Phase-continuous comparison of three all-optical time scales over 20 days

Optical frequency standards have progressed rapidly over the past two decades, leading to the anticipated redefinition of the SI second by an optical frequency. However, time scales have not yet significantly improved despite this development because they are still fully reliant on rf flywheel oscillators, mostly hydrogen masers, which impose a performance limit related to incompletely sampled noise known as the Dick effect. To best benefit from the exceptional stability and accuracy of optical frequency standards, time scales must employ optical flywheels with orders-of-magnitude better short-term (<$10^4$ s) stability than masers. Here, we introduce three optical flywheel oscillators (two cryogenic silicon cavities and one iodine optical clock) with superior short-term stability than hydrogen masers and long-term stability on par with masers. Steering each optical flywheel with a high-uptime Sr optical frequency standard generates three parallel all-optical time scales with continuous operation over >20 days. When compared with each other, these all-optical time scales achieve <$10^{-16}$ relative instability after just a few days of averaging. During typical steering gaps of ~6 hours, the accumulated time difference is ~20 ps, leading to the total time difference of <100 ps over the full measurement period. With the proliferation of long-distance optical fiber links and commercialization of optical flywheels and frequency standards, we anticipate all-optical time scales to be the future of timekeeping.