We develop a stochastic mean-field theory to describe active frequency measurements of pulsed superradiant emission, studied in a recent experiment with strontium-87 atoms trapped in an optical lattice inside an optical cavity [M. Norcia et al., Phys. Rev. X 8, 021036 (2018)]. Our theory reveals the intriguing dynamics of atomic ensembles with multiple transition frequencies, and it reproduces the superradiant beats signal, noisy power spectra, and frequency uncertainty in remarkable agreement with the experiments. Moreover, using longer superradiant pulses of similar strength and shortening the experimental duty cycle, we predict a short-term frequency uncertainty $7\times {10}^{-17}/\sqrt{\tau /s}$, which makes active frequency measurements with superradiant transitions comparable with the record performance of current frequency standards [M. Schioppo et al., Nat. Photonics 11, 48 (2017)]. Our theory combines cavity quantum electrodynamics and quantum measurement theory, and it can be readily applied to explore conditional quantum dynamics and describe frequency measurements for other processes such as steady-state superradiance and superradiant Raman lasing.

• Received 25 June 2021
• Accepted 13 December 2021

DOI:https://doi.org/10.1103/PhysRevLett.128.013604