Vacuum spin squeezing

We investigate the generation of entanglement (spin squeezing) in an optical-transition atomic clock through the coupling to an optical cavity in its vacuum state. 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, without any light applied. This scheme reveals that even an electromagnetic vacuum can constitute a useful resource for entanglement and quantum manipulation. By rotating the spin direction while coupling to the vacuum, the scheme can be extended to implement two-axis twisting resulting in stronger squeezing.