Design and performance of an absolute $^3$He/Cs magnetometer

We report on the design and performance of a highly sensitive combined $^3$He/Cs magnetometer for the absolute measurement of magnetic fields. The magnetometer relies on the magnetometric detection of the free spin precession of nuclear spin polarized $^3$He gas by optically pumped cesium magnetometers. We plan to deploy this type of combined magnetometer in an experiment searching for a permanent electric dipole moment of ultracold neutrons at the Paul Scherrer Institute (Switzerland). A prototype magnetometer was built at the University of Fribourg (Switzerland) and tested at Physikalisch-Technische Bundesanstalt (Berlin, Germany). We demonstrate that the combined magnetometer allows Cram\'er-Rao- limited field determinations with recording times in the range of $\sim 500\mathrm{s}$, measurements above $500\mathrm{s}$ being limited by the stability of the applied magnetic field. % With a $100\mathrm{s}$ recording time we were able to perform an absolute measurement of a magnetic field of $\approx1\mathrm{\mu T}$ with a standard uncertainty of $\Delta B\sim60\mathrm{fT}$, corresponding to $\Delta B/B<$6$\times$10$^{-8}$.