Quantum Vector DC Magnetometry via Selective Phase Accumulation

Precision measurement of magnetic fields is an important goal for fundamental science and practical sensing technology. Sensitive detection of a vector magnetic field is a crucial issue in quantum magnetometry, it remains a challenge to estimate a vector DC magnetic field with high efficiency and high precision. Here, we propose a general protocol for quantum vector DC magnetometry via selective phase accumulation of both non-entangled and entangled quantum probes. Based upon the Ramsey interferometry, our protocol may achieve selective phase accumulation of only one magnetic field component by inserting well-designed pulse sequence. In the parallel scheme, three parallel quantum interferometries are utilized to estimate three magnetic field components independently.In the sequential scheme, by applying a pulse sequence along different directions, three magnetic field components can be estimated simultaneously via only one quantum interferometry. In particular, if the input state is an entangled state such as the Greenberger-Horne-Zeilinger state, the measurement precisions of all three components may approach the Heisenberg limit. Our study not only develops a general protocol for measuring vector magnetic fields via quantum probes, but also provides a feasible way to achieve Heisenberg-limited multi-parameter estimation via many-body quantum entanglement.