Fons van der Laan, René Reimann, Andrei Militaru, Felix Tebbenjohanns, Dominik Windey, Martin Frimmer, Lukas Novotny
Optically levitated rotors are prime candidates for torque sensors whose precision is limited by the fluctuationsof the rotation frequency. In this work we investigate an optically levitated rotor at its fundamental thermal limitof frequency stability, where rotation-frequency fluctuations arise solely due to coupling to the thermal bath.
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Optically levitated gyroscopes with a MHz rotating micro-rotor
本文提出基于光悬浮MHz旋转球霰石微粒的转子陀螺仪，利用旋转信号检测光轴在外加角速度下的偏移，实验实现0.08°/s零偏不稳定性，并指出理论可提升至10^-9°/h。
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.
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 …
Collective-motion-enhanced acceleration sensing via an optically levitated microsphere array
提出基于光悬浮微球阵列的加速度传感方案，利用集体模式与腔耦合编码加速度信息，相比单微球方案灵敏度提升√N倍。
Driven Dissipation and Stabilization of a Levitated Rotor with Multi-Day Coherence
通过磁流体悬浮石英立方体实现非线性多模式耗散与注入锁定样稳定化，揭示低耗散悬浮固体中的新动力学行为。
A nitrogen-vacancy (NV$^-$) center in a nanodiamond, levitated in high vacuum, has recently been proposed as a probe for demonstrating mesoscopic center-of-mass superpositions \cite{Scala2013, Zhang2013} and for testing quantum gravity \cite{Albrecht2014}. Here, we study the behavior of optically levitated nanodiamonds containing NV$^-$ centers at sub-atmospheric pressures and show that while they burn in air, this can be prevented by replacing the air with nitrogen. However, in nitrogen the nanodiamonds graphitize below $\approx 10$ mB. Exploiting the Brownian motion of a levitated nanodiamon…
Optimal Position Detection of an Optically Levitated Mie Particle
本文提出信息辐射场概念并据此设计光悬浮米氏粒子位置的最优探测方案，证明高数值孔径后向探测足以通过冷却三维质心运动达到量子基态。
According to quantum theory, measurement and backaction are inextricably linked. In optical position measurements, this backaction is known as radiation pressure shot noise. In analogy, a measurement of the orientation of a mechanical rotor must disturb its angular momentum by radiation torque shot noise. In this work, we observe the shot-noise torque fluctuations arising in a measurement of the angular orientation of an optically levitated nanodumbbell. We feedback cool the dumbbell's rotational motion and investigate its reheating behavior when released from feedback. In high vacuum, the hea…
Levitated optomechanics has great potentials in precision measurements, thermodynamics, macroscopic quantum mechanics and quantum sensing. Here we synthesize and optically levitate silica nanodumbbells in high vacuum. With a linearly polarized laser, we observe the torsional vibration of an optically levitated nanodumbbell in vacuum. The linearly-polarized optical tweezer provides a restoring torque to confine the orientation of the nanodumbbell, in analog to the torsion wire which provides restoring torque for suspended lead spheres in the Cavendish torsion balance. Our calculation shows its …
Feedback cooling scheme for an optically levitated oscillator with controlled cross-talk
本文提出一种用于光学悬浮振子的3D速度反馈冷却方案，通过最小化交叉干扰实现对三个平动自由度的独立控制与冷却。
Second-harmonic generation from an optically levitated KTP nanocrystal in vacuum
研究在真空中光悬浮磷酸钛氧钾（KTP）纳米晶体并探究其二次谐波产生特性，利用光悬浮系统的高信噪比环境，激光既用于悬浮又作基波，证明光扭矩可控制纳米晶体取向，为真空非线性光学研究开辟新途径。
Understanding thermal induced escape mechanism of optically levitated sphere in vacuum
针对真空中光悬浮球受热逃逸问题，本文建立并实验验证非平衡动力学模型，阐明热致光泳放大布朗运动的逃逸机制。
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 …
We report on the electrically driven rotation of $2.4~μ$m-radius, optically levitated dielectric microspheres. Electric fields are used to apply torques to a microsphere's permanent electric dipole moment, while angular displacement is measured by detecting the change in polarization state of light transmitted through the microsphere (MS). This technique enables greater control than previously achieved with purely optical means because the direction and magnitude of the electric torque can be set arbitrarily. We measure the spin-down of a microsphere released from a rotating electric field, th…
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 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 w…
Enhanced optomechanical coupling between an optically levitated particle and an ultrahigh Q optical microcavity
提出一种结合光学镊子与超高Q环形微腔的平台，通过近场耦合实现单光子光机械耦合50倍增强，为悬浮介观粒子的量子实验铺路。
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…
PT Symmetry, induced mechanical lasing and tunable force sensing in a coupled-mode optically levitated nanoparticle
本研究从理论上探究光学悬浮耦合模纳米颗粒的PT对称特性，证实非对称光学势调制可实现PT对称机械行为与诱导机械激射，并可构建可调谐超灵敏力传感，推进了悬浮振荡器相干操控及传感应用研究。
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…
Simultaneous cooling of all six degrees of freedom of an optically levitated nanoparticle by elliptic coherent scattering
该研究利用高精细度光学腔中的椭圆相干散射，实现了高真空光镊悬浮纳米粒子全部六个平动与转动自由度的同时冷却和取向控制。
An Optomechanical Coin Flip: Wavelength-Modulated, Erbium-Powered Rotations in a Levitated System
本研究通过调节泵浦光波长，在光学悬浮的掺铒六方柱体中实现二进制旋转控制，并编码ASCII信息，观察到类似季尼别克效应的双模动态。
The linear momentum and angular momentum of virtual photons of quantum vacuum fluctuations can induce the Casimir force and the Casimir torque, respectively. While the Casimir force has been measured extensively, the Casimir torque has not been observed experimentally though it was predicted over forty years ago. Here we propose to detect the Casimir torque with an optically levitated nanorod near a birefringent plate in vacuum. The axis of the nanorod tends to align with the polarization direction of the linearly polarized optical tweezer. When its axis is not parallel or perpendicular to the…
Forces and torques exerted on dielectric disks trapped in a Gaussian standing wave are analyzed theoretically for disks of radius $2~μ\text{m}$ with index of refraction $n=1.45$ and $n=2.0$ as well as disks of radius 200 nm with $n=1.45$. Calculations of the forces and torques were conducted both analytically and numerically using a discrete-dipole approximation method. Besides harmonic terms, third order ro-translational coupling terms in the potential energy can be significant and a necessary consideration when describing the dynamics of disks outside of the Rayleigh limit. The coupling term…
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 …
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…
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 x $10^{-14}$ at the 95% confidence level for the material tested. These results provide the first direct search for single particles with charge < 0.1 e bound in macroscopic quantities of matter and demonstrate the ability to perform sensitive force measurements using optically levitated microspheres in vacuum.
Trap-to-trap free falls with an optically levitated nanoparticle
本文利用可快速开关和垂直移动的光镊，实现了电荷中性纳米粒子的自由下落与再捕获，观测到位置不确定度增大近两百倍，并提出通过线性反馈和超高真空实现毫秒级自由下落，以推动悬浮物体的大尺度离域化研究。
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.
Electron spins of diamond nitrogen-vacancy (NV) centers 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 centers 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 temper…
Mass and Shape Determination of Optically Levitated Nanoparticles
本文结合基于电荷的质量测量、光散射形状测定与阻尼率各向异性分析，首次在真空中利用光镊捕获同一组硅石纳米颗粒，实现了对其质量与形状的同步区分，为精密测量和传感实验奠定基础。
We present the first evidence of nitrogen vacancy (NV) photoluminescence from a nanodiamond suspended in a free-space optical dipole trap at atmospheric pressure. The photoluminescence rates are shown to decrease with increasing trap laser power, but are inconsistent with a thermal quenching process. For a continuous-wave trap, the neutral charge state (NV$^0$) appears to be suppressed. Chopping the trap laser yields higher total count rates and results in a mixture of both NV$^0$ and the negative charge state (NV$^-$).
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 …
Cold damping of levitated optically coupled nanoparticles
研究展示了对光结合力耦合的一对纳米粒子的简正模进行独立或同时冷阻尼，使其在5x10^{-3} mbar下降至亚开尔文温度，为介观量子相互作用和多粒子纠缠研究开辟了道路。
We describe a variety of searches for new physics beyond the Standard Model of particle physics which may be enabled in the coming years by the use of optically levitated masses in high vacuum. Such systems are expected to reach force and acceleration sensitivities approaching (and possibly eventually exceeding) the standard quantum limit over the next decade. For new forces or phenomena that couple to mass, high precision sensing using objects with masses in the fg-ng range have significant discovery potential for new physics. Such applications include tests of fundamental force laws, searche…
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…
Torque sensors such as the torsion balance enabled the first determination of the gravitational constant by Cavendish and the discovery of Coulomb's law. Torque sensors are also widely used in studying small-scale magnetism, the Casimir effect, and other applications. Great effort has been made to improve the torque detection sensitivity by nanofabrication and cryogenic cooling. The most sensitive nanofabricated torque sensor has achieved a remarkable sensitivity of $10^{-24} \rm{Nm}/\sqrt{\rm{Hz}}$ at millikelvin temperatures in a dilution refrigerator. Here we dramatically improve the torque…
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…
This paper demonstrates cooling of the center-of-mass motion of 10 $μ$m-diameter optically levitated silica spheres to an effective temperature of $50\pm22 μ$K, achieved by minimizing the technical pointing noise of the trapping laser. This low noise leads to an acceleration and force sensitivity of $95\pm41$ n$g/\sqrt{\mathrm{Hz}}$ ($g = 9.8$ m/s$^2$) and $0.95\pm0.11$ aN$/\sqrt{\mathrm{Hz}}$, respectively, at frequencies near 50 Hz. This force sensitivity is comparable to that demonstrated for optically levitated nanospheres that are $10^4$ times less massive, corresponding to an acceleratio…
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 review recent works on optomechanics of optically trapped microspheres and nanoparticles in vacuum, which provide an ideal system for studying macroscopic quantum mechanics and ultrasensitive force detection. An optically trapped particle in vacuum has an ultrahigh mechanical quality factor as it is well-isolated from the thermal environment. Its oscillation frequency can be tuned in real time by changing the power of the trapping laser. Furthermore, an optically trapped particle in vacuum may rotate freely, a unique property that does not exist in clamped mechanical oscillators. In this re…
Observation of strong and tunable light-induced dipole-dipole interactions between optically levitated nanoparticles
本研究在光学悬浮纳米粒子阵列中观测到强且可调的光诱导偶极-偶极相互作用，其源于光场相位相干性，并可通过偏振控制实现静电耦合，为可编程多体系统奠定基础。
Nanomechanical resonator based on levitated particle exhibits unique advantages in the development of ultrasensitive electric field detector. We demonstrate a three-dimensional, high-sensitivity electric field measurement technology using the optically levitated nanoparticle with a known net charge. By changing the relative position between nanoparticle and parallel electrodes, the three-dimensional electric field distribution is scanned. The measured noise equivalent electric intensity with charge amount of 100 reaches the order of {\rm{1μV/cm/H}}{\rm{z}^{\rm{1/2}}} at 1.4 \times {10^{ - 7}}m…
We report on the injection locking of an optically levitated nanomechanical oscillator (a silica nanosphere) to resonant intensity modulations of an external optical signal. We explore the characteristic features of injection locking in this system, e.g. the phase pull-in effect and the injection-induced reduction of the oscillation linewidth. Our measurements are in good agreement with theoretical predictions and deepen the analogy of injection locking in levitated optomechanical systems to that in optical systems (lasers). By measuring the force noise of our feedback cooled free-running osci…
We report on the use of 4.7-$μ$m-diameter, optically levitated, charged microspheres to image the three-dimensional force field produced by charge distributions on an Au-coated, microfabricated Si beam in vacuum. An upward-propagating, single-beam optical trap, combined with an interferometric imaging technique, provides optimal access to the microspheres for microscopy. In this demonstration, the Au-coated surface of the Si beam can be brought as close as ${\sim}10~μ$m from the center of the microsphere while forces are simultaneously measured along all three orthogonal axes, fully mapping th…
Optomechanical systems are suitable for elucidating quantum phenomena at the macroscopic scale in the sense of the mass scale. The systems should be well-isolated from the environment to avoid classical noises, which conceal quantum signals. Optical levitation is a promising way to isolate optomechanical systems from the environment. To realize optical levitation, all degrees of freedom need to be trapped. Until now, longitudinal trapping and rotational trapping of a mirror with optical radiation pressure have been studied in detail and validated with various experiments. However, less attenti…
The ability to trap and to manipulate individual atoms is at the heart of current implementations of quantum simulations, quantum computing, and long-distance quantum communication. Controlling the motion of larger particles opens up yet new avenues for quantum science, both for the study of fundamental quantum phenomena in the context of matter wave interference, and for new sensing and transduction applications in the context of quantum optomechanics. Specifically, it has been suggested that cavity cooling of a single nanoparticle in high vacuum allows for the generation of quantum states of…
Optically Levitated Nanoparticles as Receiving Antennas for Low Frequency Wireless Communication
提出基于光学悬浮纳米颗粒的低频接收天线原型，克服传统天线尺寸限制，实验验证其有效性与低误码率。
We propose a tunable resonant sensor to detect gravitational waves in the frequency range of 50-300 kHz using optically trapped and cooled dielectric microspheres or micro-discs. The technique we describe can exceed the sensitivity of laser-based gravitational wave observatories in this frequency range, using an instrument of only a few percent of their size. Such a device extends the search volume for gravitational wave sources above 100 kHz by 1 to 3 orders of magnitude, and could detect monochromatic gravitational radiation from the annihilation of QCD axions in the cloud they form around s…
Near-field GHz rotation and sensing with an optically levitated nanodumbbell
本文在真空中光学悬浮近表面二氧化硅纳米哑铃，实现 GHz 旋转、高灵敏扭矩检测及超衍射近场强度探测，并展示检测 Casimir 扭矩的潜力。
Sensing microscopic directional noise baths with an optically cooled and levitated nanoparticle
本研究利用悬浮纳米粒子传感器，通过互相关功率谱检测定向随机微观力，实现无校准的力方向测量，并探讨了向量子领域扩展的可能性。
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 report on a search for non-Newtonian forces that couple to mass, with a characteristic scale of ${\sim}10~μ$m, using an optically levitated microsphere as a precision force sensor. A silica microsphere trapped in an upward-propagating, single-beam, optical tweezer is utilized to probe for interactions sourced from a nanofabricated attractor mass with a density modulation brought into close proximity to the microsphere and driven along the axis of periodic density in order to excite an oscillating response. We obtain force sensitivity of ${\lesssim}10^{-16}~\rm{N}/\sqrt{\rm{Hz}}$. Separately…
Optimal displacement detection of arbitrarily-shaped levitated dielectric objects using optical radiation
提出基于Fisher信息的方法，实现任意形状悬浮介电物体的最优位移检测，并通过与球形粒子方法对比验证，分析了高纵横比盘状和棒状物体的检测极限。
The non-conservative, azimuthal forces associated with inhomogeneous optical-spin angular momentum play a critical role in optical trapping. Intriguingly, birefringent microspheres can be stably levitated and rapidly rotated in circularly polarized optical traps in ultra-high vacuum whereas isotropic spheres are typically destabilized and expelled, even at relatively modest pressures. Here we show that the resolution of this apparent key paradox rests in the form of the orientationally averaged, effective forces acting on the spinning birefringent particle. In particular, the effective azimuth…
Optomechanics of optically-levitated particles: A tutorial and perspective
本文以教程形式综述光悬浮粒子光力学的关键概念、实验与理论方法及当前研究进展，并展望新兴实验平台与未来理论发展方向，为初学者提供入门参考。
Nanomechanical devices have attracted the interest of a growing interdisciplinary research community, since they can be used as highly sensitive transducers for various physical quantities. Exquisite control over these systems facilitates experiments on the foundations of physics. Here, we demonstrate that an optically trapped silicon nanorod, set into rotation at MHz frequencies, can be locked to an external clock, transducing the properties of the time standard to the rod's motion with the remarkable frequency stability $f_{\rm r}/Δf_{\rm r}$ of $7.7 \times 10^{11}$. While the dynamics of th…
Spinning a levitated mechanical oscillator far into the deep-strong coupling regime
本研究实现了光悬浮纳米哑铃绕长轴的1 GHz以上受控旋转，达成耦合速率超裸振动频率两个数量级的深度强耦合，为相关量子物理研究与量子技术应用奠基，且展现纳米陀螺仪应用潜力。
Optomagnetic forces on YIG/YFeO3 microspheres levitated in chiral hollow-core photonic crystal fibre
本研究利用手性空芯光子晶体光纤悬浮YIG/YFeO3微球，通过光学扭矩诱导其旋转和磁化矢量变化，探索磁光物理新现象。
We experimentally squeeze the thermal motional state of an optically levitated nanosphere, by fast switching between two trapping frequencies. The measured phase space distribution of our particle shows the typical shape of a squeezed thermal state, from which we infer up to 2.7dB of squeezing along one motional direction. The experiment features a large number of thermal excitations, therefore remaining in the classical regime. Nevertheless, we argue that the manipulation scheme described here could be used to achieve squeezing below the zero-point level, if preceded by ground state cooling o…
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