Impacts of random filling on spin squeezing via Rydberg dressing in optical clocks

Spin squeezing via Rydberg dressing in an optical lattice can increase the accuracy of atomic clocks. The squeezing is generated when a sequence of Zeeman and long-range Ising-like interactions is applied to an array of Rydberg atoms trapped in an optical lattice. We analyze the effect of random fractional filling of the optical lattice on the spin squeezing characteristics. We compare the achievable clock stability in different lattice geometries, including unity-filled tweezer clock arrays and fractionally filled lattice clocks. We provide approximate analytical expressions and fitting functions to aid in the experimental implementation of Rydberg-dressed spin squeezing. We demonstrate that spin squeezing via Rydberg dressing in one-, two-, and three-dimensional optical lattices can significantly improve stability in the presence of random fractional filling.