Compressing the fluctuation of the magnetic field by dynamic compensation

We present a dynamic compensation method to compress the spatial fluctuation of the static magnetic field (C-field) that provides a quantization axis in the atomic fountain clock. The coil current of the C-field is point-by-point modulated in accordance with the atoms probing the magnetic field along the flight trajectory. A homogeneous field with a 0.2 nT inhomogeneity is produced compared to a 5 nT under the static magnetic field with a constant current during the Ramsey interrogation. The corresponding uncertainty associated with the second-order Zeeman shift that we calculate is improved by one order of magnitude. The technique provides an alternative method to improve the uniformity of the magnetic field, particularly for large-scale equipment that is difficult to construct with an effective magnetic shielding. Our method is simple, robust, and essentially important in frequency evaluations concerning the dominant uncertainty contribution due to the quadratic Zeeman shift.