Eavesdropping time and frequency: phase noise cancellation along a time-varying path, such as an optical fiber

Single-mode optical fiber is a highly efficient connecting medium, used not only for optical telecommunications but also for the dissemination of ultra-stable frequencies or timing signals. In 1994, Ma, Jungner, Ye and Hall described a measurement and control system to deliver the same optical frequency at two places, namely the two ends of a fiber, by eliminating the "fiber-induced phase-noise modulation, which corrupts high-precision frequency-based applications". We present a simple detection and control scheme to deliver the same optical frequency at many places anywhere along a transmission path, or in its vicinity, with a relative instability of 1 part in $10^{19}$. The same idea applies to radio frequency and timing signals. This considerably simplifies future efforts to make precise timing/frequency signals available to many users, as required in some large scale science experiments.