Machine learning assisted vector atomic magnetometry

Multiparameter sensing such as vector magnetometry often involves complex setups due to various external fields needed in explicitly connecting one measured signal to one parameter. Here, we propose a paradigm of indirect encoding for vector atomic magnetometry based on machine learning. We encode the three-dimensional magnetic-field information in the set of four simultaneously acquired signals associated with the optical rotation of a laser beam traversing the atomic sample. The map between the recorded signals and the vectorial field information is established through a pre-trained deep neural network. We demonstrate experimentally a single-shot all optical vector atomic magnetometer, with a simple scalar-magnetometer design employing only one elliptically-polarized laser beam and no additional coils. Magnetic field amplitude sensitivities of about 100 $${{{{{{{\rm{fT}}}}}}}}/\sqrt{{{{{{{{\rm{Hz}}}}}}}}}$$ fT / Hz and angular sensitivities of about $$100 \sim 200\,\mu rad/\sqrt{{{{{{{{\rm{Hz}}}}}}}}}$$ 100 ~ 200 μ r a d / Hz (for a magnetic field of around 140 nT) are derived from the neural network. Our approach can reduce the complexity of the architecture of vector magnetometers, and may shed light on the general design of multiparameter sensing.