Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Conference on Optoelectronic Science and Materials (ICOSM)

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

Xiaofei Zeng, Bin Zhang, Xiang Han, Zhijie Chen, Wei Xiong, Xinlin Chen, Guangzong Xiao, Hui Luo

Published Dec 9, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.2617367

Related papers

Detection Optimization of an Optically Trapped Microparticle in Vacuum with Kalman Filter

Shidong Xu, Ming Chen, Jianyu Yang +3 more

The optical trapping of micro-nano particles in a high vacuum has become a popular research platform in various frontier fields of physics because of its excellent isolation from the environment. The precise measurement of particle motion information is required to analyze and control particle motion modes in traps. However, the detection accuracy is limited by measurement noise and coupling signals from other axes in microparticle optical traps. In this study, we use the Kalman filter to extract the real motion information of each axis under simulation conditions, and the results show that the Kalman filter performs well in noise suppression, improving the RMSE from 12.64 to 5.18 nm and enhancing the feedback cooling performance by approximately 27% through reducing the axes’ signal coupling ratio. We believe that as a solution to these challenges, the Kalman filter will bring a significant achievement to micrometer particle optical traps in vacuums.

Photonics•Sep 27, 2022•3 citations

Hardware-in-the-loop simulation research on cooling effect of different modulated waveform signals with vacuum optical trap parameter feedback

Zhanming Hu, Huibing Han, Haonan Liu +4 more

Vacuum optical trap is a technology that captures and manipulates particles in a near-vacuum environment by means of laser mechanical effects. It is an ideal platform for precision measurement with high quality factor. Due to its low environmental damping, vacuum optical traps require feedback cooling to reduce the equivalent temperature of particle centroid motion to prevent particle escape. Parametric feedback cooling is a mainstream solution to achieve stable trapping of particles in optical traps. Monte Carlo method and finite difference method were used to simulate the displacement fluctuation of the microsphere without feedback, and the FPGA circuit was used to output control signals with different waveforms to test the feedback cooling effect. Under the premise of reaching mK cooling level, square wave control signals have advantages in fast feedback cooling, and sine wave control signals have advantages in maintaining phase matching.

International Conference on Signal Processing and Communication Technology (SPCT)•Apr 6, 2023•0 citations

Cooling of a mesoscopic single-particle harmonic oscillator using real-time digital control systems

Ashley Setter

Optically levitated systems provide an ideal environment for isolating objects extremely well from the environment such that their behaviour can be more easily studied without external influences. Moreover, using optical detection, very high levels of sensitivity to that behaviour can be achieved, allowing precise detection of their motion and measurement of forces upon such a system. In the experiment we describe in this thesis, one can construct an optical gradient force trap by simply directing a collimated light beam onto a parabolic mirror with a sufficiently high numerical aperture. The resulting focusing not only generates the optical trapping potential but also allows detection as a particle trapped at the focal spot of the mirror has the light it scatters onto the mirror collimated and sent back in the direction of the incident trapping light beam. The trap described here allows levitation of dielectric nanoparticles with radii from 10nm to 300nm at pressures from 103 —10-8 mbar. In this thesis I describe the experimental setup and the theory describing a particle levitated in this setup, detailing how, from the detected light intensity on a photodetector, we can extract the properties describing the physical system, including the frequency of motion, the damping upon the motion, the temperature associated with the motion, the radius of the trapped nanoparticle and the conversion factor which allows us to convert from the photo-current measured by the detector to the physical displacement of the particle. Cooling of the translational motion to the ground state is a much targeted goal in the field of levitated optomechanics as it has applications in producing quantum states, performing matter-wave interferometry, testing collapse models and as a very precise force sensor. In this thesis I demonstrate and investigate a number of different cooling methods applied to the translational motion. First, I describe how one can utilise an FIR (Finite Impulse Response) band-pass filter to isolate the signal due to the motion of a single translational degree of freedom and utilise this to perform active feedback cooling upon this degree of freedom. I demonstrate this by implementing an FIR filter on a FPGA (Field Programmable Gate Array) and utilising it in real-time to cool the motion to 2.5K ± 0.4 K. Secondly I utilise a tracking algorithm called a Kalman Filter, I describe how this algorithm functions to track the state of objects from noisy partial measurements of the state and how this can be applied to track levitated nanoparticles. I then detail how this was implemented in an FPGA so that the Kalman Filter could be used in real-time to estimate the position of a levitated nanoparticle. We demonstrate cooling of the translation centre-of-mass motion along the optical axis by 3 orders of magnitude to a temperature of 162mK ± 15 mK. Next I describe a classical model of the motion of a levitated nanoparticle and describe how this model can be simulated numerically to produce simulated time traces of the motion. I then demonstrate how this simulation can be used to reproduce several theoretical relations as well as reproduce experimental results and be utilised to simulate and test the performance of cooling algorithms without requiring experimental implementation. Next I use this simulation to model the effect of a Dung non-linearity in the trapping potential. I match the behaviour of the simulation when exposed to as a pulsed reduction of the laser power with the behaviour of the experimental system when exposed to the same stimulus and in doing so extract the Dung non-linearity in the optical trapping potential generated by the parabolic mirror, which takes a value of ξ = -0.100 m-2. Finally I describe a quantum model of the motion of a levitated nanosphere, which takes into account the various decoherence sources in the experimental system, namely the interaction with the background gas, the laser photons and decoherence due to the measurement. Using this I investigate several different forms of active feedback cooling, including the "optimal" cooling as determined from the tools of control theory, which takes the form of a square wave, and the more traditional sinusoidal feedback signal. In addition I compare both linear cooling by applying a force directly to the nanoparticle and quadratic cooling by modulating the power of the trapping laser. I determine that cooling to mean phonon numbers of less than 10 with the current experimental setup is achievable utilising any of the feedback schemes described here when they are tuned appropriately.

•Jan 1, 2020•0 citations

Real-time optimal quantum control of mechanical motion at room temperature

Lorenzo Magrini, Philipp Rosenzweig, Constanze Bach +6 more

Abstract The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering1. Today, the increasing demand for applied quantum technologies requires adaptation of this level of control to individual quantum systems2, 3. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback4. Successful implementations thus far include experiments on the level of optical and atomic systems5–7. Here we demonstrate real-time optimal control of the quantum trajectory8 of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3 times the zero-point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of 0.56 ± 0.02 quanta, realizing quantum ground-state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems.

•Jan 1, 2021•274 citations

Robustness of system-filter separation for the feedback control of a quantum harmonic oscillator undergoing continuous position measurement

Stuart S. Szigeti, S. J. Adlong, Michael Hush +2 more

We consider the effects of experimental imperfections on the problem of estimation-based feedback control of a trapped particle undergoing 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.

arXiv:1211.2490•Physical Review A•Jan 23, 2013•20 citations

Quantum Measurement-Based Feedback Control: A Nonsmooth Time Delay Control Approach

Shuzhi Sam Ge, Thanh Long Vu, Tong Heng Lee

This paper addresses the problem of measurement-based feedback control for quantum systems, in which the time to compute the filter-based control input is taken into account by considering the input delay. It starts with a new Lyapunov–LaSalle-like theorem for delay-dependent stochastic stability of a class of time delay stochastic nonlinear systems. Nonsmooth time delay control is then constructed to compensate for the control-computation time, which is known but arbitrarily long, while globally stabilizing the quantum filters almost surely. The nonsmooth property enables the control to deal with the symmetric topology of filter state space. The effectiveness of the proposed control is illustrated through the global stabilization of the spin-$1/2$ systems. Simulation results are presented and discussed to show the effectiveness of the proposed control.

SIAM Journal on Control and Optimization•Jan 1, 2012•25 citations
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.
The optical trapping of micro-nano particles in a high vacuum has become a popular research platform in various frontier fields of physics because of its excellent isolation from the environment. The precise measurement of particle motion information is required to analyze and control particle motion modes in traps. However, the detection accuracy is limited by measurement noise and coupling signals from other axes in microparticle optical traps. In this study, we use the Kalman filter to extract the real motion information of each axis under simulation conditions, and the results show that the Kalman filter performs well in noise suppression, improving the RMSE from 12.64 to 5.18 nm and enhancing the feedback cooling performance by approximately 27% through reducing the axes’ signal coupling ratio. We believe that as a solution to these challenges, the Kalman filter will bring a significant achievement to micrometer particle optical traps in vacuums.
Vacuum optical trap is a technology that captures and manipulates particles in a near-vacuum environment by means of laser mechanical effects. It is an ideal platform for precision measurement with high quality factor. Due to its low environmental damping, vacuum optical traps require feedback cooling to reduce the equivalent temperature of particle centroid motion to prevent particle escape. Parametric feedback cooling is a mainstream solution to achieve stable trapping of particles in optical traps. Monte Carlo method and finite difference method were used to simulate the displacement fluctuation of the microsphere without feedback, and the FPGA circuit was used to output control signals with different waveforms to test the feedback cooling effect. Under the premise of reaching mK cooling level, square wave control signals have advantages in fast feedback cooling, and sine wave control signals have advantages in maintaining phase matching.
Optically levitated systems provide an ideal environment for isolating objects extremely well from the environment such that their behaviour can be more easily studied without external influences. Moreover, using optical detection, very high levels of sensitivity to that behaviour can be achieved, allowing precise detection of their motion and measurement of forces upon such a system. In the experiment we describe in this thesis, one can construct an optical gradient force trap by simply directing a collimated light beam onto a parabolic mirror with a sufficiently high numerical aperture. The resulting focusing not only generates the optical trapping potential but also allows detection as a particle trapped at the focal spot of the mirror has the light it scatters onto the mirror collimated and sent back in the direction of the incident trapping light beam. The trap described here allows levitation of dielectric nanoparticles with radii from 10nm to 300nm at pressures from 103 —10-8 mbar. In this thesis I describe the experimental setup and the theory describing a particle levitated in this setup, detailing how, from the detected light intensity on a photodetector, we can extract the properties describing the physical system, including the frequency of motion, the damping upon the motion, the temperature associated with the motion, the radius of the trapped nanoparticle and the conversion factor which allows us to convert from the photo-current measured by the detector to the physical displacement of the particle. Cooling of the translational motion to the ground state is a much targeted goal in the field of levitated optomechanics as it has applications in producing quantum states, performing matter-wave interferometry, testing collapse models and as a very precise force sensor. In this thesis I demonstrate and investigate a number of different cooling methods applied to the translational motion. First, I describe how one can utilise an FIR (Finite Impulse Response) band-pass filter to isolate the signal due to the motion of a single translational degree of freedom and utilise this to perform active feedback cooling upon this degree of freedom. I demonstrate this by implementing an FIR filter on a FPGA (Field Programmable Gate Array) and utilising it in real-time to cool the motion to 2.5K ± 0.4 K. Secondly I utilise a tracking algorithm called a Kalman Filter, I describe how this algorithm functions to track the state of objects from noisy partial measurements of the state and how this can be applied to track levitated nanoparticles. I then detail how this was implemented in an FPGA so that the Kalman Filter could be used in real-time to estimate the position of a levitated nanoparticle. We demonstrate cooling of the translation centre-of-mass motion along the optical axis by 3 orders of magnitude to a temperature of 162mK ± 15 mK. Next I describe a classical model of the motion of a levitated nanoparticle and describe how this model can be simulated numerically to produce simulated time traces of the motion. I then demonstrate how this simulation can be used to reproduce several theoretical relations as well as reproduce experimental results and be utilised to simulate and test the performance of cooling algorithms without requiring experimental implementation. Next I use this simulation to model the effect of a Dung non-linearity in the trapping potential. I match the behaviour of the simulation when exposed to as a pulsed reduction of the laser power with the behaviour of the experimental system when exposed to the same stimulus and in doing so extract the Dung non-linearity in the optical trapping potential generated by the parabolic mirror, which takes a value of ξ = -0.100 m-2. Finally I describe a quantum model of the motion of a levitated nanosphere, which takes into account the various decoherence sources in the experimental system, namely the interaction with the background gas, the laser photons and decoherence due to the measurement. Using this I investigate several different forms of active feedback cooling, including the "optimal" cooling as determined from the tools of control theory, which takes the form of a square wave, and the more traditional sinusoidal feedback signal. In addition I compare both linear cooling by applying a force directly to the nanoparticle and quadratic cooling by modulating the power of the trapping laser. I determine that cooling to mean phonon numbers of less than 10 with the current experimental setup is achievable utilising any of the feedback schemes described here when they are tuned appropriately.
Abstract The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering1. Today, the increasing demand for applied quantum technologies requires adaptation of this level of control to individual quantum systems2, 3. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback4. Successful implementations thus far include experiments on the level of optical and atomic systems5–7. Here we demonstrate real-time optimal control of the quantum trajectory8 of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3 times the zero-point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of 0.56 ± 0.02 quanta, realizing quantum ground-state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems.
We consider the effects of experimental imperfections on the problem of estimation-based feedback control of a trapped particle undergoing 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.
This paper addresses the problem of measurement-based feedback control for quantum systems, in which the time to compute the filter-based control input is taken into account by considering the input delay. It starts with a new Lyapunov–LaSalle-like theorem for delay-dependent stochastic stability of a class of time delay stochastic nonlinear systems. Nonsmooth time delay control is then constructed to compensate for the control-computation time, which is known but arbitrarily long, while globally stabilizing the quantum filters almost surely. The nonsmooth property enables the control to deal with the symmetric topology of filter state space. The effectiveness of the proposed control is illustrated through the global stabilization of the spin-1/21/21/2 systems. Simulation results are presented and discussed to show the effectiveness of the proposed control.