L.O. limited frequency stability for passive atomic frequency standards using “square wave” frequency modulation

Atomic frequency standards using square-wave frequency modulation effectively interrogate the atomic line by switching back and forth between two frequencies with equal atomic absorption values. For a symmetric absorption line, the slope of the responses will also be equal. In the quasi-static limit this would seem to be an ideal interrogation process-the sign reversal of frequency slope can be removed by detection electronics to give an essentially unvarying and constant sensitivity to L.O. frequency variations. Such an interrogation would seem to eliminate L.O. aliasing and so relieve stringent requirements on local oscillator phase noise. However, sign changes in the interrogation and detection processes mean that the sensitivity is actually zero at some point in the cycle. We derive consequences of this fact for white phase and flicker phase noise models by an explicitly time-dependent analysis in terms of the sensitivity function g(t). We find that an optimal strategy exists for white phase L.O. noise for which g(t) takes the form of a sequence of parabolic arches, and which gives a small (×96/π⁴) improvement over simple sine-wave demodulation. We also find limiting forms that could in principle eliminate L.O, aliasing for flicker-phase noise. However, in practice the improvement shows only a logarithmic dependence on available response time and bandwidth