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arXiv:2102.07212 · Physical Review A

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

Shu-Hao Wu, Ethan Turner, Hailin Wang

Published Apr 12, 2021• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.103.042607

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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 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 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 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 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.
Nitrogen Vacancy (NV) centers are point defects in diamond that allow magnetic field sensing based on Optically Detected Magnetic Resonance (ODMR). They are processed in ultrapure single-domain CVD grown diamond crystals and can be operated at room temperature. This results in solid-state sensors with a wide variety of applications. Ensemble of NV centers can be used to perform wide-field magnetic imaging with sensitivity in the nT range. Single NV centers can also be processed, which allows sensing at the atomic scale. This possibility, combined with its unique coherence properties, make NV center an ideal candidate for quantum sensing.
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.