The 2nd harmonic signal in vapor-cell clocks & error-signal quality: Does S2 imply dS1/dΔ?

How does one directly assess the quality of a Rb atomic clock signal remotely and in real time? Typically, one monitors the clock´s 2^nd harmonic signal, S₂, which in the quasi-static approximation is a measure of the correction signal´s slope, dS₁/dΔ. Unfortunately, in real vapor-cell clocks the quasi-static approximation is not valid, and the physics relating S₂ to dS₁/dΔ is complicated and not well understood. We have begun a series of studies aimed at elucidating the relationship between S₂ and dS₁/dΔ, and here we present our preliminary results.