Evaluation of second-order Zeeman frequency shift in NTSC-F2

Caesium atomic fountain clock is a primary frequency standard, which realizes the duration of second. Its performance is mostly dominated by the frequency accuracy, and the C-field induced second-order Zeeman frequency shift is the major effect, which limits the accuracy improvement. By applying a high-precision current supply and high-performance magnetic shieldings, the C-field stability has been improved significantly. In order to achieve a uniform C-field, this paper proposes a doubly wound C-field solenoid, which compensates the radial magnetic field along the atomic flight region generated by the lead-out single wire and improves the accuracy evaluation of second-order Zeeman frequency shift. Based on the stable and uniform C-field, we launch the selected atoms to different heights and record the magnetically sensitive Ramsey transition $|F = 3, m_{F} = -1rangle to |F = 4, m_{F} = -1rangle$ central frequency, obtaining this frequency shift as 131.03$times $10$^{-15}$ and constructing the C-field profile ($sigma = 0.15$ nT). Meanwhile, during normal operation, we lock NTSC-F2 to the central frequency of the magnetically sensitive Ramsey transition $|F = 3, m_{F} = -1rangle to |F = 4, m_{F} = -1rangle$ fringe for ten consecutive days and record this frequency fluctuation in time domain. The first evaluation of second-order Zeeman frequency shift uncertainty is 0.10$times $10$^{-15}$. The total deviation of the frequency fluctuation on the clock transition induced by the C-field instability is less than 2.6$times $10$^{-17}$. Compared with NTSC-F1, NTSC-F2, there appears a significant improvement.