The 2nd harmonic signal in vapor-cell atomic clocks

The 2^nd harmonic signal has been recognized for some time as a “status-of-health” indicator for Rb clocks. Unfortunately, while the 2^nd harmonic signal can provide qualitative assessments of clock-signal health, at present there is no analytic theory capable of connecting the 2^nd harmonic to various parameters of interest. In large part, the difficulty lies in the fact that clocks operate in a regime where none of the standard approximations for solving field/matter interaction problems apply, in particular the Quasi-Static Approximation (QSA) which arguably has the greatest intuitive appeal. Here, we describe our first set of studies examining the validity of the QSA under conditions where the Rabi frequency, the field´s modulation frequency, and the atom´s dephasing rate are all nearly equal. Specifically, we examine the QSA´s prediction of the 2^nd harmonic signal amplitude as a function of microwave power. Our results suggest that the QSA can have utility for understanding the relative change in the 2^nd harmonic signal with microwave power, and therefore potential quantitative utility for understanding a Rb clock´s status-of-health.