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

An integrated system of hardware and software allowing precise definition of arbitrarily oriented magnetic fields up to |B| = 1 μT 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 ¹³³Cs ground state. Magnetic field definition over the full 4π solid angle is demonstrated with one-sigma tolerances in magnitude, orientation, and gradient of δ|B| = 0.94 nT, δθ = 5.9 mrad, and $δ|∇B|=13.0$ pT/mm, respectively. This field control is used to empirically map M_x magnetometer signal amplitude as a function of the static field (B₀) orientation.