  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 failure of the
frequency-feedback loop. Here we propose a strategy to improve the stability of
atomic clocks by interrogating two out-of-phase state sharing the same LO.
While standard Ramsey interrogation can only determine phases unambiguously in
the interval $[-\pi/2,\pi/2]$, the joint interrogation allows for an extension
to $[-\pi,\pi]$, 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 have 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.
