Local oscillator 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 quasistatic 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 sensitivity to local oscillator frequency variations. Such an interrogation would seem to eliminate L.O. aliasing and relieve stringent requirements on L.O. phase noise. Nevertheless, 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 by an analysis in terms of the sensitivity function g(t). For white phase noise, we derive an optimal form for g(t) and show that the aliased noise always diverges as g(t) approaches a constant. For flicker phase noise, we find a limiting form that could, in principle, eliminate the aliasing effect; in practice, however, the improvement is limited by a slow dependence on available bandwidth. Finally, we derive optimized forms for any phase noise spectrum.