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Hybrid trap for levitated optomechanics of mesoscopic particles

Varier, Meenakshi Mohana

Published Nov 27, 2025• 0 citations
Publisher

Abstract

In this M.Phil thesis, a hybrid trap for optomechanical studies of mesoscopic particle is investigated. It uses a Planar Paul Trap (PPT) for electrical confinement and a parabolic mirror for optical confinement. The PPT is compatible with the printed circuit board (PCB) technology making it easier to integrate with the mirror trap. This compatibility also simplifies particle loading, enhances ground state cooling and improves optical interrogation within the trap. It can create various potential landscapes of a quartic potential, including double well or inverted harmonic, and is a potential tool for investigating macroscopic quantum superposition states. This planar geometry of the Paul trap allows large optical access required for optical confinement and detection of the particle. The parabolic mirror provides the benefits of virtually no chromatic aberration, high numerical aperture and functioning as an additional RF electrode of the hybrid trap. The work includes simulations and experiments to characterize the hybrid trap by analyzing the effective trapping potential. From the numerical simulations, the ratio of axial to radial secular frequencies of the trapped particle under the RF drive is = 0.98, implying the chosen parameters of the PPT + mirror RF trap has approximately the same stiffness and hence confinement in the axial and radial directions. It is also observed that the dynamics of a single particle under the RF drive is not affected by damping and random forces in a high vacuum (∼ 10-6 mbar).

DOI
10.25949/30323557

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In this M.Phil thesis, a hybrid trap for optomechanical studies of mesoscopic particle is investigated. It uses a Planar Paul Trap (PPT) for electrical confinement and a parabolic mirror for optical confinement. The PPT is compatible with the printed circuit board (PCB) technology making it easier to integrate with the mirror trap. This compatibility also simplifies particle loading, enhances ground state cooling and improves optical interrogation within the trap. It can create various potential landscapes of a quartic potential, including double well or inverted harmonic, and is a potential tool for investigating macroscopic quantum superposition states. This planar geometry of the Paul trap allows large optical access required for optical confinement and detection of the particle. The parabolic mirror provides the benefits of virtually no chromatic aberration, high numerical aperture and functioning as an additional RF electrode of the hybrid trap. The work includes simulations and experiments to characterize the hybrid trap by analyzing the effective trapping potential. From the numerical simulations, the ratio of axial to radial secular frequencies of the trapped particle under the RF drive is = 0.98, implying the chosen parameters of the PPT + mirror RF trap has approximately the same stiffness and hence confinement in the axial and radial directions. It is also observed that the dynamics of a single particle under the RF drive is not affected by damping and random forces in a high vacuum (∼ 10-6 mbar).
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 present a hybrid trapping platform that allows us to levitate a charged nanoparticle in high vacuum using either optical fields, radio-frequency fields, or a combination thereof. Our hybrid approach combines an optical dipole trap with a linear Paul trap while maintaining a large numerical aperture (0.77 NA). We detail a controlled transfer procedure that allows us to use the Paul trap as a “safety net” to recover particles lost from the optical trap at high vacuum. The presented hybrid platform adds to the toolbox of levitodynamics and represents an important step towards fully controllable “dark” potentials, providing control in the absence of decoherence because of photon recoil. Published by the American Physical Society 2024
The levitation of condensed matter in vacuum allows the study of its physical properties under extreme isolation from the environment. It also offers a venue to investigate quantum mechanics with large systems, at the transition between the quantum and classical worlds. In this work, we study a novel hybrid levitation platform that combines a Paul trap with a weak but highly focused laser beam, a configuration that integrates a deep potential with excellent confinement and motion detection. We combine simulations and experiments to demonstrate the potential of this approach to extend vacuum trapping and interrogation to a broader range of nanomaterials, such as absorbing particles. We study the stability and dynamics of different specimens, such as fluorescent dielectric crystals and gold nanorods, and demonstrate stable trapping down to pressures of 1 mbar.
Realizing quantum superpositions of massive objects provides a pathway to explore the quantum-to-classical transition. Levitated nanoparticles appear as a promising platform for this purpose due to their large mass and unbound motion. This thesis follows the proposal that particle evolution in a double-well potential expands the particle’s motional state within an inverted harmonic region, while the quartic potential generates the non-Gaussian states needed to certify quantum delocalization. As this protocol has been recently developed, we perform experiments in the classical regime as an important milestone to identify the technical challenges and the decoherence sources. While the nanoparticle’s motional state grows linearly under free evolution, inverted harmonic potentials offer exponentially accelerated state expansion. In this thesis, we experimentally demonstrate the expansion of the center-of-mass state of a 125 nm silica nanoparticle from an initial position uncertainty of 45.6 pm to 43.4 nm within 260 μs. This expansion represents a 952-fold increase, reaching a state size comparable to the particle’s radius, and is achieved by employing an electrostatic inverted potential to disable decoherence from photon recoil. The incoherent dynamics allow us to estimate the remaining decoherence sources in the dark. To accomplish dark dynamics, we developed two segmented linear Paul trap devices providing 2D confinement while generating DC potentials in the third axis of motion: a planar micro-fabricated chip and a PCB based wheel trap. Simulations of tunable double-well potentials of tens to hundreds of micrometers based on the device layouts are performed alongside a study of the resulting classical non-Gaussian states. This work marks a key advancement in the effort to generate macroscopic quantum superpositions at unprecedented mass and length scales.