Quality estimation of non-demolition measurement with lossy atom-light hybrid interferometers

The atom-light hybrid interferometer recently attracted much attention in the research of precision metrology for its combination of light and atomic spin wave. With the AC Stark effect and proper design, it can be applied in the scheme of quantum non-demolition (QND) measurement of photon numbers. In this work, we apply the QND criteria to the scheme and theoretically derive its explicit formulas with various losses of the atomic-light hybrid interferometer. With the formulas and actual experiment parameters, we estimate and compare the performance of the vapor-atom-based and cold-atom-based hybrid interferometer in the QND measurement, analyze the influences of different kinds of losses, and provide optimized working parameter ranges of the interferometer.