Magnetic Field Vector Detection in Frequency Domain with an Optically Pumped Atomic Magnetometer

The motion of spin polarization in a high-sensitivity optically pumped atomic magnetometer is described by the Bloch equation. We propose a magnetometer having two nonparallel probe beams to measure both the x and y components of spin polarization, while a pumping beam propagates in the z direction. When a bias magnetic field is applied parallel to the pumping beam, the magnetic fields Bx and By both affect the x and y components of the spin polarization. The relation between the magnetic field and the magnetometer signal is correctly expressed in matrix form for a simple oscillating magnetic field. The relation enables us to solve the Bloch equation in the frequency domain and retrieve the original waveform of the time-dependent magnetic field waveform. This magnetometer also compensates for distortion of the waveform caused by the resonant nature of the Bloch equation. The magnetic field signal recovery is demonstrated by numerical simulation and the preferred parameter range for the proposed dual-probe magnetometer is shown. As a result, the proposed magnetometer will expand the possibility for weak magnetic field measurements, including biomagnetic fields.