic magnetometer operated in real time presents significant challenges, primarily due to sensor nonlinearity, the presence of noise, and the need for one-shot estimation. To address these challenges, we propose a comprehensive approach that integrates measurement, estimation, and control strategies. Specifically, this involves implementing a quantum nondemolition measurement based on continuous light probing of the atomic ensemble. The resulting photocurrent is then directed into an extended Kalman filter to produce instantaneous estimates of the system’s dynamical parameters. These estimates, in turn, are utilized by a linear quadratic regulator, whose output is applied back to the system through a feedback loop. This procedure automatically steers the atomic ensemble into a spin-squeezed state, yielding a quantum enhancement in precision. Furthermore, thanks to the feedback proposed, the atoms exhibit entanglement even when the measurement data are discarded. To prove that our approach constitutes the optimal strategy in realistic scenarios, we derive ultimate bounds on the estimation error applicable in the presence of both local and collective decoherence, and show that these are indeed attained. Additionally, we demonstrate that, for large ensembles, the extended Kalman filter not only reliably predicts its own estimation error in real time, but also accurately estimates spin squeezing at short timescales.
Abstract Single‐beam atomic magnetometers herald a new era of high‐precision magnetic field sensing, with applications spanning fundamental physics to biomagnetism. Nevertheless, their utility is often curtailed by quantum sensor noise, encompassing both technical and quantum‐mechanical noise. This research delves into the potential of the Kalman filter as a tool to subdue quantum sensor noise, thereby augmenting the sensitivity of single‐beam atomic magnetometers. Quantum‐mechanical noise is integrated into the system model as the process noise and measurement noise, and a discrete Kalman filter equipped with a time delay variable is employed. The findings reveal that the time delay variable significantly influences temporal signal tracing, while the discrete Kalman filter enhances sensitivity performance in frequency domain analysis, bypassing the typical sensitivity and time resolution trade‐off encountered in coherent sensing strategies. Partial‐knowledge signal scenarios are also taken into account, wherein a polynomial model is proposed to expansively render the discrete Kalman filter more relevant and adaptable to real‐world situations. Collectively, through experimentation involving sine‐like, non‐Gaussian, and medical magnetocardiography (MCG) signals, our results underscore the promising potential of the Kalman filter in enhancing the sensitivity of atomic magnetometers for practical sensing applications.
The shot-noise detection limit in current high-precision magnetometry [Nature (London) 422, 596 (2003)] is a manifestation of quantum fluctuations that scale as 1/sqrt[N] in an ensemble of N atoms. Here, we develop a procedure that combines continuous measurement and quantum Kalman filtering [Rep. Math. Phys. 43, 405 (1999)]] to surpass this conventional limit by exploiting conditional spin squeezing to achieve 1/N field sensitivity. Our analysis demonstrates the importance of optimal estimation for high bandwidth precision magnetometry at the Heisenberg limit and also identifies an approximate estimator based on linear regression.