  We use the vacuum Rabi splitting to perform quantum nondemolition (QND)
measurements that prepare a conditionally spin-squeezed state of a collective
atomic psuedo-spin. We infer a 3.4(6) dB improvement in quantum phase
estimation relative to the standard quantum limit for a coherent spin state
composed of uncorrelated atoms. The measured collective spin is composed of the
two-level clock states of nearly 10^6 Rb-87 atoms confined inside a low finesse
F = 710 optical cavity. This technique may improve atomic sensor precision
and/or bandwidth, and may lead to more precise tests of fundamental physics.
