Traditional optical atomic clocks are limited in their performance by laser frequency noise
and the intrinsic quantum noise of uncorrelated atoms. In this thesis, we advance the field of
optical clocks on both of these fronts. By developing the next generation of ultrastable laser technology,
we enable clock comparisons that have approached the quantum projection noise limit. To
go beyond this limit, we build and operate an optical clock with the capability of spin-squeezing.
Employing conditional spin squeezing via quantum nondemolition measurements based on cavity
QED, we produce a spin squeezed state that yields a spectroscopic enhancement of 1.7 dB beyond
the standard quantum limit. We then run a clock comparison between two spin squeezed
clock ensembles, making use of a movable optical lattice to individually squeeze and readout the
ensembles with cavity QED. This differential comparison between the two squeezed clocks directly
verifies enhanced clock stability of 1.9 dB beyond the quantum projection noise limit, and reaches
a measurement precision level of 10-17. This constitutes the first direct demonstration of quantum
enhanced measurement in an operational optical atomic clock.