Time delay remaining in the displacement detection of the optically trapped particles using Kalman filter

The cooling and quantum control of the optically trapped particles is a hot topic in quantum frontier research. One of the key steps is using Kalman filter to extract the particle’s motion from noisy signals. Time delays of the Kalman filters are found in the process of signal extraction. Here the particle displacements based on the parameters of actual optical trapping systems are simulated, and the time delays of the Kalman filtering process are observed by changing the oscillation periods and the relaxation time for stabilization. The results indicate that Kalman filtering can effectively compress the noises in the displacement signal and thus improve the signal-to-noise ratio. Furthermore, as smaller the signal frequency is, larger time delays are observed in the process. It shows that the time delays should be noticed and compensated. Meanwhile, it is shown that the consuming time for signal stabilizations in the filtering process and the phase of the original signal, neither of which affects the filtering effect. These simulation results are our initial explorations for the cooling of optically trapped particles in vacuum. It would provide possible help to deal with the delay mismatch resulted from Kalman filtering and for the cooling of the optically trapped particles.