Phase Analysis for Frequency Standards in the Microwave and Optical Domains

Coherent manipulation of atomic states is a key concept in high-precision spectroscopy and used in atomic fountain clocks and a number of optical frequency standards. Operation of these standards can involve a number of cyclic switching processes, which may induce cycle synchronous phase excursions of the interrogation signal and thus lead to shifts in the output of the frequency standard. We have built a FPGA-based phase analyzer to investigate these effects and conducted measurements on two frequency standards. For the caesium fountain PTB-CSF2 we were able to exclude phase variations of the microwave source at the level of a few $\mu$rad, corresponding to relative frequency shifts of less than 10$^{-16}$. In the optical domain, we investigated phase variations in PTB's Yb$^+$ optical frequency standard and made detailed measurements of AOM chirps and their scaling with duty cycle and driving power. We ascertained that cycle-synchronous as well as long-term phase excursion do not cause frequency shifts larger than 10$^{-18}$.