Improving frequency standard performance by optimized measurement feedback

We demonstrate a new approach to precision frequency standard characterization and stabilization, providing performance enhancements in the presence of non-Markovian noise in the local oscillator with "software-only" modifications. We develop a theoretical framework casting various measures for frequency standard variance in terms of frequency-domain transfer functions, incorporating the effects of feedback stabilization via a chain of Ramsey measurements. Using this framework we introduce a novel optimized \emph{hybrid feedforward} measurement protocol which employs results from multiple measurements and transfer-function-based calculations of measurement covariance given the local oscillator power spectrum. This approach exploits statistical correlations in the local oscillator frequency noise to provide high-accuracy corrections in the presence of uncompensated dead time in the measurement cycle or oscillator-frequency evolution during the Ramsey measurement period itself. We present numerical simulations of oscillator performance under competing feedback schemes and demonstrate benefits in both correction accuracy and long-term oscillator stability using hybrid feedforward.