The momentum transfer between a photon and an object defines a fundamental limit for the precision with which the object can be measured. If the object oscillates at a frequency $Ω_0$, this measurement back-action adds quanta $\hbarΩ_0$ to the oscillator's energy at a rate $Γ_{\rm recoil}$, a process called photon recoil heating, and sets bounds to quantum coherence times in cavity optomechanical systems. Here, we use an optically levitated nanoparticle in ultrahigh vacuum to directly measure $Γ_{\rm recoil}$. By means of a phase-sensitive feedback scheme, we cool the harmonic motion of the nanoparticle from ambient to micro-Kelvin temperatures and measure its reheating rate under the influence of the radiation field. The recoil heating rate is measured for different particle sizes and for different excitation powers, without the need for cavity optics or cryogenic environments. The measurements are in quantitative agreement with theoretical predictions and provide valuable guidance for the realization of quantum ground-state cooling protocols and the measurement of ultrasmall forces
Optically levitated nanoparticles in vacuum are a promising model system to test physics beyond our current understanding of quantum mechanics. Such experimental tests require extreme control over the dephasing of the levitated particle's motion. If the nanoparticle carries a finite net charge, it experiences a random Coulomb force due to fluctuating electric fields. This dephasing mechanism can be fully excluded by discharging the levitated particle. Here, we present a simple and reliable technique to control the charge on an optically levitated nanoparticle in vacuum. Our method is based on …
We implement a cold damping scheme to cool one mode of the center-of-mass motion of an optically levitated nanoparticle in ultrahigh vacuum from room temperature to a record-low temperature of 100 micro-Kelvin. The measured temperature dependence on feedback gain and thermal decoherence rate is in excellent agreement with a parameter-free model. We determine the imprecision-backaction product for our system and provide a roadmap towards ground-state cooling of optically levitated nanoparticles.
The controllable positioning of a vacuum-levitated object near a material surface is of importance for studying short-range forces, such as Casimir forces, interfacial friction forces, or gravity in yet unexplored parameter regimes. Here we optically levitate a nanoparticle in a laser beam strongly focused on a dielectric membrane. By investigating the motion of the trapped particle in vacuum, we map the position-dependent optical potential of the particle. We interferometrically measure the distance between the particle and the surface and demonstrate stable trapping in sub-wavelength proximi…
Internal Temperature and Center-of-Mass Dynamics of a Levitated Nanoparticle: A Simulator
Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales（布宜诺斯艾利斯大学，理学院）；CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA)（阿根廷国家科学研究委员会-布宜诺斯艾利斯大学，布宜诺斯艾利斯物理研究所）
Imaging-based detection of the motion of the levitated nanoparticles complements a widely-used interferometric detection method, providing a precise and robust way to estimate the position of the particle. Here, we show the camera-based feedback cooling of a charged nanoparticle levitated in a linear Paul trap. A charged nanoparticle levitated in a vacuum was observed by CMOS camera systems. The nanoparticle images were processed in realtime with a microcontroller integrated with a CMOS image sensor. The phase-delayed position signal was fed-back to one of the trap electrodes resulting in the …
The motion control of a levitated nanoparticle plays a central role in optical levitation for fundamental studies and practical applications. Here, we presented a digital parametric feedback cooling based on switching between two trapping laser intensity levels with square wave modulations. The effects of modulation depth and modulation signal phase on the cooling result were investigated in detail. With such a digital parametric feedback method, the centre-of-mass temperature of all three motional degrees of freedom can be cooled to dozens of milli-Kelvin, which paved the way to fully control…
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 sizeable contribution to its energy. To this end, we optically …
Cooling the center-of-mass motion of levitated nanoparticles provides a route to quantum experiments at mesoscopic scales. Here we demonstrate three-dimensional sympathetic cooling and detection of the center-of-mass motion of a levitated silica nanoparticle. The nanoparticle is electrostatically coupled to a feedback-cooled particle while both particles are trapped in the same Paul trap. We identify two regimes, based on the strength of the cooling: in the first regime, the sympathetically cooled particle thermalizes with the directly cooled one, while in the second regime, the sympatheticall…
Interferometric position detection of levitated particles is crucial for the centre-of-mass (CM) motion cooling and manipulation of levitated particles. In combination with balanced detection and feedback cooling, this system has provided picometer scale position sensitivity, zeptonewton force detection, and sub-millikelvin CM temperatures. In this article, we develop an analytical model of this detection system and compare its performance with experimental results allowing us to explain the presence of spurious frequencies in the spectra.
Optically levitated nanoparticles offer enormous potential for precision sensing. However, as for any other metrology device, the absolute measurement performance of a levitated-particle sensor is limited by the accuracy of the calibration relating the measured signal to an absolute displacement of the particle. Here, we suggest and demonstrate calibration protocols for levitated-nanoparticle sensors. Our calibration procedures include the treatment of anharmonicities in the trapping potential, as well as a protocol using a harmonic driving force, which is applicable if the sensor is coupled t…
We experimentally study the interference of dipole scattered light from two optically levitated nanoparticles in vacuum, which present an environment free of particle-substrate interactions. We illuminate the two trapped nanoparticles with a linearly polarized probe beam orthogonal to the propagation of the trapping laser beams. The scattered light from the nanoparticles are collected by a high numerical aperture (NA) objective lens and imaged. The interference fringes from the scattered vector light for the different dipole orientations in image and Fourier space are observed. Especially, the…
The center-of-mass motion of a single optically levitated nanoparticle resembles three uncoupled harmonic oscillators. We show how a suitable modulation of the optical trapping potential can give rise to a coupling between two of these oscillators, such that their dynamics are governed by a classical equation of motion that resembles the Schrödinger equation for a two-level system. Based on experimental data, we illustrate the dynamics of this parametrically coupled system both in the frequency and in the time domain. We discuss the limitations and differences of the mechanical analogue in com…
Coherent scattering of photons is a novel mechanism of optomechanical coupling for optically levitated nanoparticles promising strong, versatile interactions with light and between nanoparticles. We show that it allows efficient deterministic generation of Gaussian entanglement between two particles in separate tweezers. A combination of red- and blue-detuned tweezers brings a mechanical Bogoliubov mode to its ground state. An additional, dispersively coupled cavity mode can reduce noise in the orthogonal mode, resulting in strong entanglement as quantified by the logarithmic negativity and ve…
We develop a theory for cavity cooling of the center-of-mass motion of a levitated nanoparticle through coherent scattering into an optical cavity. We analytically determine the full coupled Hamiltonian for the nanoparticle, cavity, and free electromagnetic field. By tracing out the latter, we obtain a Master Equation for the cavity and the center of mass motion, where the decoherence rates ascribed to recoil heating, gas pressure, and trap displacement noise are calculated explicitly. Then, we benchmark our model by reproducing published experimental results for three-dimensional cooling. Fin…
Optically levitated nanoparticles have recently emerged as versatile platforms for investigating macroscopic quantum mechanics and enabling ultrasensitive metrology. In this article we theoretically consider two damping regimes of an optically levitated nanoparticle cooled by cavityless parametric feedback. Our treatment is based on a generalized Fokker-Planck equation derived from the quantum master equation presented recently and shown to agree very well with experiment [1]. For low damping, we find that the resulting Wigner function yields the single-peaked oscillator position distribution …
Levitated optomechanics is showing potential for precise force measurements. Here, we report a case study, to show experimentally the capacity of such a force sensor. Using an electric field as a tool to detect a Coulomb force applied onto a levitated nanosphere. We experimentally observe the spatial displacement of up to 6.6 nm of the levitated nanosphere by imposing a DC field. We further apply an AC field and demonstrate resonant enhancement of force sensing when a driving frequency, $ω_{AC}$, and the frequency of the levitated mechanical oscillator, $ω_0$, converge. We directly measure a f…
Quantum measurements of mechanical systems can produce optical squeezing via ponderomotive forces. Its observation requires high environmental isolation and efficient detection, typically achieved by using optical cavities and cryogenic cooling. Here we realize these conditions by measuring the position of an optically levitated nanoparticle at room temperature and without the overhead of an optical cavity. We use a fast heterodyne detection to reconstruct simultaneously orthogonal optical quadratures, and observe a noise reduction of $9\%\pm0.5\%$ below shot noise. Our experiment offers a nov…
We use an optimal control protocol to cool one mode of the center of mass motion of an optically levitated nanoparticle. The feedback technique relies on exerting a Coulomb force on a charged particle with a pair of electrodes and follows the control law of a linear quadratic regulator, whose gains are optimized by a machine learning algorithm in under 5 s. With a simpler and more robust setup than optical feedback schemes, we achieve a minimum center of mass temperature of 5 mK at $3\times 10^{-7}$ mbar and transients 10 to 600 times faster than cold damping. This cooling technique can be eas…
We investigate the influence of laser phase noise heating on resolved sideband cooling in the context of cooling the center-of-mass motion of a levitated nanoparticle in a high-finesse cavity. Although phase noise heating is not a fundamental physical constraint, the regime where it becomes the main limitation in Levitodynamics has so far been unexplored and hence embodies from this point forward the main obstacle in reaching the motional ground state of levitated mesoscopic objects with resolved sideband cooling. We reach minimal center-of-mass temperatures comparable to $T_{min}=10$mK at a p…
The interaction of an object with its surrounding bath can lead to a coupling between the object's internal degrees of freedom and its center-of-mass motion. This coupling is especially important for nanomechanical oscillators, which are amongst the most promising systems for preparing macroscopic objects in quantum mechanical states. Here we exploit this coupling to derive the internal temperature of a levitated nanoparticle from measurements of its center-of-mass dynamics. For a laser-trapped silica particle in high vacuum we find an internal temperature of $1000(60)\,\mathrm{K}$. The measur…
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 f…
An optically levitated nanoparticle in vacuum is a paradigm optomechanical system for sensing and studying macroscopic quantum mechanics. While its center-of-mass motion has been investigated intensively, its torsional vibration has only been studied theoretically in limited cases. Here we report the first experimental observation of the torsional vibration of an optically levitated nonspherical nanoparticle in vacuum. We achieve this by utilizing the coupling between the spin angular momentum of photons and the torsional vibration of a nonspherical nanoparticle whose polarizability is a tenso…
We demonstrate that a Kalman filter applied to estimate the position of an optically levitated nanoparticle, and operated in real-time within a Field Programmable Gate Array (FPGA), is sufficient to perform closed-loop parametric feedback cooling of the centre of mass motion to sub-Kelvin temperatures. The translational centre of mass motion along the optical axis of the trapped nanoparticle has been cooled by three orders of magnitude, from a temperature of 300K to a temperature of 162 +/- 15mK.
Local sensing of gas microflows using a levitated nanoparticle
University of Vienna（维也纳大学）；German Aerospace Center (DLR)（德国航空航天中心）；Duke University（杜克大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；The University of Melbourne（墨尔本大学）；California Institute of Technology（加州理工学院）
All three motional modes of a charged dielectric nanoparticle in a Paul trap are cooled by direct feedback to temperatures of a few mK. We test two methods, one based on electrical forces and the other on optical forces; for both methods, we find similar cooling efficiencies. Cooling is characterized for both feedback forces as a function of feedback parameters, background pressure, and the particle's position.
Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work paves the way for …
Counterintuitively, experiments show that an electromagnetically levitated particle escapes from its trap when the ambient pressure is reduced below a certain level even if the particle's motion is cooled by a resonator-based or feedback-based mechanism. Here, we theoretically show that the ambient pressure must be kept well above a critical value arising from gradient force fluctuations (viz., fluctuations in part of the EM force whose Hamiltonian is quadratic in the position of the particle). Also, we consider other force fluctuations, and determine whether different realizations of feedback…
Accurate delivery of small targets in high vacuum is a pivotal task in many branches of science and technology. Beyond the different strategies developed for atoms, proteins, macroscopic clusters and pellets, the manipulation of neutral particles over macroscopic distances still poses a formidable challenge. Here we report a novel approach based on a mobile optical trap operated under feedback control that enables long range 3D manipulation of a silica nanoparticle in high vacuum. We apply this technique to load a single nanoparticle into a high-finesse optical cavity through a load-lock vacuu…
The field of levitodynamics has made significant progress towards controlling and studying the motion of a levitated nanoparticle. Motional control relies on either autonomous feedback via a cavity or measurement-based feedback via external forces. Recent demonstrations of measurement-based ground-state cooling of a single nanoparticle employ linear velocity feedback, also called cold damping, and require the use of electrostatic forces on charged particles via external electrodes. Here we introduce a novel all-optical cold damping scheme based on spatial modulation of the trap position that i…
Quantum control of levitated dielectric particles is an emerging subject in quantum optomechanics. A major challenge is to efficiently measure and manipulate the particle's motion at the Heisenberg uncertainty limit. Here we present a nanophotonic interface suited to address this problem. By optically trapping a 150 nm silica particle and placing it in the near field of a photonic crystal cavity, we achieve tunable single-photon optomechanical coupling of up to $g_0/2π=9$ kHz, three orders of magnitude larger than previously reported for levitated cavity optomechanical systems. Efficient colle…
We experimentally observe the dipole scattering of a nanoparticle using a high numerical aperture (NA) imaging system. The optically levitated nanoparticle provides an environment free of particle-substrate interaction. We illuminate the silica nanoparticle in vacuum with a 532 nm laser beam orthogonally to the propagation direction of the 1064 nm trapping laser beam strongly focused by the same high NA objective used to collect the scattering, which results in a dark background and high signal-noise ratio. The dipole orientations of the nanoparticle induced by the linear polarization of the i…
We experimentally realize cavity cooling of all three translational degrees of motion of a levitated nanoparticle in vacuum. The particle is trapped by a cavity-independent optical tweezer and coherently scatters tweezer light into the blue detuned cavity mode. For vacuum pressures around $10^{-5}\,{\rm mbar}$, minimal temperatures along the cavity axis in the mK regime are observed. Simultaneously, the center-of-mass (COM) motion along the other two spatial directions is cooled to minimal temperatures of a few hundred $\rm mK$. Measuring temperatures and damping rates as the pressure is varie…
We report an experimental observation of a record-breaking ultra-high rotation frequency about 6 GHz in an optically levitated nanoparticle system. We optically trap a nanoparticle in the gravity direction with a high numerical aperture (NA) objective lens, which shows significant advantages in compensating the influences of the scattering force and the photophoretic force on the trap, especially at intermediate pressure (about 100 Pa). This allows us to trap a nanoparticle from atmospheric to low pressure ($10^{-3}$ Pa) without using feedback cooling. We measure a highest rotation frequency a…
Interferometric methods for detecting the motion of a levitated nanoparticle provide a route to the quantum ground state, but such methods are currently limited by mode mismatch between the reference beam and the dipolar field scattered by the particle. Here we demonstrate a self-interference method to detect the particle's motion that solves this problem. A Paul trap confines a charged dielectric nanoparticle in high vacuum, and a mirror retro-reflects the scattered light. We measure the particle's motion with a sensitivity of $1.7\times 10^{-12} \text{m}/\sqrt{\text{Hz}}$, corresponding to a…
Optically levitated nonspherical particles in vacuum are excellent candidates for torque sensing, rotational quantum mechanics, high-frequency gravitational wave detection, and multiple other applications. Many potential applications, such as detecting the Casimir torque near a birefringent surface, require simultaneous cooling of both the center-of-mass motion and the torsional vibration (or rotation) of a nonspherical nanoparticle. Here we report the first 5D cooling of a levitated nanoparticle. We cool the 3 center-of-mass motion modes and 2 torsional vibration modes of a levitated nanodumb…
Optomechanical systems explore and exploit the coupling between light and the mechanical motion of matter. A nonlinear coupling offers access to rich new physics, in both the quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising of a nanosphere levitated and cooled in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere to millikelvin temperatures for indefinite pe…
Strong coupling and dark modes in the motion of a pair of levitated nanoparticles
CNR-INO（意大利国家研究委员会红外光学研究所）；Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze（佛罗伦萨大学物理与天文系）；INFN, Sezione di Firenze（意大利国家核物理研究所佛罗伦萨分部）；European Laboratory for Non-Linear Spectroscopy (LENS)（欧洲非线性光谱学实验室）
