Quantum-amplified global-phase spectroscopy on an optical clock transition

Optical lattice clocks are at the forefront of precision metrology1, 2, 3, 4, 5–6, operating near a standard quantum limit set by quantum noise4,7. Harnessing quantum entanglement offers a promising route to surpass this limit8, 9, 10, 11, 12, 13, 14–15; however, there are practical difficulties in terms of scalability and measurement resolution requirements16,17. Here we adapt the holonomic quantum gate concept18 to develop a new Rabi-type ‘global-phase spectroscopy’ that uses the detuning-sensitive global Aharonov–Anandan phase19. With this approach, we can demonstrate quantum-amplified time-reversal spectroscopy on an optical clock transition that achieves directly measured 2.4(7) dB metrological gain and 4.0(8) dB improvement in laser noise sensitivity beyond the standard quantum limit. To this end, we introduce rotary echo to protect the dynamics from inhomogeneities in light–atom coupling and implement a laser-noise-cancelling differential measurement through symmetric phase encoding in two nuclear spin states. Our technique is not limited by measurement resolution, scales easily because of the global nature of entangling interaction and exhibits high resilience to typical experimental imperfections. We expect it to be broadly applicable to next-generation atomic clocks and other quantum sensors approaching the fundamental quantum precision limits20, 21–22. The precision of determining the phase of an optical atomic clock is increased above the standard quantum limit in a new spectroscopic method.