Short-range force detection using optically cooled levitated microspheres

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.

Near-Field GHz Rotation and Sensing with an Optically Levitated Nanodumbbell

A levitated nonspherical nanoparticle in a vacuum is ideal for studying quantum rotations and is an ultrasensitive torque detector for probing fundamental particle-surface interactions. Here, we optically levitate a silica nanodumbbell in a vacuum at 430 nm away from a sapphire surface and drive it to rotate at GHz frequencies. The relative linear speed between the tip of the nanodumbbell and the surface reaches 1.4 km s-1 at a submicrometer separation. The rotating nanodumbbell near the surface demonstrates a torque sensitivity of (5.0 ± 1.1) × 10-26 N m Hz-1/2 at room temperature. Moreover, we probed the near-field laser intensity distribution beyond the optical diffraction limit with a nanodumbbell levitated near a nanograting. Our numerical simulations show that the system can measure the Casimir torque and will improve the detection limit of non-Newtonian gravity by several orders of magnitude.

High-sensitivity force sensing using a phonon laser in an active levitated optomechanical system

Force detection with high sensitivity is of paramount importance in many fields of study, from gravitational wave detection to investigations of surface forces. Here, we propose and demonstrate a force-sensing method based on gain-enhanced nonlinearity in a nonlinear phonon laser. Experimental and simulation results show that the input force leads to the frequency shift of phonon laser, due to nonlinearity. In addition, we further investigate the influences of the pumping power, numerical aperture, and microsphere's refractive index on the performance of this force-sensing system, regarding the sensitivity and the linear response range. Our work paves a new way towards the realization of precise metrology based on the nonlinearity of phonon laser.

Simulations and theory of power spectral density functions for time-dependent and anharmonic Langevin oscillators

Simulations and theory are presented for the power spectral density functions (PSDs) of particles in time-dependent and anharmonic potentials, including the effects of a thermal environment leading to damping and fluctuating forces. We investigate three one-dimensional perturbations to the harmonic oscillator of which two are time-dependent changes in the natural frequency of the oscillator, while the other is a time-independent extension of the quadratic potential to include a quartic term. We investigate the effect of these perturbations on two PSDs of the motion that are used in experiments on trapped nano-oscillators. We also derive and numerically test the PSDs for the motion of a spherical nanoparticle in a Paul trap. We found that the simple harmonic Langevin oscillator's PSDs are good approximations for the x and y coordinates' PSDs for small values of the parameter q of the Mathieu equation, but the difference can be more than a factor of two as "q" increases. We also numerically showed that the presence of a permanent electric dipole on the nanosphere can significantly affect the PSDs in the x and y coordinates.

Laser2: A two-domain photon-phonon laser

The laser is one of the greatest inventions in history. Because of its ubiquitous applications and profound societal impact, the concept of the laser has been extended to other physical domains including phonon lasers and atom lasers. Quite often, a laser in one physical domain is pumped by energy in another. However, all lasers demonstrated so far have only lased in one physical domain. We have experimentally demonstrated simultaneous photon and phonon lasing in a two-mode silica fiber ring cavity via forward intermodal stimulated Brillouin scattering (SBS) mediated by long-lived flexural acoustic waves. This two-domain laser may find potential applications in optical/acoustic tweezers, optomechanical sensing, microwave generation, and quantum information processing. Furthermore, we believe that this demonstration will usher in other multidomain lasers and related applications.

Levitated Optomechanics with Meta-Atoms

We propose to introduce additional control in levitated optomechanics by trapping a meta-atom, i.e., a subwavelength and high-permittivity dielectric particle supporting Mie resonances. In particular, we theoretically demonstrate that optical levitation and center-of-mass ground-state cooling of silicon nanoparticles in vacuum is not only experimentally feasible but it offers enhanced performance over widely used silica particles in terms of trap frequency, trap depth, and optomechanical coupling rates. Moreover, we show that, by adjusting the detuning of the trapping laser with respect to the particle's resonance, the sign of the polarizability becomes negative, enabling levitation in the minimum of laser intensity, e.g., at the nodes of a standing wave. The latter opens the door to trapping nanoparticles in the optical near-field combining red and blue-detuned frequencies, in analogy to two-level atoms, which is of interest for generating strong coupling to photonic nanostructures and short-distance force sensing.

Theoretical Analysis and Experimental Verification of the Influence of Polarization on Counter-Propagating Optical Tweezers

Counter-propagating optical tweezers are experimental platforms for the frontier exploration of science and precision measurement. The polarization of the trapping beams significantly affects the trapping status. Using the T-matrix method, we numerically analyzed the optical force distribution and the resonant frequency of counter-propagating optical tweezers in different polarizations. We also verified the theoretical result by comparing it with the experimentally observed resonant frequency. Our analysis shows that polarization has little influence on the radial axis motion, while the axial axis force distribution and the resonant frequency are sensitive to polarization change. Our work can be used in designing harmonic oscillators which can change their stiffness conveniently, and monitoring polarization in counter-propagating optical tweezers.

Interaction between an Optically Levitated Nanoparticle and Its Thermal Image: Internal Thermometry via Displacement Sensing

We propose and theoretically analyze an experiment where displacement sensing of an optically levitated nanoparticle in front of a surface can be used to measure the induced dipole-dipole interaction between the nanoparticle and its thermal image. This is achieved by using a surface that is transparent to the trapping light but reflective to infrared radiation, with a reflectivity that can be time modulated. This dipole-dipole interaction relies on the thermal radiation emitted by a silica nanoparticle having sufficient temporal coherence to correlate the reflected radiation with the thermal fluctuations of the dipole. The resulting force is orders of magnitude stronger than the thermal gradient force, and it strongly depends on the internal temperature of the nanoparticle for a particle-to-surface distance greater than two micrometers. We argue that it is experimentally feasible to use displacement sensing of a levitated nanoparticle in front of a surface as an internal thermometer in ultrahigh vacuum. Experimental access to the internal physics of a levitated nanoparticle in vacuum is crucial to understanding the limitations that decoherence poses to current efforts devoted to preparing a nanoparticle in a macroscopic quantum superposition state.

An apparatus for in-vacuum loading of nanoparticles into an optical trap

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.

Observation and control of Casimir effects in a sphere-plate-sphere system

A remarkable prediction of quantum field theory is that there are quantum electromagnetic fluctuations (virtual photons) everywhere, which leads to the intriguing Casimir effect. While the Casimir force between two objects has been studied extensively for several decades, the Casimir force between three objects has not been measured yet. Here, we report the experimental demonstration of an object under the Casimir force exerted by two other objects simultaneously. Our Casimir system consists of a micrometer-thick cantilever placed in between two microspheres, forming a unique sphere-plate-sphere geometry. We also propose and demonstrate a three-terminal switchable architecture exploiting opto-mechanical Casimir interactions that can lay the foundations of a Casimir transistor. Beyond the paradigm of Casimir forces between two objects in different geometries, our Casimir transistor represents an important development for controlling three-body virtual photon interactions and will have potential applications in sensing and information processing.

Dipole moment background measurement and suppression for levitated charge sensors

Optically levitated macroscopic objects are a powerful tool in the field of force sensing, owing to high sensitivity, absolute force calibration, environmental isolation, and the advanced degree of control over their dynamics that have been achieved. However, limitations arise from the spurious forces caused by electrical polarization effects that, even for nominally neutral objects, affect the force sensing because of the interaction of dipole moments with gradients of external electric fields. Here, we introduce a technique to measure, model, and eliminate dipole moment interactions, limiting the performance of sensors using levitated objects. This process leads to a noise-limited measurement with a sensitivity of 3.3 × 10^-5 e. As a demonstration, this is applied to the search for unknown charges of a magnitude much below that of an electron or for exceedingly small unbalances between electron and proton charges.

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.

Searching for Chameleon Dark Energy with Mechanical Systems

A light scalar field framework of dark energy, sometimes referred to as quintessence, introduces a fifth force between normal matter objects. Screening mechanisms, such as the chameleon model, allow the scalar field to be almost massless on cosmological scales while simultaneously evading laboratory constraints. We explore the ability of existing mechanical systems to directly detect the fifth force associated with chameleons in an astrophysically viable regime where it could be dark energy. We provide analytical expressions for the weakest accessible chameleon model parameters in terms of experimentally tunable variables and apply our analysis to two mechanical systems: levitated microspheres and torsion balances, showing that the current generation of these experiments have the sensitivity to rule out a significant portion of the proposed chameleon parameter space. We also indicate regions of theoretically well-motivated chameleon parameter space to guide future experimental work.

Optical cold damping of neutral nanoparticles near the ground state in an optical lattice

We propose and demonstrate purely optical feedback cooling of neutral nanoparticles in an optical lattice to an occupation number of 0.85 ± 0.20. The cooling force is derived from the optical gradients of displaced optical lattices produced with two sidebands on the trapping laser. To achieve highly accurate position observations required for cooling near the ground state, we reduce the laser intensity noise to a relative power noise of 6×10^-8/Hz in a frequency band of 30 kHz to 600 kHz. We establish a reproducible method for neutralizing nanoparticles at high vacuum via a combination of discharging and irradiating an ultraviolet light. Our results form an important basis for the investigation of quantum mechanical properties of ultracold nanoparticles and are also useful for precision measurements with neutral nanoparticles.

A Chemical Nanoreactor Based on a Levitated Nanoparticle in Vacuum

A single levitated nanoparticle is used as a nanoreactor for studying surface chemistry at the nanoscale. Optical levitation under controlled pressure, surrounding gas composition, and humidity provides extreme control over the nanoparticle, including dynamics, charge, and surface chemistry. Using a single nanoparticle avoids ensemble averages and allows studying how the presence of silanol groups at its surface affects the adsorption and desorption of water from the background gas with excellent spatial and temporal resolution. Herein, we demonstrate the potential of this versatile platform by studying the Zhuravlev model in silica particles. In contrast to standard methods, our system allowed the observation of an abrupt and irreversible change in scattering cross section, mass, and mechanical eigenfrequency during the dehydroxylation process, indicating changes in density, refractive index, and volume.

Scanning force sensing at micrometer distances from a conductive surface with nanospheres in an optical lattice

The center-of-mass motion of optically trapped dielectric nanoparticles in a vacuum is extremely well decoupled from its environment, making a powerful tool for measurements of feeble subattonewton forces. We demonstrate a method to trap and maneuver nanoparticles in an optical standing wave potential formed by retroreflecting a laser beam from a metallic mirror surface. We can reliably position a ∼170nm diameter silica nanoparticle at distances of a few hundred nanometers to tens of micrometers from the surface of a gold-coated silicon mirror by transferring it from a single-beam tweezer trap into the standing wave potential. We can further measure forces experienced by the particle while scanning the two-dimensional space parallel to the mirror surface, and we find no significant excess force noise in the vicinity of the surface. This method may enable three-dimensional scanning force sensing near surfaces using optically trapped nanoparticles, promising for high-sensitivity scanning force microscopy, tests of the Casimir effect, and tests of the gravitational inverse square law at micrometer scales.

Searching for New Physics with a Levitated-Sensor-Based Gravitational-Wave Detector

The levitated sensor detector (LSD) is a compact resonant gravitational-wave (GW) detector based on optically trapped dielectric particles that is under construction. The LSD sensitivity has more favorable frequency scaling at high frequencies compared to laser interferometer detectors such as LIGO and VIRGO. We propose a method to substantially improve the sensitivity by optically levitating a multilayered stack of dielectric discs. These stacks allow the use of a more massive levitated object while exhibiting minimal photon recoil heating due to light scattering. Over an order of magnitude of unexplored frequency space for GWs above 10 kHz is accessible with an instrument 10 to 100 meters in size. Particularly motivated sources in this frequency range are gravitationally bound states of the axion from quantum chromodynamics with decay constant near the grand unified theory scale that form through black hole superradiance and annihilate to GWs. The LSD is also sensitive to GWs from binary coalescence of sub-solar-mass primordial black holes and as-yet unexplored new physics in the high-frequency GW window.

Numerical Analysis of Optical Trapping Force Affected by Lens Misalignments

Geometrical optics approximation is a classic method for calculating the optical trapping force on particles whose sizes are larger than the wavelength of the trapping light. In this study, the effect of the lens misalignment on optical force was analyzed in the geometrical optics regime. We used geometrical optics to analyze the influence of off-axis placement and the tilt of the lens on the trapping position and stiffness in an optical trap. Numerical calculation results showed that lens tilting has a greater impact on the optical trap force than the off-axis misalignments, and both misalignments will couple with each other and cause a shift of the equilibrium point and the asymmetry of the optical trap stiffness in different ways. Our research revealed the asymmetry in optical traps caused by lens misalignment and can provide guidance for optimize lens placement in future experiments.

Levitodynamics: Levitation and control of microscopic objects in vacuum

[Figure: see text].

Vibrational modes in an optically levitated droplet

Levitation by optical tweezers provides a unique non-invasive tool for investigating a microscale object without external perturbations. Here we experimentally levitate a micrometer-sized water droplet in the air using an optical tweezer. Meanwhile, vibrational modes of a levitated water droplet are excited by modulating the trapping laser. From their backscattered light, vibrational modes with mode numbers are observed in the spectra. Additionally, their corresponding free spectral ranges are analyzed and compared with theory and numerical simulations. This Letter, establishing a non-invasive and all-optical detection technique of optomechanical properties of levitated droplets, paves the way for their practical applications in aerosol and biomedical science.

Laser refrigeration of optically levitated sodium yttrium fluoride nanocrystals

Solid state laser refrigeration can cool optically levitated nanocrystals in an optical dipole trap, allowing for internal temperature control by mitigating photothermal heating. This work demonstrates cooling of ytterbium-doped cubic sodium yttrium fluoride nanocrystals to 252 K on average with the most effective crystal cooling to 241 K. The amount of cooling increases linearly with the intensity of the cooling laser and is dependent on the pressure of the gas surrounding the nanocrystal. Cooling optically levitated nanocrystals allows for crystals prone to heating to be studied at lower pressures than currently achievable and for temperature control and stabilization of trapped nanocrystals.

Optomechanical controlling of intermolecular interaction and the application in molecular self-assembly

In this paper, we combined cavity optomechanics and quantum mechanical mechanism of van der Waals force to study the dynamic behavior of interacting bimolecules in the plasmonic localized field, and extend it to the interacting multi-molecular system. We explored how plasmonic optomechanical coupling affects the strength of intermolecular interactions. Based on our results, we propose to use optical field to modulate the intermolecular interaction potential in plasmonic cavity, which can be utilized in the enhancement of the efficiency of the molecular self-assembly process and controlling the yield of the reaction in an optical environment. This research extends molecular optomechanics from intramolecular interactions to intermolecular interactions and may has high application potential in some nanostructure synthesis.

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.

Realization of a complete Stern-Gerlach interferometer: Toward a test of quantum gravity

The Stern-Gerlach effect, found a century ago, has become a paradigm of quantum mechanics. Unexpectedly, until recently, there has been little evidence that the original scheme with freely propagating atoms exposed to gradients from macroscopic magnets is a fully coherent quantum process. Several theoretical studies have explained why a Stern-Gerlach interferometer is a formidable challenge. Here, we provide a detailed account of the realization of a full-loop Stern-Gerlach interferometer for single atoms and use the acquired understanding to show how this setup may be used to realize an interferometer for macroscopic objects doped with a single spin. Such a realization would open the door to a new era of fundamental probes, including the realization of previously inaccessible tests at the interface of quantum mechanics and gravity.

Optimized anti-reflection core-shell microspheres for enhanced optical trapping by structured light beams

In this paper, we study the optical trapping of anti-reflection core-shell microspheres by regular Gaussian beam and several structured beams including radially polarized Gaussian, petal, and hard-aperture-truncated circular Airy beams. We show that using an appropriate anti-reflection core-shell microsphere for the optical trapping by several structured light beams can dramatically enhance the strength of the trap compared to the trapping by the common Gaussian beam. The optimal core-shell thickness ratio that minimizes the scattering force is obtained for polystyrene-silica and anatase-amorphous titania microspheres, such that the core-shells act as anti-reflection coated microspheres. We show that the trapping strength of the anti-reflection coated microparticles trapped by the common Gaussian beam is enhanced up to 2-fold compared to that of trapped uncoated microparticles, while the trapping of anti-reflection coated microparticles, by the radially polarized beam, is strengthened up to 4-fold in comparison to that of the trapped uncoated microparticles by the Gaussian beam. Our results indicate that for anatase-amorphous titania microparticles highest trap strength is obtained by radially polarized beam, while for the polystyrene-silica microparticles, the strongest trapping is achieved by the petal beam.

Detecting Acceleration-Enhanced Vacuum Fluctuations with Atoms Inside a Cavity

Some of the most prominent theoretical predictions of modern times, e.g., the Unruh effect, Hawking radiation, and gravity-assisted particle creation, are supported by from the fact that various quantum constructs like particle content and vacuum fluctuations of a quantum field are observer-dependent. Despite being fundamental in nature, these predictions have not yet been experimentally verified because one needs extremely strong gravity (or acceleration) to bring them within the existing experimental resolution. In this Letter, we demonstrate that a post-Newtonian rotating atom inside a far-detuned cavity experiences strongly modified quantum fluctuations in the inertial vacuum. As a result, the emission rate of an excited atom gets enhanced significantly along with a shift in the emission spectrum due to the change in the quantum correlation under rotation. We propose an optomechanical setup that is capable of realizing such acceleration-induced particle creation with current technology. This provides a novel and potentially feasible experimental proposal for the direct detection of noninertial quantum field theoretic effects.

Fine features of optical potential well induced by nonlinearity

Particles trapped by optical tweezers, behaving as mechanical oscillators in an optomechanical system, have found tremendous applications in various disciplines and are still arousing research interest in frontier and fundamental physics. These optically trapped oscillators provide compact particle confinement and strong oscillator stiffness. But these features are limited by the size of the focused light spot of a laser beam, which is typically restricted by the optical diffraction limit. Here, we propose to build an optical potential well with fine features assisted by the nonlinearity of the particle material, which is independent of the optical diffraction limit. We show that the potential well shape can have super-oscillation-like features and a Fano-resonance-like phenomenon, and the width of the optical trap is far below the diffraction limit. A particle with nonlinearity trapped by an ordinary optical beam provides a new platform with a sub-diffraction potential well and can have applications in high-accuracy optical manipulation and high-precision metrology.

High sensitivity, levitated microsphere apparatus for short-distance force measurements

A high sensitivity force sensor based on dielectric microspheres in vacuum, optically trapped by a single, upward-propagating laser beam, is described. Off-axis parabolic mirrors are used both to focus the 1064 nm trapping beam and to recollimate it to provide information on the horizontal position of the microsphere. The vertical degree of freedom is readout by forming an interferometer between the light retroreflected by the microsphere and a reference beam, hence eliminating the need for auxiliary beams. The focus of the trapping beam has a 1/E² radius of 3.2 µm and small non-Gaussian tails, suitable for bringing devices close to the trapped microsphere without disturbing the optical field. Electrodes surrounding the trapping region provide excellent control of the electric field, which can be used to drive the translational degrees of freedom of a charged microsphere and the rotational degrees of freedom of a neutral microsphere, coupling to its electric dipole moment. With this control, the charge state can be determined with single electron precision, the mass of individual microspheres can be measured, and empirical calibrations of the force sensitivity can be made for each microsphere. A force noise of <1 × 10^-17 N/Hz, which is comparable to previous reports, is measured on all three degrees of freedom for 4.7 µm diameter, 84 pg silica microspheres. Various devices have been brought within 1.6 µm of the surface of a trapped microsphere. Metrology in the trapping region is provided by two custom-designed microscopes providing views in the horizontal and one of the vertical planes. The apparatus opens the way to performing high sensitivity three-dimensional force measurements at a short distance.

Higher order correlations in a levitated nanoparticle phonon laser

We present theoretical and experimental investigations of higher order correlations of mechanical motion in the recently demonstrated optical tweezer phonon laser, consisting of a silica nanosphere trapped in vacuum by a tightly focused optical beam [R. M. Pettit et al., Nature Photonics 13, 402 (2019)]. The nanoparticle phonon number probability distribution is modeled with the master equation formalism in order to study its evolution across the lasing threshold. Up to fourth-order equal-time correlation functions are then derived from the probability distribution. Subsequently, the master equation is transformed into a nonlinear quantum Langevin equation for the trapped particle's position. This equation yields the non-equal-time correlations, also up to fourth order. Finally, we present experimental measurements of the phononic correlation functions, which are in good agreement with our theoretical predictions. We also compare the experimental data to existing analytical Ginzburg-Landau theory where we find only a partial match.

Optomechanics with levitated particles

Optomechanics is concerned with the use of light to control mechanical objects. As a field, it has been hugely successful in the production of precise and novel sensors, the development of low-dissipation nanomechanical devices, and the manipulation of quantum signals. Micro- and nano-particles levitated in optical fields act as nanoscale oscillators, making them excellent low-dissipation optomechanical objects, with minimal thermal contact to the environment when operating in vacuum. Levitated optomechanics is seen as the most promising route for studying high-mass quantum physics, with the promise of creating macroscopically separated superposition states at masses of 10⁶ amu and above. Optical feedback, both using active monitoring or the passive interaction with an optical cavity, can be used to cool the centre-of-mass of levitated nanoparticles well below 1 mK, paving the way to operation in the quantum regime. In addition, trapped mesoscopic particles are the paradigmatic system for studying nanoscale stochastic processes, and have already demonstrated their utility in state-of-the-art force sensing.

Cooling of a levitated nanoparticle to the motional quantum ground state

Quantum control of complex objects in the regime of large size and mass provides opportunities for sensing applications and tests of fundamental physics. The realization of such extreme quantum states of matter remains a major challenge. We demonstrate a quantum interface that combines optical trapping of solids with cavity-mediated light-matter interaction. Precise control over the frequency and position of the trap laser with respect to the optical cavity allowed us to laser-cool an optically trapped nanoparticle into its quantum ground state of motion from room temperature. The particle comprises 108 atoms, similar to current Bose-Einstein condensates, with the density of a solid object. Our cooling technique, in combination with optical trap manipulation, may enable otherwise unachievable superposition states involving large masses.

Motional Sideband Asymmetry of a Nanoparticle Optically Levitated in Free Space

The hallmark of quantum physics is Planck's constant h, whose finite value entails the quantization that gave the theory its name. The finite value of h gives rise to inevitable zero-point fluctuations even at vanishing temperature. The zero-point fluctuation of mechanical motion becomes smaller with growing mass of an object, making it challenging to observe at macroscopic scales. Here, we transition a dielectric particle with a diameter of 136 nm from the classical realm to the regime where its zero-point motion emerges as a sizable contribution to its energy. To this end, we optically trap the particle at ambient temperature in ultrahigh vacuum and apply active feedback cooling to its center-of-mass motion. We measure an asymmetry between the Stokes and anti-Stokes sidebands of photons scattered by the levitated particle, which is a signature of the particle's quantum ground state of motion.

Cold Damping of an Optically Levitated Nanoparticle to Microkelvin Temperatures

We implement a cold-damping scheme to cool one mode of the center-of-mass motion of an optically levitated nanoparticle in ultrahigh vacuum (10^{-8}  mbar) from room temperature to a record-low temperature of 100  μK. The measured temperature dependence on the feedback gain and thermal decoherence rate is in excellent agreement with a parameter-free model. For the first time, we determine the imprecision-backaction product for a levitated optomechanical system and discuss the resulting implications for ground-state cooling of an optically levitated nanoparticle.

Stochastic thermodynamics of nonharmonic oscillators in high vacuum

We perform an analytic study on the stochastic thermodynamics of a small classical particle trapped in a time-dependent single-well potential in the highly underdamped limit. It is shown that the nonequilibrium probability density function for the system's energy is a Maxwell-Boltzmann distribution (as in equilibrium) with a closed form time-dependent effective temperature and fractional degrees of freedom. We also find that the solvable model satisfies the Crooks fluctuation theorem, as expected. Moreover, we compute the average work in this isothermal process and characterize analytically the optimal protocol for minimum work. The optimal protocol presents an initial and a final jump which correspond to adiabatic processes linked by a smooth exponential time-dependent part for all kinds of single-well potentials. Furthermore, we argue that this result connects two distinct relevant experimental setups for trapped nanoparticles, the levitated particle in a harmonic trap, and the free particle in a box, as they are limiting cases of the general single-well potential and display the time-dependent optimal protocols. Finally, we highlight the connection between our system and an equivalent model of a gas of Brownian particles.

Precision ultrasound sensing on a chip

Ultrasound sensors have wide applications across science and technology. However, improved sensitivity is required for both miniaturisation and increased spatial resolution. Here, we introduce cavity optomechanical ultrasound sensing, where dual optical and mechanical resonances enhance the ultrasound signal. We achieve noise equivalent pressures of 8-300 μPa Hz-1/2 at kilohertz to megahertz frequencies in a microscale silicon-chip-based sensor with >120 dB dynamic range. The sensitivity far exceeds similar sensors that use an optical resonance alone and, normalised to the sensing area, surpasses previous air-coupled ultrasound sensors by several orders of magnitude. The noise floor is dominated by collisions from molecules in the gas within which the acoustic wave propagates. This approach to acoustic sensing could find applications ranging from biomedical diagnostics, to autonomous navigation, trace gas sensing, and scientific exploration of the metabolism-induced-vibrations of single cells.

More than two decades trapped

Optical tweezers, crowned by Nobel Prize the first time in 1990s, have widely impacted the research landscape of atom cooling, particle manipulation/sorting, and biology. After more than two decades of steady development, it received the deserving recognition once again in 2018. Unprecedented advancements across various disciplines are believed to be spurred furthermore by this important tool of optical manipulation.

Sensing Static Forces with Free-Falling Nanoparticles

Miniaturized mechanical sensors rely on resonant operation schemes, unsuited to detect static forces. We demonstrate a nanomechanical sensor for static forces based on an optically trapped nanoparticle in vacuum. Our technique relies on an off-resonant interaction of the particle with a weak static force, and a resonant readout of the displacement caused by this interaction. We demonstrate a sensitivity of 10 aN to static gravitational and electric forces. Our work provides a tool for the closer investigation of short-range forces, and marks an important step towards the realization of matter-wave interferometry with macroscopic objects.

Tests of chameleon gravity

Theories of modified gravity, where light scalars with non-trivial self-interactions and non-minimal couplings to matter-chameleon and symmetron theories-dynamically suppress deviations from general relativity in the solar system. On other scales, the environmental nature of the screening means that such scalars may be relevant. The highly-nonlinear nature of screening mechanisms means that they evade classical fifth-force searches, and there has been an intense effort towards designing new and novel tests to probe them, both in the laboratory and using astrophysical objects, and by reinterpreting existing datasets. The results of these searches are often presented using different parametrizations, which can make it difficult to compare constraints coming from different probes. The purpose of this review is to summarize the present state-of-the-art searches for screened scalars coupled to matter, and to translate the current bounds into a single parametrization to survey the state of the models. Presently, commonly studied chameleon models are well-constrained but less commonly studied models have large regions of parameter space that are still viable. Symmetron models are constrained well by astrophysical and laboratory tests, but there is a desert separating the two scales where the model is unconstrained. The coupling of chameleons to photons is tightly constrained but the symmetron coupling has yet to be explored. We also summarize the current bounds on f(R) models that exhibit the chameleon mechanism (Hu and Sawicki models). The simplest of these are well constrained by astrophysical probes, but there are currently few reported bounds for theories with higher powers of R. The review ends by discussing the future prospects for constraining screened modified gravity models further using upcoming and planned experiments.

Enhanced sensing of millicharged particles using nonlinear effects in an optomechanical system

Particles with electric charge 10^-14 e in bulk mass are not excluded by present experiments. In the present letter we provide a feasible scheme to measure the millicharged particles via the optical cavity coupled to a levitated nanosphere. The results show that the optical probe spectrum of the nano-oscillator presents a tiny shift due to the existence of millicharged particles. Compare to the previous experiment the sensitivity can be improved by the using of a specific geometry to generate an electric field gradient and a pump-probe scheme to read the weak frequency shift. Owing to the very narrow linewidth(10^-6 Hz) of the optical Kerr peak on the spectrum, this shift will be more obvious, which makes the millicharges more easy to be detectable. The technique proposed here paves the way for new applications for probing dark matter and nonzero charged neutrino in the condensed matter.

Elliptical orbits of microspheres in an evanescent field

We examine the motion of periodically driven and optically tweezed microspheres in fluid and find a rich variety of dynamic regimes. We demonstrate, in experiment and in theory, that mean particle motion in 2D is rarely parallel to the direction of the applied force and can even exhibit elliptical orbits with nonzero orbital angular momentum. The behavior is unique in that it depends neither on the nature of the microparticles nor that of the excitation; rather, angular momentum is introduced by the particle's interaction with the anisotropic fluid and optical trap environment. Overall, we find this motion to be highly tunable and predictable.

Search for Screened Interactions Associated with Dark Energy below the 100 μm Length Scale

We present the results of a search for unknown interactions that couple to mass between an optically levitated microsphere and a gold-coated silicon cantilever. The scale and geometry of the apparatus enable a search for new forces that appear at distances below 100  μm and which would have evaded previous searches due to screening mechanisms. The data are consistent with electrostatic backgrounds and place upper limits on the strength of new interactions at <0.1  fN in the geometry tested. For the specific example of a chameleon interaction with an inverse power law potential, these results exclude matter couplings β>5.6×10^{4} in the region of parameter space where the self-coupling Λ≳5  meV and the microspheres are not fully screened.

Electron spin control of optically levitated nanodiamonds in vacuum

Electron spins of diamond nitrogen-vacancy (NV) centres are important quantum resources for nanoscale sensing and quantum information. Combining NV spins with levitated optomechanical resonators will provide a hybrid quantum system for novel applications. Here we optically levitate a nanodiamond and demonstrate electron spin control of its built-in NV centres in low vacuum. We observe that the strength of electron spin resonance (ESR) is enhanced when the air pressure is reduced. To better understand this system, we investigate the effects of trap power and measure the absolute internal temperature of levitated nanodiamonds with ESR after calibration of the strain effect. We also observe that oxygen and helium gases have different effects on both the photoluminescence and the ESR contrast of nanodiamond NV centres, indicating potential applications of NV centres in oxygen gas sensing. Our results pave the way towards a levitated spin–optomechanical system for studying macroscopic quantum mechanics.

Hybrid systems coupling electron spins and optomechanical responses are of potential use in quantum information systems and sensing technology. Here, the authors demonstrate optical levitation of nanodiamonds and the control of their nitrogen vacancy spins in vacuum.

Subfemtonewton Force Spectroscopy at the Thermal Limit in Liquids

We demonstrate thermally limited force spectroscopy using a probe formed by a dielectric microsphere optically trapped in water near a dielectric surface. We achieve force resolution below 1 fN in 100 s, corresponding to a 2 Å rms displacement of the probe. Our measurement combines a calibrated evanescent wave particle tracking technique and a lock-in detection method. We demonstrate the accuracy of our method by measurement of the height-dependent force exerted on the probe by an evanescent wave, the results of which are in agreement with Mie theory calculations.

Measuring the charge density of a tapered optical fiber using trapped microparticles

We report the measurements of charge density of tapered optical fibers using charged particles confined in a linear Paul trap at ambient pressure. A tapered optical fiber is placed across the trap axis at a right angle, and polystyrene microparticles are trapped along the trap axis. The distance between the equilibrium position of a positively charged particle and the tapered fiber is used to estimate the amount of charge per unit length of the fiber without knowing the amount of charge of the trapped particle. The charge per unit length of a tapered fiber with a diameter of 1.6 μm was measured to be 2-1+3×10^-11 C/m.

Simultaneous cooling of coupled mechanical oscillators using whispering gallery mode resonances

We demonstrate simultaneous center-of-mass cooling of two coupled oscillators, consisting of a microsphere-cantilever and a tapered optical fiber. Excitation of a whispering gallery mode (WGM) of the microsphere, via the evanescent field of the taper, provides a transduction signal that continuously monitors the relative motion between these two microgram objects with a sensitivity of 3 pm. The cavity enhanced optical dipole force is used to provide feedback damping on the motion of the micron-diameter taper, whereas a piezo stack is used to damp the motion of the much larger (up to 180 μm in diameter), heavier (up to 1.5 × 10(-7) kg) and stiffer microsphere-cantilever. In each feedback scheme multiple mechanical modes of each oscillator can be cooled, and mode temperatures below 10 K are reached for the dominant mode, consistent with limits determined by the measurement noise of our system. This represents stabilization on the picometer level and is the first demonstration of using WGM resonances to cool the mechanical modes of both the WGM resonator and its coupling waveguide.

Cancellation of non-conservative scattering forces in optical traps by counter-propagating beams

Non-conservative forces in optical tweezers generate undesirable behavior, such as particle loss due to radiation pressure and the preclusion of the thermodynamic equilibrium. Here, we rigorously derive criteria for the elimination of non-conservative forces, and describe how these criteria can be met by a large class of counter-propagating, focused optical beams.

Cavity cooling a single charged levitated nanosphere

Optomechanical cavity cooling of levitated objects offers the possibility for laboratory investigation of the macroscopic quantum behavior of systems that are largely decoupled from their environment. However, experimental progress has been hindered by particle loss mechanisms, which have prevented levitation and cavity cooling in a vacuum. We overcome this problem with a new type of hybrid electro-optical trap formed from a Paul trap within a single-mode optical cavity. We demonstrate a factor of 100 cavity cooling of 400 nm diameter silica spheres trapped in vacuum. This paves the way for ground-state cooling in a smaller, higher finesse cavity, as we show that a novel feature of the hybrid trap is that the optomechanical cooling becomes actively driven by the Paul trap, even for singly charged nanospheres.

Search for millicharged particles using optically levitated microspheres

We report results from a search for stable particles with charge ≳10^{-5}e in bulk matter using levitated dielectric microspheres in high vacuum. No evidence for such particles was found in a total sample of 1.4 ng, providing an upper limit on the abundance per nucleon of 2.5×10^{-14} at the 95% confidence level for the material tested. These results provide the first direct search for single particles with charge ≲0.1e bound in macroscopic quantities of matter and demonstrate the ability to perform sensitive force measurements using optically levitated microspheres in vacuum.