We propose a three-axis closed-loop optically pumped magnetometer with high sensitivity. The closed-loop magnetometer has a three-axis sensitivity of approximately 30 fT/Hz1/2 using two orthogonal laser beams for pumping and probing the alkali metal atoms. In the closed-loop mode, the dynamic range is improved from ±5 nT to ±150 nT. The bandwidth is increased from about 100 Hz to over 2 kHz with 10 kHz modulation fields in x- and y-axes and another 6 kHz modulation field along the z-axis. Compared with single-axis or dual-axis magnetometers, the proposed magnetometer not only provides the direction and magnitude of the magnetic field but also has high robustness in a challenging environment. The magnetometer has applications in biomagnetic measurements, magnetic resonance imaging, and fundamental physics.

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The single-beam miniaturized atomic magnetometer with modulated magnetic field is one of the most capable approaches to biomagnetic measurements. The transmission intensity of the pumping beam is critical to the sensitivity of the magnetometer, which is affected by the density of alkali metal and the polarization of atomic spin. In this study, we investigated into the influence of three variables: the temperature of atomic vapour; the amplitude of the modulated magnetic field; the frequency of modulated magnetic field on the transmission intensity of pumping beam. We have defined their relationship into a function, and the calculated values through theoretical analysis have a high degree of fit with the measured values of numerous experiments. It is discovered that the transmission intensity decreases with the increase in temperature, and this effect is modified by the modulation index. A compact magnetometer is developed as a proof of concept based on single-beam scheme. The volume of this magnetometer is 10 cm 3 , and its dual axis sensitivity are both 30 fT/Hz 1/2 . Based on this relationship we find that two major improvements are achieved by separating the DC and AC components of transmission intensity: 1. Realizing closed-loop temperature control for atomic vapour which improved the stability of the magnetometer. 2. Achieving closed-loop dual axis magnetic measurements under a single-beam scheme, which extends the magnetometer's scope of application.

The comprehensive influence of the amplitude and frequency of the modulated magnetic field and the magnitude of the bias magnetic field on the performance of an atomic magnetometer have been investigated. Under different magnetic fields, the combined action of the spin precession signal caused by a high-amplitude magnetic field and the influence of magnetic field on relaxation makes the time domain output signal and the amplitude of the first to fourth harmonics show different characteristics, which cannot be explained by the classical analytical calculation solution. By considering the influence of the magnetic field on the transverse relaxation, a more complete model is constructed to explain the phenomenon with a numerical solution, and the overall fit is 93.26%. Based on the single beam and magnetic field modulation scheme, a compact magnetometer is constructed for verification, with a volume of 56.7 cm3 and a sensitivity of 30 fT/Hz1/2.

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