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.