Clock laser noise constraining synchronous comparison of spin-squeezed optical clocks

Spin squeezing has been recognized as a powerful tool to overcome the quantum projection noise limit that is imposed on optical clocks with uncorrelated atoms. Yet, the full potential of spin squeezing remains underutilized in precision measurement, due to the limited Ramsey dark period, which is much shorter than 1 s-level atom-laser and 10 s-level atom-atom coherence times. Here, we numerically study the impact of the clock laser noise on the synchronous comparison of spin-squeezed optical clocks. We restrict ourselves to one-axis twisting and measurement-induced spin squeezing protocols that have recently been demonstrated on optical lattice clocks. The simulation results illustrate that for typical lattice clocks with 10³ atoms, the metrological enhancement induced by spin squeezing is only attainable for a dark period of less than 0.1 s using the state-of-the-art clock laser. Therefore, further improvement of the clock laser is necessary to bring spin squeezing into the full play.