Since their invention in the 1980s [1], optical tweezers have found a wide range of applications, from biophotonics and mechanobiology to microscopy and optomechanics [2, 3, 4, 5]. Simulations of the motion of microscopic particles held by optical tweezers are often required to explore complex phenomena and to interpret experimental data [6, 7, 8, 9]. For the sake of computational efficiency, these simulations usually model the optical tweezers as an harmonic potential [10, 11]. However, more physically-accurate optical-scattering models [12, 13, 14, 15] are required to accurately model more onerous systems; this is especially true for optical traps generated with complex fields [16, 17, 18, 19]. Although accurate, these models tend to be prohibitively slow for problems with more than one or two degrees of freedom (DoF) [20], which has limited their broad adoption. Here, we demonstrate that machine learning permits one to combine the speed of the harmonic model with the accuracy of optical-scattering models. Specifically, we show that a neural network can be trained to rapidly and accurately predict the optical forces acting on a microscopic particle. We demonstrate the utility of this approach on two phenomena that are prohibitively slow to accurately simulate otherwise: the escape dynamics of swelling microparticles in an optical trap, and the rotation rates of particles in a superposition of beams with opposite orbital angular momenta. Thanks to its high speed and accuracy, this method can greatly enhance the range of phenomena that can be efficiently simulated and studied.
We study the cooling of a dielectric nanoscale particle trapped in an optical cavity. We derive the frictional force for motion in the cavity field, and show that the cooling rate is proportional to the square of oscillation amplitude and frequency. Both the radial and axial centre-of-mass motion of the trapped particle, which are coupled by the cavity field, are cooled. This motion is analogous to two coupled but damped pendulums. Our simulations show that the nanosphere can be cooled to 1/e of its initial momentum over time scales of hundredths of milliseconds.
We report on rotating an optically trapped silica nanoparticle in vacuum by transferring spin angular momentum of light to the particle's mechanical angular momentum. At sufficiently low damping, realized at pressures below $10^{-5}$ mbar, we observe rotation frequencies of single 100 nm particles exceeding 1 GHz. We find that the steady-state rotation frequency scales linearly with the optical trapping power and inversely with pressure, consistent with theoretical considerations based on conservation of angular momentum. Rapidly changing the polarization of the trapping light allows us to ext…
Optical vortex beams carry orbital angular momentum and thus exert torque on illuminated objects. A dielectric microtool - a microbarbell - is used in a two-laser optical tweezers to measure the torque of a focused optical vortex. The tool was either freely rotating due to the applied torque or set into oscillations by the counteracting force. Four different trapping configurations provided different ways of sensing the torque and gave consistent results. The value of torque was determined by confronting the experimental results with numerical and analytical models.
We investigate the dynamics of high aspect ratio nanowires trapped axially in a single gradient force optical tweezers. A power spectrum analysis of the Brownian dynamics reveals a broad spectral resonance of the order of a kHz with peak properties that are strongly dependent on the input trapping power. Modelling of the dynamical equations of motion of the trapped nanowire that incorporate non-conservative effects through asymmetric coupling between translational and rotational degrees of freedom provides excellent agreement with the experimental observations. An associated observation of per…
The optical trapping of polymeric nanofibers and the characterization of the rotational dynamics are reported. A strategy to apply a torque to a polymer nanofiber, by tilting the trapped fibers using a symmetrical linear polarized Gaussian beam is demonstrated. Rotation frequencies up to 10 Hz are measured, depending on the trapping power, the fiber length and the tilt angle. A comparison of the experimental rotation frequencies in the different trapping configurations with calculations based on optical trapping and rotation of linear nanostructures through a T-Matrix formalism, accurately rep…
We present a method to measure the optical torque applied to particles of arbitrary shape held in an optical trap, inferred from the change of angular momentum of light induced by the particle. All torque components can be determined from a single interference pattern recorded by a camera in the back focal plane of a high-NA condenser collecting all forward scattered light. We derive explicit expressions mapping the measured complex field in this plane to the torque components. The required phase is retrieved by an iterative algorithm, using the known position of the optical traps as constrain…
We report on the observation and measurement of the transfer of transverse angular momentum to birefringent particles several wavelengths in size. A trapped birefringent particle is much larger than the nano-particles systems for which transverse angular momentum was previously investigated. The larger birefringent particle interacts more strongly with both the trapping beam and fluid surrounding it. This technique could be used to transfer transverse angular momentum for studies of diverse micro-systems. Thus, it can be used for investigation of the dynamics of complex fluids in 3D as well as…
We optically trap freestanding single metallic chiral nanoparticles using a standing-wave optical tweezer. We also incorporate within the trap a polarimetric setup that allows to perform in situ chiral recognition of single enantiomers. This is done by measuring the S_3 component of the Stokes vector of a light beam scattered off the trapped nanoparticle in the forward direction. This unique combination of optical trapping and chiral recognition, all implemented within a single setup, opens new perspectives towards the control, recognition, and manipulation of chiral objects at nanometer scale…
As a first approximation, the forces acting on optically trapped particles are commonly assumed to be conservative. The influence of the nonconservative force has been shown to be negligible in overdamped liquid environments. However, its impact in the underdamped regime remains unexplored. Here, we experimentally study the combined effects of gradient and scattering forces on the nonlinear dynamics of trapped particles at various air pressures, leading to significant low-frequency noise excess along the optical axis and the emergence of toroidal Brownian vortices. Our results supported, by nu…
We investigate the emission of single photons from CdSe/CdS dot-in-rods which are optically trapped in the focus of a deep parabolic mirror. Thanks to this mirror, we are able to image almost the full 4$π$ emission pattern of nanometer-sized elementary dipoles and verify the alignment of the rods within the optical trap. From the motional dynamics of the emitters in the trap we infer that the single-photon emission occurs from clusters comprising several emitters. We demonstrate the optical trapping of rod-shaped quantum emitters in a configuration suitable for efficiently coupling an ensemble…
Optically trapped nanoparticles have recently emerged as exciting candidates for tests of quantum mechanics at the macroscale and as versatile platforms for ultrasensitive metrology. Recent experiments have demonstrated parametric feedback cooling, nonequilibrium physics, and temperature detection, all in the classical regime. Here we provide the first quantum model for trapped nanoparticle cooling and force sensing. In contrast to existing theories, our work indicates that the nanomechanical ground state may be prepared without using an optical resonator; that the cooling mechanism correspond…
When studying the motion of optically trapped particles on the $μs$ time scale, in low viscous media such as air, inertia cannot be neglected. Resolution of unusual and interesting behaviour not seen in colloidal trapping experiments is possible. In attempt to explain the phenomena we use power spectral methods to perform a parameter study of the Brownian motion of optically trapped liquid aerosol droplets concentrated around the critically damped regime. We present evidence that the system is suitably described by a simple harmonic oscillator model which must include a description of Faxén's …
We study the dynamics of phase defects trapped in a finite optically imprinted ring lattice in binary polariton condensates, under the influence of the cross-interaction (CI) between the condensates in different spin components and the spin-orbit interaction (SOI). In this configuration, we find that a vortex circulates unidirectionally in optically induced orbits because of the Magnus force acting in the polariton fluid, and the vortex' angular velocity is influenced by the SOI and CI. Interestingly, in our system, these two interactions can also lead to elongated and frozen phase defects, fo…
Calibration of optically trapped particles in-vivo has been complicated given the frequency dependence and spatial inhomogeneity of the cytoplasmic viscosity, and the requirement of accurate knowledge of the medium refractive index. Further, it has been demonstrated that the medium viscosity is dependent upon the measurement probe leading to reliability issues for measurements with even micrometer sized particles. Here, we employ a recent extension of Jeffery's model of viscoelasticity in the microscopic domain to fit the passive motional power spectra of micrometer-sized optically trapped par…
Collective coherent scattering of laser light induces strong light forces between polarizable point particles. These dipole forces are strongly enhanced in magnitude and distance within the field of an optical waveguide so that at low temperature the particles self-order in strongly bound regular patterns. The stationary configurations typically exhibit super-radiant scattering with strong particle and light confinement. Here we study collective excitations of such self-consistent crystalline particle-light structures as function of particle number and pump strength. Multiple scattering and ab…
We review recent works on optomechanics of optically trapped microspheres and nanoparticles in vacuum, which provide an ideal system for studying macroscopic quantum mechanics and ultrasensitive force detection. An optically trapped particle in vacuum has an ultrahigh mechanical quality factor as it is well-isolated from the thermal environment. Its oscillation frequency can be tuned in real time by changing the power of the trapping laser. Furthermore, an optically trapped particle in vacuum may rotate freely, a unique property that does not exist in clamped mechanical oscillators. In this re…
The dynamics of an optically trapped particle are often determined by measuring intensity shifts of the back-scattered light from the particle using position sensitive detectors. We present a technique which measures the phase of the back-scattered light using balanced detection in an external Mach-Zender interferometer scheme where we separate out and beat the scattered light from the bead and that from the top surface of our trapping chamber. The technique has improved axial motion resolution over intensity-based detection, and can also be used to measure lateral motion of the trapped partic…
Ellipsoidal micron-sized colloidal particles can oscillate spontaneously when trapped in a focused laser beam. If two oscillating particles are held in proximity their oscillations synchronize through hydrodynamic interactions. The degree of synchronization depends on the distance between the oscillators and on their orientation. Due to the anisotropic nature of hydrodynamic coupling the synchronization is strongest when particles are arranged along the direction of oscillations. Similar behavior is observed for many oscillating particles arranged in a row. Experimental observations are well r…
We propose a mass sensor using optically trapped and cooled dielectric microdisks with "measuring after cooling" scheme. The center-of-mass motion of a trapped particle in vacuum can experience extremely low dissipation resulting in robust decoupling from the heat bath. Thus the measurement can be accomplished in a short time before a jump in the phonon number after the optomechanical cooling is finished. This method can lead to 10^(-6) dalton mass sensitivity which is a thousand times smaller than the mass of one electron.
We propose and evaluate a new type of optical force microscope based on a standing wave optical trap. Our microscope, calibrated in-situ and operating in a dynamic mode, is able to trap, without heating, a single metallic nanoparticle of 150 nm that acts as a highly sensitive probe for external radiation pressure. An Allan deviation-based stability analysis of the setup yields an optimal 0.1 Hz measurement bandwidth over which the microscope is thermally limited. Over this bandwidth, and with a genuine sine-wave external drive, we demonstrate an optical force resolution down to 3 fN in water a…
Single-particle tracking and optical tweezers are powerful techniques for studying diverse processes at the microscopic scale. The stochastic behavior of a microscopically observable particle contains information about its interaction with surrounding molecules, and an optical tweezer can further facilitate this observation with its ability to constrain the particle to an area of interest. Although these techniques found their initial applications in biology, they can also shed new light on colloid and interface phenomena by unveiling nanoscale morphologies and molecular-level interactions in …
The optical binding of many particles has great potential to achieve the wide-area formation of a "crystal" of small materials. Unlike conventional optical binding, where the whole assembly of targeted particles is irradiated with light, if one can indirectly manipulate remote particles using a single trapped particle through optical binding, the degrees of freedom to create ordered structures will be greatly enhanced. In this Letter, we theoretically investigate the dynamics of the assembly of gold nanoparticles that is manipulated using a single particle trapped by a focused laser. As a resu…
We report a weighing metrology experiment of a single silica microsphere optically trapped and immersed in air. Based on fluctuations about thermal equilibrium, three different mass measurements are investigated, each arising from one of two principle methods. The first method is based on spectral analysis and enables simultaneous extraction of various system parameters. Additionally, the spectral method yields a mass measurement with systematic relative uncertainty of 3.0\% in 3~s and statistical relative uncertainty of 0.9\% across several trapping laser powers. Parameter values learned from…
Coherent bosonic ensembles offer the promise of harnessing quantum effects in photonic and quantum circuits. In the dynamic equilibrium regime, the application of polariton condensates is hindered by exciton-polariton scattering induced de-coherence in the presence of a dark exciton reservoir. By spatially separating the condensate from the reservoir, we drive the system into the weak interaction regime, where the ensemble coherence time exceeds the individual particle lifetime by nearly three orders of magnitude. The observed nanosecond coherence provides an upper limit for polariton self-int…
Forces and torques exerted on dielectric disks trapped in a Gaussian standing wave are analyzed theoretically for disks of radius $2~μ\text{m}$ with index of refraction $n=1.45$ and $n=2.0$ as well as disks of radius 200 nm with $n=1.45$. Calculations of the forces and torques were conducted both analytically and numerically using a discrete-dipole approximation method. Besides harmonic terms, third order ro-translational coupling terms in the potential energy can be significant and a necessary consideration when describing the dynamics of disks outside of the Rayleigh limit. The coupling term…
Using an optical tweezers apparatus, we demonstrate three-dimensional control of nanodiamonds in solution with simultaneous readout of ground-state electron-spin resonance (ESR) transitions in an ensemble of diamond nitrogen-vacancy (NV) color centers. Despite the motion and random orientation of NV centers suspended in the optical trap, we observe distinct peaks in the measured ESR spectra qualitatively similar to the same measurement in bulk. Accounting for the random dynamics, we model the ESR spectra observed in an externally applied magnetic field to enable d.c. magnetometry in solution. …
Photophoretic force due to the optically-induced thermal effect provides an effective way to manipulate the light-absorbing particles suspended in ambient gases. However, how this force temporally responds to the intensity modulation of the illumination light is unclear. Here, by vertically trapping a micron-sized absorbing particle with a negative photophoretic force generated by a focused Gaussian beam, we demonstrate that the temporal change in the photophoretic force in response to the intensity modulation is remarkably slow (with a time constant up to ~1 s) due to the slow change in the p…
Experimental observations suggest that there are differences between the behavior of particles optically trapped in air and trapped in a liquid phase. We present a modified version of Mie Debye Spherical Aberration theory to numerically simulate such optical system in attempt to explain and predict these effects. The model incorporates Mie scattering and focussing of the trapping beam through media of stratified refractive index. Our results show a geometrical optics approach cannot correctly describe our system and that spherical aberration must be included. We successfully qualitatively expl…
Particles trapped in the evanescent field of an ultrathin optical fibre inter-act over very long distances via multiple scattering of the fibre-guided fields. In ultrathin fibres that support higher order modes, these interac-tions are stronger and exhibit qualitatively new behaviour due to the cou-pling of different fibre modes, which have different propagation wave-vectors, by the particles. Here, we study one dimensional longitudinal opti-cal binding interactions of chains of 3 μm polystyrene spheres under the influence of the evanescent fields of a two-mode microfibre. The observa-tion of …
Trapping and manipulation of particles using laser beams has become an important tool in diverse fields of research. In recent years, particular interest is given to the problem of conveying optically trapped particles over extended distances either down or upstream the direction of the photons momentum flow. Here, we propose and demonstrate experimentally an optical analogue of the famous Archimedes' screw where the rotation of a helical-intensity beam is transferred to the axial motion of optically-trapped micro-meter scale airborne carbon based particles. With this optical screw, particles …
Since the early work by Ashkin in 1970, optical trapping has become one of the most powerful tools for manipulating small particles, such as micron sized beads or single atoms. The optical trapping mechanism is based on the interaction energy of a dipole and the electric field of the laser light. In atom trapping, the dominant contribution typically comes from the allowed optical transition closest to the laser wavelength, whereas for mesoscopic particles it is given by the bulk polarizability of the material. These two different regimes of optical trapping have coexisted for decades without a…
We show that nonlinear dynamics in diode lasers with optical injection leads to frequency tunable microwave sidebands which are suitable for atomic physics experiments. We demonstrate the applicability of the sidebands in an experiment where rubidium atoms are magneto-optically trapped with both the trap and the re-pump optical frequencies derived from one optically injected laser. We find linewidth narrowing in the optical spectrum of the injected laser at both the injection frequency and the sideband frequency. With strong optical injection which leads to frequency locking we find a complete…
We present a simple and effective method of loading particles into an optical trap in air at atmospheric pressure. Material which is highly absorptive at the trapping laser wavelength, such as tartrazine dye, is used as media to attach photoluminescent diamond nanocrystals. The mix is burnt into a cloud of air-borne particles as the material is swept near the trapping laser focus on a glass slide. Particles are then trapped with the laser used for burning or transferred to a second laser trap at a different wavelength. Evidence of successfully loading diamond nanocrystals into the trap present…
We present a technique, based on atoms coupled to an optical cavity, for non-destructive detection of trapped ions. We demonstrate the vacuum-Rabi splitting (VRS), arising due to the collective strong coupling of ultracold Rb atoms to a cavity, to change in presence of trapped Rb+ ions. The Rb+ ions are optically dark and the Rb atoms are prepared in a dark magneto-optical trap (MOT). The VRS is measured on an optically open transition of the initially dark Rb atoms. The measurement itself is fast, non-destructive and has sufficient fidelity to permit the measurement of atomic-state selective …
We propose a tunable resonant sensor to detect gravitational waves in the frequency range of 50-300 kHz using optically trapped and cooled dielectric microspheres or micro-discs. The technique we describe can exceed the sensitivity of laser-based gravitational wave observatories in this frequency range, using an instrument of only a few percent of their size. Such a device extends the search volume for gravitational wave sources above 100 kHz by 1 to 3 orders of magnitude, and could detect monochromatic gravitational radiation from the annihilation of QCD axions in the cloud they form around s…
