An accurate system for optimal state estimation of a levitated nanoparticle

Experimental setups involving optically levitated nanoparticles are widely used nowadays to study physical phenomena in various fields including biophysics, sensing or quantum mechanics. We focus on parametric cooling of the particle's center-of-mass motion, where the intensity of a laser beam forming an optical trap is modulated to counteract the nanoparticles motion and cools it down to temperatures in the micro-Kelvin regime. Such experimental setups require tight control of the modulation frequency and phase, and are typically prone to measurement noise in the control loop. In this paper we investigate a new approach that incorporates additional knowledge of the physical system and noise characteristics by employing a Kalman filter in the feedback loop, with the aim to improve the overall cooling performance of the experimental arrangement. We develop an accurate state estimation system that is able to control the particle's position along one motional axis. The system acquires analog measurement signals and transforms them into the digital domain to be processed by a Kalman filter running at a sample rate of 500kSample/s with single-precision floating point arithmetic. The state estimation is then converted back to the analog domain to be fed back to the experimental setup. Our closed-loop, full-system simulation confirms the proposed approach achieves cooling improvements in the order of 20%. Further, we provide preliminary experimental tests of the technique. The presented system serves as a starting point for more involved experimental analyses and cooling setups where all three motional axes are controlled via Kalman-filtered feedback signals.