Levitated Optomechanics Research Articles

Hybrid Paul-optical trap with large optical access for levitated optomechanics

We present a hybrid trapping platform that allows us to levitate a charged nanoparticle in high vacuum using either optical fields, radio-frequency fields, or a combination thereof. Our hybrid approach combines an optical dipole trap with a linear Paul trap while maintaining a large numerical aperture (0.77 NA). We detail a controlled transfer procedure that allows us to use the Paul trap as a “safety net” to recover particles lost from the optical trap at high vacuum. The presented hybrid platform adds to the toolbox of levitodynamics and represents an important step towards fully controllable “dark” potentials, providing control in the absence of decoherence because of photon recoil. Published by the American Physical Society 2024

An on-demand source of nanoparticles for optomechanics

The generation of nanoparticles on demand, with good control over their size and shape, has been a challenge for nanotechnology and the rapidly growing field of levitated optomechanics. Here, we present the preparation, launch, and detection of single nanoparticles in both a buffer gas and in vacuum. A tightly focused ultrashort laser beam with low energy is used to melt, form, and release individual particles. Surface tension supports the creation of spherical particles from molten droplets whose radii can be controlled, here in the range r=80−200 nm, by varying the pulse energy. The particle source is compact and compatible with high vacuum. It can be applied equally to dielectrics and metals as demonstrated here for silicon and gold. The method is unique in its capability to generate pristine silicon spheres directly in vacuum, which would rapidly oxidize when formed in air. Silicon is of interest for levitated optomechanics, cavity cooling, and emerging quantum interference experiments because of its high infrared polarizability and its low work function. Combining the source with an infrared cavity, we characterize the launch velocity and transit dynamics for silicon and gold nanoparticles in a high-finesse cavity field.

Mechanical Detection of Nuclear Decays.

We report the detection of individual nuclear α decays through the mechanical recoil of the entire micron-sized particle in which the decaying nuclei are embedded. Momentum conservation ensures that such measurements are sensitive to any particles emitted in the decay, including neutral particles that may otherwise evade detection with existing techniques. Detection of the minuscule recoil of an object more than 10^{12} times more massive than the emitted particles is made possible by recently developed techniques in levitated optomechanics, which enable high-precision optical control and measurement of the mechanical motion of optically trapped particles. Observation of a change in the net charge of the particle coincident with the recoil allows decays to be identified with background levels at the micro-Becquerel level. The techniques developed here may find use in fields ranging from nuclear forensics to dark matter and neutrino physics.

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.

Cavity-mediated long-range interactions in levitated optomechanics

AbstractThe ability to engineer cavity-mediated interactions has emerged as a powerful tool for the generation of non-local correlations and the investigation of non-equilibrium phenomena in many-body systems. Levitated optomechanical systems have recently entered the multiparticle regime, which promises the use of arrays of strongly coupled massive oscillators to explore complex interacting systems and sensing. Here we demonstrate programmable cavity-mediated interactions between nanoparticles in vacuum by combining advances in multiparticle optical levitation and cavity-based quantum control. The interaction is mediated by photons scattered by spatially separated particles in a cavity, resulting in strong coupling that is long-range in nature. We investigate the scaling of the interaction strength with cavity detuning and interparticle separation and demonstrate the tunability of interactions between different mechanical modes. Our work will enable the exploration of many-body effects in nanoparticle arrays with programmable cavity-mediated interactions, generating entanglement of motion, and the use of interacting particle arrays for optomechanical sensing.

Sensing directional noise baths in levitated optomechanics

Optomechanical devices are being harnessed as sensors of ultraweak forces for applications ranging from inertial sensing to the search for the elusive dark matter. For the latter, there is a focus on detection of either higher energy single recoils or ultralight, narrow-band sources; a directional signal is expected. However, the possibility of searching for a stochastic stream of weak impulses, or more generally a directional broadband signal, need not be excluded; with this and other applications in mind, we apply Gaussian white noise impulses with a well defined direction Ψ to a levitated nanosphere trapped and 3D cooled in an optical tweezer. We find that cross-correlation power spectra offer a calibration-free distinctive signature of the presence of a directional broadband force and its orientation quadrant, unlike normal power spectral densities (PSDs). We obtain excellent agreement between theoretical and experimental results. With calibration we are able to measure the angle Ψ, akin to a force compass in a plane. We discuss prospects for extending this technique into the quantum regime and compare the expected behavior of quantum baths and classical baths. Published by the American Physical Society 2024

Synchronization of spin-driven limit cycle oscillators optically levitated in vacuum

We explore, experimentally and theoretically, the emergence of coherent coupled oscillations and synchronization between a pair of non-Hermitian, stochastic, opto-mechanical oscillators, levitated in vacuum. Each oscillator consists of a polystyrene microsphere trapped in a circularly polarized, counter-propagating Gaussian laser beam. Non-conservative, azimuthal forces, deriving from inhomogeneous optical spin, push the micro-particles out of thermodynamic equilibrium. For modest optical powers each particle shows a tendency towards orbital circulation. Initially, their stochastic motion is weakly correlated. As the power is increased, the tendency towards orbital circulation strengthens and the motion of the particles becomes highly correlated. Eventually, centripetal forces overcome optical gradient forces and the oscillators undergo a collective Hopf bifurcation. For laser powers exceeding this threshold, a pair of limit cycles appear, which synchronize due to weak optical and hydrodynamic interactions. In principle, arrays of such Non-Hermitian elements can be arranged, paving the way for opto-mechanical topological materials or, possibly, classical time crystals. In addition, the preparation of synchronized states in levitated optomechanics could lead to new and robust sensors or alternative routes to the entanglement of macroscopic objects.

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.

Nonlinear multi-frequency phonon lasers with active levitated optomechanics

Phonon lasers, which exploit coherent amplifications of phonons, are a means to explore nonlinear phononics, image nanomaterial structures and operate phononic devices. Recently, a phonon laser governed by dispersive optomechanical coupling has been demonstrated by levitating a nanosphere in an optical tweezer. Such levitated optomechanical devices, with minimal noise in high vacuum, can allow flexible control of large-mass objects without any internal discrete energy levels. However, it is challenging to achieve phonon lasing with levitated microscale objects because optical scattering losses are much larger than at the nanoscale. Here we report a nonlinear multi-frequency phonon laser with a micro-size sphere, which is governed by dissipative coupling. The active gain provided by a Yb3+-doped system plays a key role. It achieves three orders of magnitude for the amplitude of the fundamental-mode phonon lasing, compared with the passive device. In addition, nonlinear mechanical harmonics can emerge spontaneously above the lasing threshold. Furthermore, we observe coherent correlations of phonons for both the fundamental mode and its harmonics. Our work drives the field of levitated optomechanics into a regime where it becomes feasible to engineer collective motional properties of typical micro-size objects.

Controlling mode orientations and frequencies in levitated cavity optomechanics

The $x$-$y$ motion of a nanosphere levitated in a tweezer trap in a cavity has applications as a quantum sensor for the direction of ultraweak external forces. The backaction of the optical field of the cavity rotates the orientation of the $x$-$y$ modes. An experimental demonstration shows the accurate measurement, control, and even suppression of the change in orientation relative to the lab frame.

Dry launching of silica nanoparticles in vacuum

Clean loading of silica nanoparticles with a radius as small as ∼50 nm is required for experiments in levitated optomechanics that operate in ultra-high vacuum. We present a cheap and simple experimental method for dry launching of silica nanoparticles by shaking from a polytetrafluoroethylene surface (PTFE). We report on the successful launching of single silica nanoparticles with a minimum radius of 43 nm, which is enabled by the low stiction to the launching surface. Nanoparticles with radii of 43 and 71.5 nm are launched with a high flux and small spread. The measured velocities are significantly smaller than 1 m/s. The demonstrated launching method allows for controlled loading of dry nanoparticles with radii as small as 43 nm into optical traps in (ultra-)high vacuum, although we anticipate that loading of smaller sizes is equally feasible.

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 107g, which is sufficient to overcome stiction forces between glass nanoparticles and a glass substrate for particles as small as 170nm in diameter. Particles with sizes ranging from 170nm to ∼10μm have been successfully loaded into optical traps at pressures ranging from 1bar to 0.6mbar. 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 of high-order imaginary Poynting momentum optomechanics in structured light

The imaginary Poynting momentum (IPM) of light has been captivated as an unusual origin of optical forces. However, the IPM force is predicted only for dipolar magnetoelectric particles that are hardly used in optical manipulation experiments. Here, we report a whole family of high-order IPM forces for not only magnetoelectric but also generic Mie particles, assisted with their excited higher multipoles within. Such optomechanical manifestations derive from a nonlocal contribution of the IPM to the optical force, which can be remarkable even when the incident IPM is small. We observe the high-order optomechanics in a structured light beam, which, despite carrying no angular momentum, is able to set normal microparticles into continuous rotation. Our results provide unambiguous evidence of the ponderomotive nature of the IPM, expand the classification of optical forces, and open new possibilities for levitated optomechanics and micromanipulations.

Levitated optomechanics: From single to many-body physics

The levitated optomechanics, because of its ultra-high mechanical Q > 1010, is considered to be one of the best testbeds for macroscopic quantum superpostions. In this perspective, we give a brief review on the development of the levitated optomechanics, focusing on the macroscopic quantum phenomena, and the applications in quantum precision measurement. The levitated nanodiamond with built-in nitrogen-vacancy centers is discussed as an example. Finally, we discuss the future dirctions of the levtated optomechanics, such as the space-based experiments, the arrays of levitated optomechanics and applications in quantum simulation.

All-optical sub-Kelvin sympathetic cooling of a levitated microsphere in vacuum

We demonstrate all-optical sympathetic cooling of a laser-trapped microsphere to sub-Kelvin temperatures, mediated by optical binding to a feedback-cooled adjacent particle. Our study opens prospects for multi-particle quantum entanglement and sensing in levitated optomechanics.

Mechanical Squeezing via Unstable Dynamics in a Microcavity.

We theoretically show that strong mechanical quantum squeezing in a linear optomechanical system can be rapidly generated through the dynamical instability reached in the far red-detuned and ultrastrong coupling regime. We show that this mechanism, which harnesses unstable multimode quantum dynamics, is particularly suited to levitated optomechanics, and we argue for its feasibility for the case of a levitated nanoparticle coupled to a microcavity via coherent scattering. We predict that for submillimeter-sized cavities the particle motion, initially thermal and well above its ground state, becomes mechanically squeezed by tens of decibels on a microsecond timescale. Our results bring forth optical microcavities in the unresolved sideband regime as powerful mechanical squeezers for levitated nanoparticles, and hence as key tools for quantum-enhanced inertial and force sensing.

Position measurement of a dipolar scatterer via self-homodyne detection

We describe a technique to measure the position of a dipolar scatterer based on self-homodyne detection of the scattered light. The method can theoretically reach the Heisenberg limit, at which information gained about the position is constrained only by the back-action of the scattered light. The technique has applications in the fields of levitated optomechanics and trapped ions and is generally applicable to the position determination of confined light scatterers.

Control and measurement of electric dipole moments in levitated optomechanics

Levitated optomechanical systems are rapidly becoming leading tools for precision sensing, enabling a high level of control over the sensor's center of mass motion, rotation and electric charge state. Higher-order multipole moments in the charge distribution, however, remain a major source of backgrounds. By applying controlled precessive torques to the dipole moment of a levitated microsphere in vacuum, we demonstrate cancellation of dipole-induced backgrounds by 2 orders of magnitude. We measure the dipole moments of ng-mass spheres and determine their scaling with sphere size, finding that the dominant torques arise from induced dipole moments related to dielectric-loss properties of the SiO$_2$ spheres. Control of multipole moments in the charge distribution of levitated sensors is a key requirement to sufficiently reduce background sources in future applications.

Stroboscopic high-order nonlinearity for quantum optomechanics

High-order quantum nonlinearity is an important prerequisite for the advanced quantum technology leading to universal quantum processing with large information capacity of continuous variables. Levitated optomechanics, a field where motion of dielectric particles is driven by precisely controlled tweezer beams, is capable of attaining the required nonlinearity via engineered potential landscapes of mechanical motion. Importantly, to achieve nonlinear quantum effects, the evolution caused by the free motion of mechanics and thermal decoherence have to be suppressed. For this purpose, we devise a method of stroboscopic application of a highly nonlinear potential to a mechanical oscillator that leads to the motional quantum non-Gaussian states exhibiting nonclassical negative Wigner function and squeezing of a nonlinear combination of mechanical quadratures. We test the method numerically by analyzing highly instable cubic potential with relevant experimental parameters of the levitated optomechanics, prove its feasibility within reach, and propose an experimental test. The method paves a road for experiments instantaneously transforming a ground state of mechanical oscillators to applicable nonclassical states by nonlinear optical force.

Coherent-scattering two-dimensional cooling in levitated cavity optomechanics

The strong light-matter optomechanical coupling offered by Coherent Scattering (CS) set-ups have allowed the experimental realisation of quantum ground state cavity cooling of the axial motion of a levitated nanoparticle [U. Deli\'{c} et al., Science 367, 892 (2020)]. An appealing milestone is now quantum 2D cooling of the full in-plane motion, in any direction in the transverse plane. By a simple adjustment of the trap polarisation, one obtains two nearly equivalent modes, with similar frequencies $\omega_{x}\sim\omega_{y}$ and optomechanical couplings $g_{x}\simeq g_{y}$ -- in this experimental configuration we identify an optimal trap ellipticity, nanosphere size and cavity linewidth which allows for efficient 2D cooling. Moreover, we find that 2D cooling to occupancies $n_{x}+n_{y}\lesssim1$ at moderate vacuum ($10^{-6}$ mbar) is possible in a "Goldilocks" zone bounded by $\sqrt{\kappa\Gamma/4}\lesssim g_{x},g_{y}\lesssim|\omega_{x}-\omega_{y}|\lesssim\kappa$, where one balances the need to suppress dark modes whilst avoiding far-detuning of either mode or low cooperativities, and $\kappa$ ($\Gamma$) is the cavity decay rate (motional heating rate). With strong-coupling regimes $g_{x},g_{y}\gtrsim\kappa$ in view one must consider the genuine three-way hybridisation between $x$, $y$ and the cavity light mode resulting in hybridized bright/dark modes. Finally, we show that bright/dark modes in the levitated set-up have a simple geometrical interpretation, related by rotations in the transverse plane, with implications for directional sensing.