An elementary quantum network of entangled optical atomic clocks

Optical atomic clocks are our most precise tools to measure time and frequency 1 – 3 . Precision frequency comparisons between clocks in separate locations enable one to probe the space–time variation of fundamental constants 4 , 5 and the properties of dark matter 6 , 7 , to perform geodesy 8 – 10 and to evaluate systematic clock shifts. Measurements on independent systems are limited by the standard quantum limit; measurements on entangled systems can surpass the standard quantum limit to reach the ultimate precision allowed by quantum theory—the Heisenberg limit. Although local entangling operations have demonstrated this enhancement at microscopic distances 11 – 16 , comparisons between remote atomic clocks require the rapid generation of high-fidelity entanglement between systems that have no intrinsic interactions. Here we report the use of a photonic link 17 , 18 to entangle two 88 Sr + ions separated by a macroscopic distance 19 (approximately 2 m) to demonstrate an elementary quantum network of entangled optical clocks. For frequency comparisons between the ions, we find that entanglement reduces the measurement uncertainty by nearly √(2) , the value predicted for the Heisenberg limit. Today’s optical clocks are typically limited by dephasing of the probe laser 20 ; in this regime, we find that entanglement yields a factor of 2 reduction in the measurement uncertainty compared with conventional correlation spectroscopy techniques 20 – 22 . We demonstrate this enhancement for the measurement of a frequency shift applied to one of the clocks. This two-node network could be extended to additional nodes 23 , to other species of trapped particles or—through local operations—to larger entangled systems.