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

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