FPGA Implementation of a Kalman-Based Motion Estimator for Levitated Nanoparticles

Jiawei Liao, Michael Jost, Michael Schaffner, Michele Magno, Matthias Korb, Luca Benini, Felix Tebbenjohanns, Rene Reimann, Vijay Jain, Michael Gross, Andrei Militaru, Martin Frimmer, Lukas Novotny

Optically trapped nanoparticles are used in various fields ranging from biophysics to precision sensing. An optically trapped nanoparticle can be regarded as a harmonic oscillator driven by the thermal fluctuations of its environment. Unlocking the potential of optically levitated systems for precision measurements in the classical and the quantum regime requires cooling of the particle motion. In parametric feedback cooling, the center-of-mass motion of a nanoparticle optically levitated in a vacuum is reduced by temporally modulating the optical trapping potential. This technique requires a precise measurement of the particle's motion to derive the feedback signal and is prone to measurement noise and inevitable thermal process noise. In a state-of-the-art implementation, the feedback signal is derived from a simple phase-locked loop (PLL). Kalman filters are regularly deployed in a variety of application scenarios to improve system performance under noisy conditions. In this paper, we investigate theoretically and experimentally the performance of parametric feedback cooling, where the measurement signal is Kalman filtered before entering the PLL. Compared to sole PLL cooling, our numerical full-system simulations show a 20% reduction of the residual motional energy of a trapped nanoparticle in the presence of the Kalman filter. We detail a field-programmable gate array-based implementation of a Kalman filter and evaluate its performance in-field.

DOI

Nanonewton Force Generation and Detection Based on a Sensitive Torsion Pendulum

Chen, S.-J.; Pan, S.-S.

In this paper, we introduce an experiment based on a sensitive torsion pendulum for measuring and calibrating small forces at the nanonewton scale. The force standard for calibration is the universal gravitation between four masses separated by known distances. It is realized by two test masses suspended as part of the torsion pendulum and two source masses on a rotation table. Two force-generation mechanisms, namely, the optical force from the radiation pressure and the electrostatic force by the capacitive actuation unit, are designed and will be calibrated by the gravitational force. We present our recent results on radiation pressure measurements and describe the design of the capacitive displacement sensing/actuating unit.

DOI