Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Spin-based continuous Bayesian magnetic-field estimations aided by feedback control

Ethan Turner, Shu-Hao Wu, Xinzhu Li, Hailin Wang

Published Nov 7, 2022• 9 citations
Publisher

Abstract

We demonstrate continuous real-time Bayesian estimations of magnetic-field fluctuations by monitoring single-photon emissions from a diamond nitrogen vacancy center under the setting of coherent population trapping, for which the time sequence of the single-photon emissions is correlated with the underlying magnetic-field fluctuations. The Bayesian estimations are combined with a feedback loop and are followed by a separate verification and optimization process, which uses the spin-dephasing rate in the presence of the feedback as a cost function. The dephasing rate is measured with Ramsey interferometry and is minimized by systematically varying the statistical parameters used in the estimations. The Bayesian estimations aided by the feedback and verification enable continuous real-time sensing at the single-photon level regardless of the prior availability of the statistical parameters of the underlying dynamics.

DOI
10.1103/physreva.106.052603

Related papers

Continuous real-time sensing with a nitrogen-vacancy center via coherent population trapping

Shu-Hao Wu, Ethan Turner, Hailin Wang

We propose and theoretically analyze the use of coherent population trapping of a single diamond nitrogen-vacancy (NV) center for continuous real-time sensing. The formation of the dark state in coherent population trapping prevents optical emissions from the NV center. Fluctuating magnetic fields, however, can kick the NV center out of the dark state, leading to a sequence of single-photon emissions. A time series of the photon counts detected can be used for magnetic field estimations, even when the average photon count per update time interval is much smaller than 1. For a theoretical demonstration, the nuclear spin bath in a diamond lattice is used as a model fluctuating magnetic environment. For fluctuations with known statistical properties, such as an Ornstein-Uhlenbeck process, Bayesian inference-based estimators can lead to an estimation variance that approaches the classical Cramer-Rao lower bound and can update dynamical information in real time with the detection of just a single photon. Real-time sensing using coherent population trapping adds a powerful tool to the emerging technology of quantum sensing.

arXiv:2102.07212•Physical Review A•Apr 12, 2021•18 citations

Real-time magnetometry via coherent population trapping in a nitrogen vacancy center

Hailin Wang

We report the experimental demonstration of real-time magnetometry by detecting fluorescence from a nitrogen vacancy center in the setting of coherent population trapping and by estimating magnetic fields from the time series of the observed photon counts. We show that by taking into consideration the statistical properties of magnetic field fluctuations, a Bayesian inference-based estimator can effectively update dynamical information of the field in real time with the detection of just a single photon.

Optical and Quantum Sensing and Precision Metrology II•Mar 9, 2022•0 citations

Real-time magnetometry with coherent population trapping in a nitrogen-vacancy center

Ethan Turner, Shu-Hao Wu, Xinzhu Li +1 more

We demonstrate real-time magnetometry by detecting fluorescence from a nitrogen-vacancy center in the setting of coherent population trapping and by estimating the magnetic field from the time series of the observed photon counts, which are correlated with the underlying field variation. The proof-of-principle experiment uses an external time-varying magnetic field that follows an Ornstein-Uhlenbeck (OU) process. A conventional estimator based on the use of average photon counts per relevant time interval is susceptible to photon number shot noise and performs poorly at relatively low average photon counts. In comparison, by taking into consideration the statistical properties of the OU process, a Bayesian inference-based estimator can effectively update dynamical information of the field in real time with the detection of just a single photon.

Physical Review A•Jan 20, 2022•11 citations

Real-Time Magnetometry Using Dark States of a Nitrogen Vacancy Center

Ethan Turner, Shu-Hao Wu, Xinzhu Li +1 more

We demonstrate real-time magnetometry by detecting fluorescence from a nitrogen vacancy center in the setting of coherent population trapping and by estimating magnetic field from the time series of the observed photon counts, which are correlated with the underlying field. The proof-of-principle experiment uses an external time-varying magnetic field that follows an Ornstein-Uhlenbeck (OU) process. By taking into consideration the statistical properties of the OU process, a Bayesian inference-based estimator can effectively update dynamical information of the field in real time with the detection of just a single photon.

arXiv:2111.09943•Nov 18, 2021•0 citations

Efficient Real-Time Spin Readout of Nitrogen-Vacancy Centers Based on Bayesian Estimation

Jixing Zhang, Tianzheng Liu, Heng Yuan +8 more

This article introduces a real-time Bayesian estimation algorithm aimed at enhancing the spin readout efficiency of the nitrogen vacancy (NV) center ensemble in the diamond. By integrating both the prior probability distribution and the fluorescence likelihood function, stemming from the implementation of the NV center dynamics model, we offered an innovative solution to surpass the Cramer–Rao lower bound of the readout variance and improve the readout efficiency. The proposed real-time Bayesian estimation readout algorithm was experimentally realized by combining high-performance acquisition and processing hardware, and the Rabi oscillation experiments divulged that the signal-to-noise ratio of our approach was improved by 28.6%. This research illustrates the potential of the Bayesian estimation readout to enhance the NV ensemble's sensing capabilities and support the development of compact and scalable quantum sensors devices on a monolithic platform.

arXiv:2302.06310•IEEE Transactions on Industrial Electronics•Jan 24, 2024•6 citations

Bayesian estimation for quantum sensing in the absence of single-shot detection

Hossein T. Dinani, Dominic William Berry, Raúl González Brouwer +2 more

Quantum information protocols, such as quantum error correction and quantum phase estimation, have been widely used to enhance the performance of quantum sensors. While these protocols have relied on single-shot detection, in most practical applications only an averaged readout is available, as in the case of room-temperature sensing with the electron spin associated with a nitrogen-vacancy center in diamond. Here, we theoretically investigate the application of the quantum phase estimation algorithm for high dynamic-range magnetometry, when single-shot readout is not available. We show that, even in this case, Bayesian estimation provides a natural way to efficiently use the available information. We apply Bayesian analysis to achieve an optimized sensing protocol for estimating a time-independent magnetic field with a single electron spin associated to a nitrogen-vacancy center at room temperature and show that this protocol improves the sensitivity over previous protocols by more than a factor of 3. Moreover, we show that an extra enhancement can be achieved by considering the timing information in the detector clicks.

arXiv:1806.01249•Physical review. B./Physical review. B•Mar 11, 2019•50 citations
We demonstrate continuous real-time Bayesian estimations of magnetic-field fluctuations by monitoring single-photon emissions from a diamond nitrogen vacancy center under the setting of coherent population trapping, for which the time sequence of the single-photon emissions is correlated with the underlying magnetic-field fluctuations. The Bayesian estimations are combined with a feedback loop and are followed by a separate verification and optimization process, which uses the spin-dephasing rate in the presence of the feedback as a cost function. The dephasing rate is measured with Ramsey interferometry and is minimized by systematically varying the statistical parameters used in the estimations. The Bayesian estimations aided by the feedback and verification enable continuous real-time sensing at the single-photon level regardless of the prior availability of the statistical parameters of the underlying dynamics.
We propose and theoretically analyze the use of coherent population trapping of a single diamond nitrogen-vacancy (NV) center for continuous real-time sensing. The formation of the dark state in coherent population trapping prevents optical emissions from the NV center. Fluctuating magnetic fields, however, can kick the NV center out of the dark state, leading to a sequence of single-photon emissions. A time series of the photon counts detected can be used for magnetic field estimations, even when the average photon count per update time interval is much smaller than 1. For a theoretical demonstration, the nuclear spin bath in a diamond lattice is used as a model fluctuating magnetic environment. For fluctuations with known statistical properties, such as an Ornstein-Uhlenbeck process, Bayesian inference-based estimators can lead to an estimation variance that approaches the classical Cramer-Rao lower bound and can update dynamical information in real time with the detection of just a single photon. Real-time sensing using coherent population trapping adds a powerful tool to the emerging technology of quantum sensing.
We report the experimental demonstration of real-time magnetometry by detecting fluorescence from a nitrogen vacancy center in the setting of coherent population trapping and by estimating magnetic fields from the time series of the observed photon counts. We show that by taking into consideration the statistical properties of magnetic field fluctuations, a Bayesian inference-based estimator can effectively update dynamical information of the field in real time with the detection of just a single photon.
We demonstrate real-time magnetometry by detecting fluorescence from a nitrogen-vacancy center in the setting of coherent population trapping and by estimating the magnetic field from the time series of the observed photon counts, which are correlated with the underlying field variation. The proof-of-principle experiment uses an external time-varying magnetic field that follows an Ornstein-Uhlenbeck (OU) process. A conventional estimator based on the use of average photon counts per relevant time interval is susceptible to photon number shot noise and performs poorly at relatively low average photon counts. In comparison, by taking into consideration the statistical properties of the OU process, a Bayesian inference-based estimator can effectively update dynamical information of the field in real time with the detection of just a single photon.
We demonstrate real-time magnetometry by detecting fluorescence from a nitrogen vacancy center in the setting of coherent population trapping and by estimating magnetic field from the time series of the observed photon counts, which are correlated with the underlying field. The proof-of-principle experiment uses an external time-varying magnetic field that follows an Ornstein-Uhlenbeck (OU) process. By taking into consideration the statistical properties of the OU process, a Bayesian inference-based estimator can effectively update dynamical information of the field in real time with the detection of just a single photon.
This article introduces a real-time Bayesian estimation algorithm aimed at enhancing the spin readout efficiency of the nitrogen vacancy (NV) center ensemble in the diamond. By integrating both the prior probability distribution and the fluorescence likelihood function, stemming from the implementation of the NV center dynamics model, we offered an innovative solution to surpass the Cramer–Rao lower bound of the readout variance and improve the readout efficiency. The proposed real-time Bayesian estimation readout algorithm was experimentally realized by combining high-performance acquisition and processing hardware, and the Rabi oscillation experiments divulged that the signal-to-noise ratio of our approach was improved by 28.6%. This research illustrates the potential of the Bayesian estimation readout to enhance the NV ensemble's sensing capabilities and support the development of compact and scalable quantum sensors devices on a monolithic platform.
Quantum information protocols, such as quantum error correction and quantum phase estimation, have been widely used to enhance the performance of quantum sensors. While these protocols have relied on single-shot detection, in most practical applications only an averaged readout is available, as in the case of room-temperature sensing with the electron spin associated with a nitrogen-vacancy center in diamond. Here, we theoretically investigate the application of the quantum phase estimation algorithm for high dynamic-range magnetometry, when single-shot readout is not available. We show that, even in this case, Bayesian estimation provides a natural way to efficiently use the available information. We apply Bayesian analysis to achieve an optimized sensing protocol for estimating a time-independent magnetic field with a single electron spin associated to a nitrogen-vacancy center at room temperature and show that this protocol improves the sensitivity over previous protocols by more than a factor of 3. Moreover, we show that an extra enhancement can be achieved by considering the timing information in the detector clicks.