  We have investigated the benefits of spin squeezed states for clocks operated
with typical Brownian frequency noise-limited laser sources. Based on an
analytic model of the closed servo-loop of an optical atomic clock, we can give
quantitative predictions on the optimal clock stability for a given dead time
and laser noise. Our analytic predictions are in very good agreement with
numerical simulations of the closed servo-loop. We find that for usual cyclic
Ramsey interrogation of single atomic ensembles with dead time, even with the
current most stable lasers spin squeezing can only improve the clock stability
for ensembles below a critical atom number of about one thousand in an optical
Sr lattice clock. Even with a future improvement of the laser performance by
one order of magnitude the critical atom number still remains below 100,000. In
contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks,
can already benefit from squeezed states with current clock lasers.
