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We propose a strategy to measure weak static magnetic fields withnitrogen-vacancy color center in diamond. Inspired by avian magnetoreceptionmodels, we consider the feasibility of utilizing quantum coherence phenomena tomeasure weak static magnetic fields. Nitrogen-vacancy (NV) color centers areregarded as the ideal platform to study quantum sciences as a result of itslong coherence time up to a millisecond timescale. In high-purity diamond,hyperfine interaction with 13C nuclear spins dominates the decoherence process.In this paper, we numerically simulate the decoherence process between 0 and +1of the individual NV color center spin in 13C nuclear baths with various ofmagnitudes of external magnetic fields. By applying Hahn echo into the system,we obtain the coherence of NV color center spin as a function of totalevolution time and magnetic field. Furthermore we obtain the high-accuracyrelationship between the three decoherence-characteristic timescales, i.e. T_W,T_R, T_2, and magnetic field B. And we draw a conclusion that T_R has thehighest sensitivity about magnetic field among the three time-scales. Thus, fora certain NV color center, T_R can be the scale for the magnitude of magneticfield, or rather, the component along the NV electronic spin axis. Whenmeasuring an unknown magnetic field, we adjust the NV axis to three mutuallyorthogonal directions respectively. By this means, we obtain the threecomponents of the magnetic field and thus the magnitude and direction of theactual magnetic field. The accuracy could reach 60 nT/Hz^{1/2},and could begreatly improved by using an ensemble of NV color centers or diamond crystalspurified with 12C atoms.

Measurement of weak static magnetic fields with nitrogen-vacancy color center