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 field-programmable gate array (FPGA)-based phase analyzer to investigate these effects and conducted measurements on two kinds of frequency standards. For the caesium fountains PTB-CSF1 and PTB-CSF2, we were able to exclude phase variations of the microwave source at the level of a few microradians, 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 acousto-optic modulator (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
.