  We investigate the generation of entanglement (spin squeezing) in an
optical-transition atomic clock through the coupling to a vacuum
electromagnetic field that is enhanced by an optical cavity. We show that if
each atom is prepared in a superposition of the ground state and a long-lived
electronic excited state, and viewed as a spin-1/2 system, then the collective
vacuum light shift entangles the atoms, resulting in a squeezed distribution of
the ensemble collective spin. This scheme reveals that even a vacuum field can
be a useful resource for entanglement and quantum manipulation. The method is
simple and robust since it requires neither the application of light nor
precise frequency control of the ultra-high-finesse cavity. Furthermore, the
scheme can be used to implement two-axis twisting by rotating the spin
direction while coupling to the vacuum, resulting in stronger squeezing.
