## Real-time synchronization feedbacks for single-atom frequency standards

##### Authors
Mirrahimi, Mazyar
Rouchon, Pierre
##### Description
Simple feedback loops, inspired from extremum-seeking, are proposed to lock a probe-frequency to the transition frequency of a single quantum system following quantum Monte-Carlo trajectories. Two specific quantum systems are addressed, a 2-level one and a 3-level one that appears in coherence population trapping and optical pumping. For both systems, the feedback algorithm is shown to be convergent in the following sense: the probe frequency converges in average towards the system-transition one and its standard deviation can be made arbitrarily small. Closed-loop simulations illustrate robustness versus jump-detection efficiency and modeling errors.
Comment: 20 pages, 4 figures
##### Keywords
Mathematical Physics, 34F05, 93D15, 37N20