Quantum vector DC magnetometry via selective phase accumulation

Precision measurement of magnetic fields is a crucial issue in both fundamental scientific research and practical sensing technology. The sensitive detection of a vector magnetic field poses a significant challenge in quantum magnetometry, particularly in estimating a vector DC magnetic field with high precision. Here, we propose a comprehensive protocol for quantum vector DC magnetometry, utilizing selective phase accumulation in both non-entangled and entangled quantum probes. Building upon the principles of Ramsey interferometry, our protocol enables the selective accumulation of phase for a specific magnetic field component by incorporating a meticulously designed pulse sequence. In the individual measurement scheme, we employ three individual quantum interferometries to independently estimate each of the three magnetic field components. Alternatively, in the simultaneous measurement scheme, the application of a pulse sequence along different directions enables the simultaneous estimation of all three magnetic field components using only one quantum interferometry. Notably, by employing an entangled state (such as the Greenberger-Horne-Zeilinger state) as the input state, the measurement precisions of all three components may reach the Heisenberg limit. This study not only establishes a general protocol for measuring vector magnetic fields using quantum probes, but also presents a viable pathway for achieving entanglement-enhanced multi-parameter estimation.