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

Atomic systems offer opportunities for noninvasive, accurate vector magnetometers that operate at ambient temperature and are conducive to miniaturization. Here, we demonstrate an unshielded three-axis vector magnetometer whose operation is based on the angle-dependent relative amplitude of cavity-enhanced magneto-optical double-resonance features in a room-temperature atomic ensemble. We determine the vector magnetic field value by sweeping the microwave frequency across all Zeeman sublevels and measuring optical transmission at seven double-resonance features, whose amplitudes vary as the orientation of the external static magnetic field (B→ext) changes with respect to the optical and microwave field polarization directions. Due to the complex dynamics of optical pumping and broadening mechanisms in the Doppler-broadened ensemble, we use a convolutional neural network model to account for details in our measurement spectra; this analysis determines the magnetic field direction with an accuracy of 1° and its amplitude with an accuracy of 56 nT measured at the near-Earth-field value of 50 μT.