Phase Analysis for Frequency Standards in the Microwave and Optical Domains

TL;DR

This paper presents a phase analysis method using FPGA to investigate phase excursions in microwave and optical frequency standards, demonstrating negligible impact on frequency accuracy.

Contribution

The study introduces a FPGA-based phase analyzer and provides detailed measurements of phase excursions, showing they do not significantly affect frequency standard accuracy.

Findings

Phase variations in microwave source are below 10^{-16}

Optical phase excursions do not cause shifts larger than 10^{-18}

Detailed analysis of AOM chirps and duty cycle effects

Abstract

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$^{-18}$.