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According to the Einstein's theory of relativity, the passage of time changesin a gravitational field. On earth, raising a clock by one centimetre increasesits tick rate by 1.1 parts in 10$^{18}$, enabling optical clocks to performprecision geodesy. Here, we demonstrate geopotentiometry by determining theheight difference of master and slave clocks separated by 15 km withuncertainty of 5 cm. The subharmonic of the master clock is delivered through atelecom fibre to phase-lock and synchronously interrogate the slave clock. Thisprotocol rejects laser noise in the comparison of two clocks, which improvesthe stability of measuring the gravitational red shift. Such phase-coherentlyoperated clocks facilitate proposals for linking clocks and interferometers.Over half a year, 11 measurements determine the fractional frequency differencebetween the two clocks to be $1,652.9(5.9)\times 10^{-18}$, or a heightdifference of 1,516(5) cm, consistent with an independent measurement bylevelling and gravimetry. Our system is as a building block of an internet ofclocks, consisting of a master and a number of slave clocks, which will provide"quantum benchmarks" that are height references with dynamic response.

Real-time geopotentiometry with synchronously linked optical lattice clocks