Noise considerations for locking to the center of a Lorentzian line

Many areas of science require locking a probe signal to the center of a Lor entzian line. In this paper we experimentally explore the limits to the res olution for locking a sine-wave modulated probe signal to a Lorentzian line . Surprisingly we find that in some cases relatively high-frequency phase m odulation (PM) noise on the probe signal (even 100 times the Linewidth of t he resonance) can significantly degrade the stability of the lock The 6.835 -GHz hyperfine transition in Rb-87 was used as a test bed for these studies because it affords very high resolution for investigating this effect. The details presented here should prove useful for testing a complete theory o f this effect and give some insight into the requirements of PM noise of lo cal oscillators to be locked to a Lorentzian line. [S1050-2947(99)02401-4].