Real-time synchronization feedbacks for single-atom frequency standards: V - and Λ-structure systems

This paper proposes simple feedback loops, inspired from extremum-seeking, that use the photon emission times of a single quantum system following quantum Monte-Carlo trajectories in order to lock in real time a probe frequency to the system´s transition frequency. Two specific settings are addressed: a 3-level system coupling one ground to two excited states (one highly unstable and one metastable) and a 3-level system coupling one excited to two ground states (both metastable). Analytical proofs and simulations show the accurate and robust convergence of probe frequency to system-transition frequency in the two cases.