Robust Optical-Levitation-Based Metrology of Nanoparticle's Position and Mass

Gradient and curl optical torques

Optical forces and torques offer the route towards full degree-of-freedom manipulation of matter. Exploiting structured light has led to the discovery of gradient and curl forces, and nontrivial optomechanical manifestations, such as negative and lateral optical forces. Here, we uncover the existence of two fundamental torque components, which originate from the reactive helicity gradient and momentum curl of light, and which represent the rotational analogues to the gradient and curl forces, respectively. Based on the two components, we introduce and demonstrate the concept of lateral optical torques, which act transversely to the spin of illumination. The orbital angular momentum of vortex beams is shown to couple to the curl torque, promising a path to extreme torque enhancement or achieving negative optical torques. These results highlight the intersection between the areas of structured light, Mie-tronics and rotational optomechanics, even inspiring new paths of manipulation in acoustics and hydrodynamics.

Optically levitated micro gyroscopes with an MHz rotational vaterite rotor

The field of levitated optomechanics has experienced significant advancements in manipulating the translational and rotational dynamics of optically levitated particles and exploring their sensing applications. The concept of using optically levitated particles as gyroscopes to measure angular motion has long been explored but has not yet been proven either theoretically or experimentally. In this study, we present the first rotor gyroscope based on optically levitated high-speed rotating particles. The gyroscope is composed of a micrometer-size ellipsoidal vaterite particle that is driven to rotate at MHz frequencies in a vacuum environment. When an external angular velocity is input, the optical axis deviates from its initial position, resulting in changes in the frequency and amplitude of the rotational signal. By analyzing these changes, the angular velocity of the input can be accurately detected, making it the smallest rotor gyroscope in the world. The angular rate bias instability of the gyroscope is measured to be 0.08°/s and can be further improved to as low as 10-9°/h theoretically by cooling the motion and increasing the angular moment of the levitated particle. Our work opens a new application paradigm for levitated optomechanical systems and may pave the way for the development of quantum rotor gyroscopes.

Quantum control and Berry phase of electron spins in rotating levitated diamonds in high vacuum

Levitated diamond particles in high vacuum with internal spin qubits have been proposed for exploring macroscopic quantum mechanics, quantum gravity, and precision measurements. The coupling between spins and particle rotation can be utilized to study quantum geometric phase, create gyroscopes and rotational matter-wave interferometers. However, previous efforts in levitated diamonds struggled with vacuum level or spin state readouts. To address these gaps, we fabricate an integrated surface ion trap with multiple stabilization electrodes. This facilitates on-chip levitation and, for the first time, optically detected magnetic resonance measurements of a nanodiamond levitated in high vacuum. The internal temperature of our levitated nanodiamond remains moderate at pressures below 10-5 Torr. We have driven a nanodiamond to rotate up to 20 MHz (1.2 × 109 rpm), surpassing typical nitrogen-vacancy (NV) center electron spin dephasing rates. Using these NV spins, we observe the effect of the Berry phase arising from particle rotation. In addition, we demonstrate quantum control of spins in a rotating nanodiamond. These results mark an important development in interfacing mechanical rotation with spin qubits, expanding our capacity to study quantum phenomena.

Mass measurement under medium vacuum in optically levitated nanoparticles based on Maxwell speed distribution law

As one of the directions of optical levitation technology, the mass measurement of micro-nano particles has always been a research hotspot in extremely weak mechanical measurements. When nanoscale particles are trapped in an optical trap, parameters such as density, diameter, and shape are unknown. Here we propose what we believe to be a new method to measure mass by fitting particle motion information to the Maxwell speed distribution law, with an accuracy better than 7% at 10 mbar. This method has the characteristics of requiring no external driving force, no precise natural frequency, no prior information such as density, and non-destructive testing within the medium vacuum range. With the increasing iterations, the uncertainty of mass measurement is reduced, and the accuracy of mass measurement of levitated particles is verified under multiple air pressures. It provides what we believe is a new method for the future non-destructive testing of nanoscale particles, and provides an apparently new way for the sensing measurement and metrology application fields of levitation dynamics systems.

Experiment and theory of the complex refractive index of dense colloidal media

The complex refractive index is analyzed by measuring its scattering attenuation μ s, group index n g, and group velocity dispersion (GVD) for 100 nm diameter silica nanoparticles dispersed in water. The experiments were performed for wavelengths between 410 nm and 930 nm. The experimental results were compared with different mixing models for the complex refractive index of colloidal suspensions. The group index linearly scaled with the volume fraction both in experiment and for all tested models. It was found that the GVD has a nonlinear dependence on volume fraction in agreement with the coupled dipole model of Parola et al. [J. Chem. Phys.141, 124902 (2014)JCPSA60021-960610.1063/1.4895961] The scattering attenuation is in good agreement with both the coupled dipole model and the low frequency quasi-crystalline approximation [J. Electromagn. Waves Appl.2, 757 (1988)JEWAE50920-507110.1163/156939388X00053] that take particle correlations into account. With an iterative fitting procedure of all the data based on both the coupled dipole model and the quasi-crystalline approximation, the refractive index, porosity, and size of the nanoparticles were determined. We determined that the coupled dipole model is in best agreement with the data.

Nanoscale feedback control of six degrees of freedom of a near-sphere

Manipulating the rotational as well as the translational degrees of freedom of rigid bodies has been a crucial ingredient in diverse areas, from optically controlled micro-robots, navigation, and precision measurements at macroscale to artificial and biological Brownian motors at nanoscale. Here, we demonstrate feedback cooling of all the angular motions of a near-spherical neutral nanoparticle with all the translational motions feedback-cooled to near the ground state. The occupation numbers of the three translational motions are 6 ± 1, 6 ± 1, and 0.69 ± 0.18. A tight, anisotropic optical confinement allows us to clearly observe three angular oscillations and to identify the ratio of two radii to the longest radius with a precision of 0.08 %. We develop a thermometry for three angular oscillations and realize feedback cooling of them to temperatures of lower than 0.03 K by electrically controlling the electric dipole moment of the nanoparticle.

Structured-light displacement detection method using split-waveplate for dual-beam optical tweezers

Structured-light displacement detection method is an innovative approach with extremely high sensitivity for measuring the displacement of a levitated particle. This scheme includes two key components, a split-waveplate (SWP) and a single-mode fiber. In this work, we further investigated the influence of SWP installation on this method regarding the sensitivity of displacement detection. The results indicate that the sensitivity increases with the expanding of SWP offset in the effective range. In addition, we found this method has a significant tolerance rate, with an extensive SWP offset effective range of 5%-25%. However, an excessive offset can render this method ineffective. More interestingly, we demonstrated the feasibility of rotating the SWP to detect displacement in different directions. Our research contributes to guiding the structured-light detection methods in practical applications and expanding their applications in fundamental physics.

Gradient torque and its effect on rotational dynamics of optically trapped non-spherical particles in the elliptic Gaussian beam

Rotational motion of the optically trapped particle is a topic of enduring interest, while the changes of angular velocity in one rotation period remain largely unexplored. Here, we proposed the optical gradient torque in the elliptic Gaussian beam, and the instantaneous angular velocities of alignment and fluctuant rotation of the trapped non-spherical particles are investigated for the first time. The fluctuant rotations of optically trapped particles are observed, and the angular velocity fluctuated twice per rotation period, which can be used to determine the shape of trapped particles. Meanwhile, a compact optical wrench is invented based on the alignment, and its torque is adjustable and is larger than the torque of a linearly polarized wrench with the same power. These results provide a foundation for precisely modelling the rotational dynamics of optically trapped particles, and the presented wrench is expected to be a simple and practical micro-manipulating tool.

High-power continuous-wave optical waveguiding in a silica micro/nanofibre

As miniature fibre-optic platforms, micro/nanofibres (MNFs) taper-drawn from silica fibres have been widely studied for applications from optical sensing, nonlinear optics to optomechanics and atom optics. While continuous-wave (CW) optical waveguiding is frequently adopted, so far almost all MNFs are operated in low-power region (e.g., <0.1 W). Here, we demonstrate high-power low-loss CW optical waveguiding in MNFs around 1550-nm wavelength. We show that a pristine MNF, even with a diameter down to 410 nm, can waveguide an optical power higher than 10 W, which is about 30 times higher than demonstrated previously. Also, we predict an optical damage threshold of 70 W. In high-power CW waveguiding MNFs, we demonstrate high-speed optomechanical driving of microparticles in air, and second harmonic generation efficiency higher than those pumped by short pulses. Our results may pave a way towards high-power MNF optics, for both scientific research and technological applications.

Enhanced sensing of optomechanically induced nonlinearity by linewidth suppression and optical bistability in cavity-waveguide systems

We study the enhanced sensing of optomechanically induced nonlinearity (OMIN) in a cavity-waveguide coupled system. The Hamiltonian of the system is anti-PT symmetric, with the two involved cavities being dissipatively coupled via the waveguide. The anti-PT symmetry may break down when a weak waveguide-mediated coherent coupling is introduced. However, we find a strong bistable response of the cavity intensity to the OMIN near the cavity resonance, benefiting from linewidth suppression caused by the vacuum induced coherence. The joint effect of optical bistability and the linewidth suppression is inaccessible by the anti-PT symmetric system involving only dissipative coupling. Due to that, the sensitivity measured by an enhancement factor is greatly enhanced by two orders of magnitude compared to that for the anti-PT symmetric model. Moreover, the enhancement factor shows resistance to a reasonably large cavity decay and robustness to fluctuations in the cavity-waveguide detuning. Based on the integrated optomechanical cavity-waveguide systems, the scheme can be used for sensing different physical quantities related to the single-photon coupling strength and has potential applications in high-precision measurements with systems involving Kerr-type nonlinearity.

Electromagnetic Forces and Torques: From Dielectrophoresis to Optical Tweezers

Electromagnetic forces and torques enable many key technologies, including optical tweezers or dielectrophoresis. Interestingly, both techniques rely on the same physical process: the interaction of an oscillating electric field with a particle of matter. This work provides a unified framework to understand this interaction both when considering fields oscillating at low frequencies─dielectrophoresis─and high frequencies─optical tweezers. We draw useful parallels between these two techniques, discuss the different and often unstated assumptions they are based upon, and illustrate key applications in the fields of physical and analytical chemistry, biosensing, and colloidal science.

Recent Progress on Optical Micro/Nanomanipulations: Structured Forces, Structured Particles, and Synergetic Applications

Optical manipulation has achieved great success in the fields of biology, micro/nano robotics and physical sciences in the past few decades. To date, the optical manipulation is still witnessing substantial progress powered by the growing accessibility of the complex light field, advanced nanofabrication and developed understandings of light-matter interactions. In this perspective, we highlight recent advancements of optical micro/nanomanipulations in cutting-edge applications, which can be fostered by structured optical forces enabled with diverse auxiliary multiphysical field/forces and structured particles. We conclude with our vision of ongoing and futuristic directions, including heat-avoided and heat-utilized manipulation, nonlinearity-mediated trapping and manipulation, metasurface/two-dimensional material based optical manipulation, as well as interface-based optical manipulation.

Differential displacement measurement of the levitated particle using D-shaped mirrors in the optical tweezers

Displacement measurement using a D-shaped mirror is a key technology in optical tweezers, which have emerged as an important tool for precision measurement. In this paper, we first study the influences of installation errors for the D-shaped mirror on the displacement measurement. The calibration factor and sensitivity of the different installation parameters are quantified. The results show that the variation of the calibration factor obeys the cosine curve with the angle error, and the sensitivity increases exponentially with the translation error. Besides, we find that the translation error will also lead to crosstalk between transverse and axial displacement. Our work will contribute to improving the performance of optical tweezers for the application in precision measurement and basic physics.

Levitodynamics: Levitation and control of microscopic objects in vacuum

[Figure: see text].

3D calibration of microsphere position in optical tweezers using the back-focal-plane interferometry method

This paper presents a method to directly calibrate the position of a trapped micro-sphere in optical tweezers utilizing its interference pattern formed at the back focal plane (BFP). Through finite difference time domain (FDTD) and scalar diffraction theorem, the scattering field complex amplitude of the near and far fields can be simulated after interference between the trapped sphere and focus Gaussian beam. The position of the trapped sphere can be recovered and calibrated based on a back focal plane interferometry (BFPI) algorithm. Theoretical results demonstrate that optical tweezers with a larger numerical aperture (NA) Gaussian beam will yield a better detection sensitivity but with a smaller linear range. These results were experimentally validated by trapping a microsphere in a single beam optical tweezer. We used an extra focused laser to manipulate the trapped sphere and then compared its position in the images and that obtained using the BFP method. The interference pattern from simulation and experiments showed good agreement, implying that the calibration factor can be deduced from simulation and requires no intermediate calculation process. These results provide a pathway to obtain the calibration factor, enable a faster and direct measurement of the sphere position, and show possibilities for adjusting the crosstalk and nonlinearity inside an optical trap.

Fast size estimation of single-levitated nanoparticles in a vacuum optomechanical system

Optical trapping of single nanoparticles in vacuum has various applications in both precise measurements and fundamental physics. However, to date, the number and size of randomly loaded nanoparticles in an optical trap is difficult to determine unless in vacuum. In this Letter, an efficient method for nanoparticle size estimation in an optical tweezer system before the evacuation of air was proposed and demonstrated experimentally, using scattering light from levitated particles. The particle radii deduced from the scattering light power in our proposal and from the kinetic theory of particles in gas match well (with the differences of less than 10%). For sample particles with radii ranging within 50-100 nm, we also provide a preselection rule based on this method, where over half of the trapped particles are verified as single particles. Such a particle analysis method is applicable also for the size estimation of levitated diamond particles, gold particles, and other plasmonic particles and can be applied to discovering novel scattering effects.

Centrifugal motion of an optically levitated particle

Levitated optomechanical systems experience a tremendous development on detecting weak force and torque with the center of mass motion and rotation of the levitated particle. Here the levitated optomechanical system is established on a rotating platform, and the centrifugal motion of the particle is observed after rotating the optical platform. The centrifugal displacement of the particle is experimentally proven to show a quadratic function relation with the rotation speed, and the stiffness of the trap and the mass of the levitated particle are obtained from it separately. Furthermore, the centrifugal motion makes the particle deviate from the laser focus center, which would decrease the particle spin speed. These results will help to understand the centrifugal motion and fully consider this effect when the optomechanical system rotates.

Nonlinearity-induced nanoparticle circumgyration at sub-diffraction scale

The ability of light beams to rotate nano-objects has important applications in optical micromachines and biotechnology. However, due to the diffraction limit, it is challenging to rotate nanoparticles at subwavelength scale. Here, we propose a method to obtain controlled fast orbital rotation (i.e., circumgyration) at deep subwavelength scale, based on the nonlinear optical effect rather than sub-diffraction focusing. We experimentally demonstrate rotation of metallic nanoparticles with orbital radius of 71 nm, to our knowledge, the smallest orbital radius obtained by optical trapping thus far. The circumgyration frequency of particles in water can be more than 1 kHz. In addition, we use a femtosecond pulsed Gaussian beam rather than vortex beams in the experiment. Our study provides paradigms for nanoparticle manipulation beyond the diffraction limit, which will not only push toward possible applications in optically driven nanomachines, but also spur more fascinating research in nano-rheology, micro-fluid mechanics and biological applications at the nanoscale.

Rotational Doppler cooling and heating

Doppler cooling is a widely used technique to laser cool atoms, molecules, and nanoparticles by exploiting the Doppler shift associated with translational motion. The rotational Doppler effect arising from rotational coordinate transformation should similarly enable optical manipulation of the rotational motion of nanosystems. Here, we show that rotational Doppler cooling and heating (RDC and RDH) effects embody rich and unexplored physics, including an unexpected strong dependence on particle morphology. For geometrically constrained particles, cooling and heating are observed at red- or blue-detuned laser frequencies relative to particle resonances. In contrast, for nanosystems that can be modeled as solid particles, RDH appears close to resonant illumination, while detuned frequencies produce cooling of rotation. We further predict that RDH can lead to optomechanical spontaneous chiral symmetry breaking, where an achiral particle under linearly polarized illumination starts spontaneously rotating. Our results open up new exciting possibilities to control the rotational motion of nanosystems.