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

TL;DR

This paper analyzes how experimental imperfections affect the stability of feedback control in quantum harmonic oscillators, demonstrating robustness in cooling a Bose-Einstein condensate despite common technical limitations.

Contribution

It provides a detailed analysis of the robustness of system-filter separation in quantum feedback control under realistic experimental imperfections.

Findings

Control scheme remains stable with detector inefficiency and noise

Cooling of BEC is feasible despite parameter miscalibrations

System stability is maintained under time delays and technical noise

Abstract

We consider the effects of experimental imperfections on the problem of estimation-based feedback control of a trapped particle under continuous position measurement. These limitations violate the assumption that the estimator (i.e. filter) accurately models the underlying system, thus requiring a separate analysis of the system and filter dynamics. We quantify the parameter regimes for stable cooling, and show that the control scheme is robust to detector inefficiency, time delay, technical noise, and miscalibrated parameters. We apply these results to the specific context of a weakly interacting Bose-Einstein condensate (BEC). Given that this system has previously been shown to be less stable than a feedback-cooled BEC with strong interatomic interactions, this result shows that reasonable experimental imperfections do not limit the feasibility of cooling a BEC by continuous measurement and feedback.