Tri-axial time-dependent magnetic field calibrated in-situ by harmonic analysis of adiabatically evolving atomic spins

We introduce a methodology to calibrate in situ a set of coils generating bi- or tri-axial magnetic fields, at frequencies where a calibration performed under static conditions would be inaccurate. The methodology uses harmonic analysis of one component of the magnetization of an atomic sample whose spins adiabatically follow an ad hoc applied time-dependent field. The procedure enables the identification of phases and amplitudes of the coil currents required to produce a dynamic magnetic field with the assigned polarization. This determines coil constants that can be subsequently used to produce arbitrary three-dimensional time-dependent fields.