End-to-end topology for fiber comb based optical frequency transfer at the $10^{-21}$ level

We introduce a simple and robust scheme for optical frequency transfer of an ultra-stable source light field via an optical frequency comb to a field at a target optical frequency, where highest stability is required, e.g. for the interrogation of an optical clock. The scheme relies on a topology for end-to-end suppression of the influence of optical path-length fluctuations, which is attained by actively phase-stabilized delivery, combined with common-path propagation. This approach provides a robust stability improvement without the need for additional isolation against environmental disturbances such as temperature, pressure or humidity changes. We measure residual frequency transfer instabilities by comparing the frequency transfers carried out with two independent combs simultaneously. Residual fractional frequency instabilities between two systems of $8\times10^{-18}$ at 1 s and $3\times10^{-21}$ at $10^5$ s averaging time are observed. We discuss the individual noise contributions to the residual instability. The presented scheme is technically simple, robust against environmental parameter fluctuations, and enables an ultra-stable frequency transfer, e.g. to optical clock lasers or to lasers in gravitational wave detectors.