High-precision control of static magnetic field magnitude, orientation, and gradient using optically pumped vapour cell magnetometry

Abstract: An integrated system of hardware and software allowing precise definition of arbitrarily oriented magnetic fields up to |B| = 1 {\mu}T within a five-layer mumetal shield is described. The system is calibrated with reference to magnetic resonance observed between Zeeman states of the 6S$_{1/2}$ F = 4 $^{133}$Cs ground state. Magnetic field definition over the full 4{\pi} solid angle is demonstrated, with one-sigma tolerances in magnitude, orientation and gradient of {\delta}|B| = 0.94 nT, {\delta}{\theta} = 5.9 mrad and {\delta}$\nabla$ B = 13.0 pT/mm, respectively. This field control is used to empirically map Mx magnetometer signal amplitude as a function of the static field (B0) orientation.