Strong Mitigation of the Magnetic-Field-Induced Frequency Shift in Coherent-Population-Trapping Atomic Clocks

We study the magnetic-field-induced frequency shift (MFS) of the clock (``0--0'') transition in coherent-population-trapping (CPT) microwave atomic clock. It is shown that the use of the Pound-Drever-Hall-like (PDH) technique for frequency locking provides brilliant opportunities for mitigating the MFS. Using a $0.125$ cm$^3$ rubidium vapor cell with a buffer gas, we have measured a residual sensitivity of the clock transition frequency to be $\approx\,72$ $\mu$Hz/mG over $\approx\,$$6$ mG interval. It means that a fractional frequency shift is extremely small ($\approx\,$$1$$\,\times\,$$10^{-14}$ mG$^{-1}$). The results contribute to the development of a new-generation CPT-based miniature atomic clock (MAC) with improved long-term frequency stability. The proposed method is quite general and can be used for other excitation schemes in atomic clocks, including Ramsey-like techniques.