Real-time synchronization feedbacks for single-atom frequency standards

TL;DR

This paper introduces simple real-time feedback loops for stabilizing the frequency of a probe to match the transition frequency of single quantum systems, demonstrating convergence and robustness through simulations.

Contribution

It proposes a novel, simple feedback method inspired by extremum-seeking for quantum frequency stabilization, applicable to 2-level and 3-level systems.

Findings

Feedback algorithms converge on the system transition frequency.

Probe frequency standard deviation can be minimized.

Robustness demonstrated against detection inefficiencies and modeling errors.

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.