Many experiments involving cold and ultracold atomic gases require very precise control of magnetic fields that couple to and drive the atomic spins. Examples include quantum control of atomic spins, quantum control and quantum simulation in optical
lattices, and studies of spinor Bose condensates. This makes accurate cancellation of the (generally time dependent) background magnetic field a critical factor in such experiments. We describe a technique that uses the atomic spins themselves to measure DC and AC components of the background field independently along three orthogonal axes, with a resolution of a few tens of uG in a bandwidth of ~1 kHz. Once measured, the background field can be cancelled with three pairs of compensating coils driven by arbitrary waveform generators. In our laboratory, the magnetic field environment is sufficiently stable for the procedure to reduce the field along each axis to less than ~50 uG rms, corresponding to a suppression of the AC part by about one order of magnitude. This suggests our approach can provide access to a new low-field regime in cold-atom experiments.
