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 its 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 (an 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 three measurement cycles, and thereby improved the stability scaling from tau(-1/2) to tau(-1) during the three measurement cycles. 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.