Bias-Field-Free Operation of Nitrogen-Vacancy Ensembles in Diamond for Accurate Vector Magnetometry

Accurate measurement of vector magnetic fields is critical for applications including navigation, geoscience, and space exploration. Nitrogen-vacancy ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mrow> <a:mi mathvariant="normal">N</a:mi> </a:mrow> </a:mrow> </a:math> <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mrow> <d:mi mathvariant="normal">V</d:mi> </d:mrow> </d:math> ) center spin ensembles offer a promising solution for high-sensitivity vector magnetometry, as their different orientations in the diamond lattice measure different components of the magnetic field. However, the bias magnetic field typically used to separate signals from each <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mrow> <g:mi mathvariant="normal">N</g:mi> </g:mrow> </g:mrow> </g:math> <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mrow> <j:mi mathvariant="normal">V</j:mi> </j:mrow> </j:math> orientation introduces inaccuracy from drifts in permanent magnets or coils. Here, we present a novel bias-field-free approach that labels the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:mrow> <m:mi mathvariant="normal">N</m:mi> </m:mrow> </m:mrow> </m:math> <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mrow> <p:mi mathvariant="normal">V</p:mi> </p:mrow> </p:math> orientations via the direction of the microwave (MW) field in a variable-pulse-duration Ramsey sequence used to manipulate the spin ensemble. Numerical simulations demonstrate the possibility to isolate each orientation’s signal with subnanotesla accuracy in most terrestrial fields, even without precise MW field calibration, at only a moderate cost to sensitivity. We also provide proof-of-principle experimental validation, observing relevant features that evolve as expected with the applied magnetic field. Looking forward, by removing a key source of drift, the proposed protocol lays the groundwork for future deployment of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mrow> <s:mrow> <s:mi mathvariant="normal">N</s:mi> </s:mrow> </s:mrow> </s:math> <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mrow> <v:mi mathvariant="normal">V</v:mi> </v:mrow> </v:math> magnetometers in high-accuracy or long-duration missions.