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

Improving the clock stability is of fundamental importance for the development of quantum-enhanced metrology. One of the main limitations arises from the randomly fluctuating local oscillator (LO) frequency, which introduces "phase slips"for long interrogation times and hence the failure of the frequency-feedback loop. Here we propose a strategy to improve the stability of atomic clocks by interrogating two atomic ensembles sharing the same LO. The two ensembles are prepared in coherent spin states pointing along orthogonal directions in the Bloch sphere. While standard Ramsey interrogation can only determine phases unambiguously in the interval [-p/2,p/2], the joint interrogation allows for an extension to [-p,p], resulting in a relaxed restriction of the Ramsey time and improvement of absolute clock stability. Theoretical predictions are supported by ab initio numerical simulation for white and correlated LO noise. While our basic protocol uses uncorrelated atoms, we further extended it to include spin-squeezing and further improving the scaling of clock stability with the number of atoms. Our protocol can be readily tested in current state-of-the-art experiments.