Phase locking a clock oscillator to a coherent atomic ensemble

The sensitivity of an atomic interferometer increases when the phase evolution of its quantum superposition state is measured over a longer interrogation interval. In practice, a limit is set by the measurement process, which returns not the phase, but its projection in terms of population difference on two energetic levels. The phase interval over which the relation can be inverted is thus limited to the interval $[-pi/2,pi/2]$; going beyond it introduces an ambiguity in the read out, hence a sensitivity loss. Here, we extend the unambiguous interval to probe the phase evolution of an atomic ensemble using coherence preserving measurements and phase corrections, and demonstrate the phase lock of the clock oscillator to an atomic superposition state. We propose a protocol based on the phase lock to improve atomic clocks under local oscillator noise, and foresee the application to other atomic interferometers such as inertial sensors.