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International Conference on Signal Processing and Communication Technology (SPCT)

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, Gongchang Wang, Huiying Fan, Qiongnan Huang, Fang Lin

Published Apr 6, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2673781

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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.
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 motion control of a levitated nanoparticle plays a central role in optical levitation for fundamental studies and practical applications. Here, we presented digital parametric feedback cooling based on square wave modulation by switching trapping laser intensity between two levels. The effects of the modulation depth and modulation signal phase on the cooling result were investigated in detail. Using such a digital parametric feedback method, the center-of-mass temperature of all three motional degrees of freedom can be cooled to dozens of millikelvin. The flexibility and agility of the digital feedback control pave the way for a variety of motion control modes.
To control the motion of a trapped particle and prevent quantum state decoherence, cooling is required. In order to trap particles that do not offer cooling transitions, sympathetic cooling can be used. We are going to investigate the effects that arise from changing the trapping waveform applied to a Paul trap. We are especially interested in the comparison of the sympathetic cooling performance of the sinusoidal wave with its alternatives. We investigate different waveforms such as normal sine driven traps, but also traps driven with a saw-tooth, triangle, or square waveforms. From the simulation results, cooling rates as well as stability parameters are extracted. Ours findings indicate potential benefits of further in-depth studies on the key properties that trap driving waveforms should possess to enhance the sympathetic cooling efficiency in Paul traps.
We demonstrate a simple and robust geometry for optical trapping in vacuum of a single nanoparticle based on a parabolic mirror and the optical gradient force, and we demonstrate rapid parametric feedback cooling of all three motional degrees of freedom from room temperature to a few mK. A single laser at 1550nm, and a single photodiode, are used for trapping, position detection, and cooling for all three dimensions. Particles with diameters from 26nm to 160nm are trapped without feedback to 10−5^{-5}−5mbar and with feedback engaged the pressure is reduced to 10−6^{-6}−6mbar. Modifications to the harmonic motion in the presence of noise and feedback are studied, and an experimental mechanical quality factor >4×107>4\times 10^7>4×107 is estimated.
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.