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Photonics

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

Shidong Xu, Ming Chen, Jianyu Yang, Xingfan Chen, Nan Li, Huizhu Hu

Published Sep 27, 2022• 3 citations
Publisher

Abstract

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.

DOI
10.3390/photonics9100700

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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.
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.
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.
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.
We describe the design, construction, and operation of an apparatus that utilizes a piezoelectric transducer for in-vacuum loading of nanoparticles into an optical trap for use in levitated optomechanics experiments. In contrast to commonly used nebulizer-based trap-loading methods that generate aerosolized liquid droplets containing nanoparticles, the method produces dry aerosols of both spherical and high-aspect ratio particles ranging in size by approximately two orders of magnitude. The device has been shown to generate accelerations of order 107 g, which is sufficient to overcome stiction forces between glass nanoparticles and a glass substrate for particles as small as 170 nm in diameter. Particles with sizes ranging from 170 nm to ∼10μm have been successfully loaded into optical traps at pressures ranging from 1 bar to 0.6 mbar. We report the velocity distribution of the particles launched from the substrate, and our results indicate promise for direct loading into ultra-high-vacuum with sufficient laser feedback cooling. This loading technique could be useful for the development of compact fieldable sensors based on optically levitated nanoparticles as well as matter–wave interference experiments with ultra-cold nano-objects, which rely on multiple repeated free-fall measurements and thus require rapid trap re-loading in high vacuum conditions.