Accelerating the Averaging Rate of Atomic Ensemble Clock Stability using   Atomic Phase Lock
  We experimentally demonstrated that the stability of an atomic clock improves at fastest rate $\tau^{-1}$ (where $\tau$ is the averaging time) when the phase of a local oscillator is genuinely compared to the continuous phase of many atoms in a single trap (atomic phase lock). For this demonstration, we developed a simple method that repeatedly monitors the atomic phase while retaining its coherence by observing only a portion of the whole ion cloud. Using this new method, we measured the continuous phase over 3 measurement cycles, and thereby improved the stability scaling from $\tau^{-1/2}$ to $\tau^{-1}$ during the 3 measurement cycles.   %Compared with the standard method that initialize phase during each measurement cycle, the long term stability was improved by a factor of $\sqrt{n_{cp}}$ (where $n_{cp}$ is the number of continuous phase measurements).   This simple method provides a path by which atomic clocks can approach a quantum projection noise limit, even when the measurement noise is dominated by the technical noise. 
Nobuyasu Shiga, Michiaki Mizuno, Kohta Kido, Piyaphat Phoonthong,   Kunihiro Okada
quant-ph physics.atom-ph physics.plasm-ph