Magnetic field stabilization system for atomic physics experiments

Atomic physics experiments commonly use millitesla-scale magnetic fields to provide a quantization axis. As atomic transition frequencies depend on the amplitude of this field, many experiments require a stable absolute field. Most setups use electromagnets, which require a power supply stability not usually met by commercially available units. We demonstrate stabilization of a field of 14.6 mT to 4.3 nT rms noise (0.29 ppm), compared to noise of $\gtrsim$ 100 nT without any stabilization. The rms noise is measured using a field-dependent hyperfine transition in a single $^{43}$Ca$^+$ ion held in a Paul trap at the centre of the magnetic field coils. For the $^{43}$Ca$^+$ "atomic clock" qubit transition at 14.6 mT, which depends on the field only in second order, this would yield a projected coherence time of many hours. Our system consists of a feedback loop and a feedforward circuit that control the current through the field coils and could easily be adapted to other field amplitudes, making it suitable for other applications such as neutral atom traps.
Comment: 6 pages, 5 figures