Quantum dynamic response-based NV-diamond magnetometry: Robustness to decoherence and applications in motion detection of magnetic nanoparticles

We propose a quantum sensing protocol that leverages the dynamical response of physical observables to quenches in quantum systems. Specifically, we use the nitrogen-vacancy (NV) color center in diamond to realize both scalar and vector magnetometry via quantum response. Furthermore, we suggest a method for detecting the instantaneous motion of magnetic nanoparticles. To achieve this, we derive the closed exact form of the Berry curvature corresponding to NV centers and design quenching protocols to extract the Berry curvature via dynamical response. By constructing and solving nonlinear equations, the magnetic field and instantaneous motion velocity of the magnetic nanoparticle can be deduced. We investigate the feasibility of our sensing scheme in the presence of decoherence and show through numerical simulations that it is robust to decoherence. Intriguingly, we have observed that a vanishing nuclear spin polarization in diamond benefits our dynamic sensing scheme, which stands in contrast with conventional Ramsey-based schemes. In comparison with Ramsey-based sensing schemes, our proposed scheme can sense an arbitrary time-dependent magnetic field if its time dependence is nearly adiabatic.