Ramsey-comb spectroscopy: Theory and signal analysis

We recently demonstrated that the spectroscopic accuracy and resolution of optical frequency combs can be obtained from a series of Ramsey-like measurements using only two amplified frequency comb pulses at variable delays. In this work we present a comprehensive analytical framework of this Ramsey-comb method in both time and frequency domains. It is shown that as opposed to traditional forms of spectroscopy, the signal analysis can be performed purely in the time domain, based on the temporal phases of the individual Ramsey signals. We give a detailed description of the robust fitting algorithm relying solely on this phase information and discuss special features such as an insensitivity to (transition-independent) spectral line-broadening mechanisms and constant phase shifts, e.g., due to the ac Stark effect from the excitation pulses themselves. The precision and resolution of the Ramsey-comb fitting method is assessed via numerical simulations, including cases of transition-dependent broadening mechanisms and phase shifts.