Displacement Measurement Svstem Of Micro-Particles Opticallv Levitated In Vacuum

Optical levitation in vacuum attracts increasing attention in optomechanics.Micro-and nanoparticles optically levitated in vacuum acts as mechanical oscillators with high mechanical quality and low-dissipation.,which provide a candidate platform for precision measurement.Based on this platform,center-of-mass temperature of the particle can be cooled from room temperature to below 1mK or even to the quantum ground state,which provides a good experimental method for related research in the field of quantum.Feedback cooling is critical for optical levitation in vacuum and the displacement detection of optically levitated particles in vacuum is the premise and foundation of feedback cooling technology.In order to improve the cooling performance of optical tweezers,it is of great significance to investigate a displacement detection system with high sensitivity.The interferometric displacement detection combined with the D-shaped mirror and the balanced detector has the advantages of high detection sensitivity,high sampling bandwidth and high spatial resolution,and is currently the mainstream solution for displacement detection in optical tweezers.In this paper,based on the interference detection scheme,particles trapped in the dual-beam optical trap are detected in vacuum,and a signal acquisition system based on FPGA is designed and implemented.The data is transmitted to the host computer through the USB communication module.The data processing and analysis software is developed based on the VC platform MFC framework to realize the connection of data to the user terminal and subsequent processing including data de-frame processing,storage,conversion of detection data,FFT transformation,and real-time display.In order to measure the measurement noise in the displacement signal,center-of-mass motion equation of the particle is first established according to the force model of optically levitated micro-particles,and motion of the particles optically levitated in vacuum is simulated on the MATLAB platform based on harmonic oscillator model taking into account the random Brownian force during motion and the measurement noise during signal detection.The Kalman filter algorithm is designed to filter the displacement measurement values with noise.After filtering,the root-mean-square error of measurement is reduced from 1 nm to 0.27 nm.The algorithm is applied to the actual displacement data collected by the host computer software.The results show that the root-mean-square error of the measurement after filtering is reduced from 2.8 nm to 1.1 nm.Other parameters remain unchanged,filtering is performed at 6 Pa pressure,and the root-mean-square error of the displacement is reduced from 5.2 nm to 2.1 nm,which verifies the effectiveness of the algorithm in high vacuum.Our work has laid a solid foundation for the measurement and processing of particle displacement in vacuum optical tweezers system.