Robustness of System-Filter Separation for the Feedback Control of a Quantum Harmonic Oscillator Undergoing Continuous Position Measurement

摘要

We consider the effects of experimental imperfections on the problem ofestimation-based feedback control of a trapped particle under continuousposition measurement. These limitations violate the assumption that theestimator (i.e. filter) accurately models the underlying system, thus requiringa separate analysis of the system and filter dynamics. We quantify theparameter regimes for stable cooling, and show that the control scheme isrobust to detector inefficiency, time delay, technical noise, and miscalibratedparameters. We apply these results to the specific context of a weaklyinteracting Bose-Einstein condensate (BEC). Given that this system haspreviously been shown to be less stable than a feedback-cooled BEC with stronginteratomic interactions, this result shows that reasonable experimentalimperfections do not limit the feasibility of cooling a BEC by continuousmeasurement and feedback.