Microwave-optical double-resonance vector magnetometry with warm Rb atoms

Developing a non-invasive, accurate vector magnetometer that operates at ambient temperature and is conducive to miniaturization and is self-calibrating is a significant challenge. Here, we present an unshielded three-axis vector magnetometer whose operation is based on the angle-dependent relative amplitude of magneto-optical double-resonance features in a room-temperature atomic ensemble. Magnetic-field-dependent double resonance features change the transmission of an optical probe tuned to the D2 optical transition of $^{87}$Rb in the presence of a microwave field driving population between the Zeeman sublevels of the ground state hyperfine levels $F = 1$ and $F = 2$. Sweeping the microwave frequency over all Zeeman sublevels results in seven double-resonance features, whose amplitudes vary as the orientation of the external static magnetic field changes with respect to the optical and microwave field polarization directions. Using a convolutional neural network model, the magnetic field direction is measured in this proof-of-concept experiment with an accuracy of 1{\deg} and its amplitude near 50 $\mu$T with an accuracy of 115 nT.