Robust gigahertz-range ac magnetometry with an ensemble of N − V centers in diamond using concatenated continuous dynamical decoupling

Subpicotesla level magnetometry has been demonstrated using negatively charged nitrogen-vacancy ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">N</a:mi> <a:mtext>−</a:mtext> <a:mi>V</a:mi> </a:math> ) centers in diamond by increasing the number of spins simultaneously used for sensing in an <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi mathvariant="normal">N</d:mi> <d:mtext>−</d:mtext> <d:mi>V</d:mi> </d:math> ensemble. However, such scale-up often introduces spatial inhomogeneities in detuning and control field amplitudes, which degrade sensitivity. Although several techniques have been utilized to overcome these challenges, including pulsed dynamical decoupling or shaped pulses, these are not generally compatible with the current state-of-the-art techniques for GHz-range ac magnetometry with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi mathvariant="normal">N</g:mi> <g:mtext>−</g:mtext> <g:mi>V</g:mi> </g:math> ensembles, which are typically based on Rabi oscillations. In this work, we experimentally demonstrate GHz-range ac magnetometry using a large ensemble of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi mathvariant="normal">N</j:mi> <j:mtext>−</j:mtext> <j:mi>V</j:mi> </j:math> centers under spatially inhomogeneous drive fields by employing concatenated continuous dynamical decoupling, which is designed for robustness against such imperfections. We compare its performance with the conventional direct Rabi method and show that the robust dressed states in our method extend significantly the measuring range to weaker signals in GHz-range ac magnetometry.