We describe protocols for passive atomic clocks based on quantum interrogation of the atoms. Unlike previous techniques, our protocols are adaptive and take advantage of prior information about the clock's state. To reduce deviations from an ideal clock, each interrogation is optimized by means of a semidefinite program for atomic state preparation and measurement whose objective function depends on the prior information. Our knowledge of the clock's state is maintained according to a Bayesian model that accounts for noise and measurement results. We implement a full simulation of a running clock with power-law noise models and find significant improvements by applying our techniques.

• Received 15 April 2014

DOI:https://doi.org/10.1103/PhysRevA.90.042310