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Improving the clock stability is of fundamental importance for thedevelopment of quantum-enhanced metrology. One of the main limitations arisesfrom the randomly-fluctuating local oscillator (LO) frequency, which introduces"phase slips" for long interrogation times and hence failure of thefrequency-feedback loop. Here we propose a strategy to improve the stability ofatomic clocks by interrogating two out-of-phase state sharing the same LO.While standard Ramsey interrogation can only determine phases unambiguously inthe interval $[-\pi/2,\pi/2]$, the joint interrogation allows for an extensionto $[-\pi,\pi]$, resulting in a relaxed restriction of the Ramsey time andimprovement of absolute clock stability. Theoretical predictions are supportedby ab-initio numerical simulation for white and correlated LO noise. While ourbasic protocol uses uncorrelated atoms, we have further extended it to includespin-squeezing and further improving the scaling of clock stability with thenumber of atoms. Our protocol can be readily tested in current state-of-the-artexperiments.

Improved absolute clock stability by the joint interrogation of two atomic states