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

**Authors**: M. Mirrahimi, P. Rouchon Siam J. Control Optim. Vol. 48, No. 4, pp. 2820–2839, 2009, DOI: 10.1137/080726355

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.

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**BibTeX**:

@Article{,

author = {M. Mirrahimi, P. Rouchon},

title = {Real-time synchronization feedbacks for single-atom frequency standards},

journal = {Siam J. Control Optim.},

volume = {48},

number = {4},

pages = {2820–2839},

year = {2009},

abstract = {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.},

location = {},

keywords = {quantum Monte-Carlo trajectories, extremum seeking, feedback, synchronization, quantum systems}}