Geopotential measurements with synchronously linked optical lattice clocks

According to Einstein's theory of relativity, the passage of time changes in a gravitational field(1,2). On Earth, raising a clock by 1 cm increases its apparent tick rate by 1.1 parts in 10(18), allowing chronometric levelling(3) through comparison of optical clocks(1,4,5). Here, we demonstrate such geopotential measurements by determining the height difference of master and slave clocks separated by 15 km with an uncertainty of 5 cm. A subharmonic of the master clock laser is delivered through a telecom fibre(6) to synchronously operate(7) the distant clocks. Clocks operated under such phase coherence reject clock laser noise and facilitate proposals for linking clocks(8,9) and interferometers(10). Taken over half a year, 11 measurements determine the fractional frequency difference between the two clocks to be 1,652.9(5.9) x 10(-18), consistent with an independent measurement by levelling and gravimetry(11). Our system demonstrates a building block for an internet of clocks, which may constitute 'quantum benchmarks', serving as height references with dynamic responses.