  Squeezed many-body states of atoms are a valuable resource for high precision
frequency metrology and could tremendously boost the performance of atomic
lattice clocks. Here, we theoretically demonstrate a viable approach to spin
squeezing in lattice clocks via optical dressing of one clock state to a highly
excited Rydberg state, generating switchable atomic interactions. For realistic
experimental parameters, this is shown to generate over 10 dB of squeezing in a
few microseconds interaction time without affecting the subsequent clock
interrogation.
