Nuclear spin metrology with nitrogen vacancy center in diamond for axion dark matter detection

We present a method to directly detect the axion dark matter using nitrogen vacancy centers in diamonds. In particular, we use metrology leveraging the nuclear spin of nitrogen to detect axion-nucleus couplings. This is achieved through protocols designed for dark matter searches, which introduce a novel approach of quantum sensing techniques based on the nitrogen vacancy center. Although the coupling strength of the magnetic fields with nuclear spins is three orders of magnitude smaller than that with electron spins for conventional magnetometry, the axion interaction strength with nuclear spins is the same order of magnitude as that with electron spins. Furthermore, we can take advantage of the long coherence time by using the nuclear spins for the axion dark matter detection. Our method has the potential to be sensitive to a broad frequency range <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mo>≲</a:mo><a:mn>100</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mrow><a:mi>Hz</a:mi></a:mrow></a:mrow></a:math> corresponding to the axion mass <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>m</c:mi></c:mrow><c:mrow><c:mi>a</c:mi></c:mrow></c:msub><c:mo>≲</c:mo><c:mn>4</c:mn><c:mo>×</c:mo><c:msup><c:mrow><c:mn>10</c:mn></c:mrow><c:mrow><c:mo>−</c:mo><c:mn>13</c:mn></c:mrow></c:msup><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>eV</c:mi></c:mrow></c:math>. We present the detection limit of our method for both the axion-neutron and the axion-proton couplings and discuss its significance in comparison with other proposed ideas. We also show that the sensitivities of the NV center sensor to various spin species will open up new directions for constructing protocols that can mitigate magnetic noise effects.