Levitated optomechanics has great potential 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. This levitated nanodumbbell torsion balance is a novel analog of the Cavendish torsion balance, and provides rare opportunities to observe the Casimir torque and probe the quantum nature of gravity as proposed recently. With a circularly polarized laser, we drive a 170-nm-diameter nanodumbbell to rotate beyond 1 GHz, which is the fastest nanomechanical rotor realized to date. Smaller silica nanodumbbells can sustain higher rotation frequencies. Such ultrafast rotation may be used to study material properties and probe vacuum friction.

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 tensor. The torsional vibration frequency can be one order of magnitude higher than its center-of-mass motion frequency, which is promising for ground state cooling. We propose a simple yet novel scheme to achieve ground state cooling of its torsional vibration with a linearly-polarized Gaussian cavity mode. A levitated nonspherical nanoparticle in vacuum will also be an ultrasensitive nanoscale torsion balance with a torque detection sensitivity on the order of 10 −29 N · m/ √ Hz under realistic conditions. An optically levitated dielectric particle in vacuum [1][2][3] is an ultrasensitive detector for force sensing [4,5], millicharge searching [6] and other applications [7,8]. It will provide a great platform to test fundamental theories such as objective collapse models [9, 10] and quantum gravity [11] when its mechanical motion can be cooled to the quantum regime [12,13]. Recently, feedback cooling of the center-of-mass (COM) motion of a levitated nanosphere to about 450 µK (about 63 phonons at 150 kHz) [14], and cavity cooling of the COM motion of a nanosphere to a few mK [15] were demonstrated. The vibration mode would have already been in ground state at 450 µK [14] if its frequency is above 10 MHz. Increasing the vibration frequency of the nanoparticle can be a key to achieve ground state cooling. However, this can not be achieved by simply increasing the intensity of the trapping laser, which induces heating and subsequently causes the loss of the nanoparticle [4,16]. Besides COM motion, a pioneering work has proposed to use multiple Laguerre-Gaussian (LG) cavity modes to achieve angular trapping of a dielectric rod and cool its torsional vibration (TOR) to the ground state [12]. This was later generalized to micro-windmills [17], which have better overlap with LG cavity modes. These intriguing proposals of torsional optomechanics, however, have not been realized experimentally yet.In this work, we report the first experimental observation of the torsional vibration of an optically levitated nonspherical nanoparticle in vacuum, and show that the torsional frequency can be one order of magnitude higher than the COM frequency at the same laser intensity. We explain our observation using a model of an ellipsoidal nanoparticle levitated by a linearly-polarized Gaussian beam. For an ellipsoid much smaller than the wavelength of the trapping laser, its polarizability is a tensor due to its geometry [18]. In a linearly polariz...

Torque sensors such as the torsion balance enabled the first determination of the gravitational constant by Cavendish [1] and the discovery of Coulomb's law. Torque sensors are also widely used in studying small-scale magnetism [2,3], the Casimir effect [4], and other applications [5]. 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 Nm/ √Hz at millikelvin temperatures in a dilution refrigerator [6]. Here we dramatically improve the torque detection sensitivity by developing an ultrasensitive torque sensor with an optically levitated nanorotor in vacuum. We measure a torque as small as (1.2±0.5)×10 −27 Nm in 100 seconds at room temperature. Our system does not require complex nanofabrication or cryogenic cooling. Moreover, we drive a nanoparticle to rotate at a record high speed beyond 5 GHz (300 billion rpm). Our calculations show that this system will be able to detect the long-sought vacuum friction [7-10] near a surface under realistic conditions. The optically levitated nanorotor will also have applications in studying nanoscale magnetism [2,3] and quantum geometric phase [11].

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.

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 five-dimensional cooling of a levitated nanoparticle. We cool the three center-of-mass motion modes and two torsional vibration modes of a levitated nanodumbbell in a linearly polarized laser simultaneously. The only uncooled rigid-body degree of freedom is the rotation of the nanodumbbell around its long axis. This free rotation mode does not couple to the optical tweezers directly. Surprisingly, we observe that it strongly affects the torsional vibrations of the nanodumbbell. This work deepens our understanding of the nonlinear dynamics and rotation coupling of a levitated nanoparticle and paves the way towards full quantum control of its motion.

Nonequilibrium processes of small systems such as molecular machines are ubiquitous in biology, chemistry, and physics but are often challenging to comprehend. In the past two decades, several exact thermodynamic relations of nonequilibrium processes, collectively known as fluctuation theorems, have been discovered and provided critical insights. These fluctuation theorems are generalizations of the second law and can be unified by a differential fluctuation theorem. Here we perform the first experimental test of the differential fluctuation theorem using an optically levitated nanosphere in both underdamped and overdamped regimes and in both spatial and velocity spaces. We also test several theorems that can be obtained from it directly, including a generalized Jarzynski equality that is valid for arbitrary initial states, and the Hummer-Szabo relation. Our study experimentally verifies these fundamental theorems and initiates the experimental study of stochastic energetics with the instantaneous velocity measurement.

We present a microfluidic network-based combinatorial dilution device to generate on-demand combinatorial dilutions of all input samples in the range of a 3D simplex-centroid. The device consists of an initial concentration control module and a combinatorial dilution module. In the initial concentration control module, the concept of using a single common channel has been incorporated to generate desirable concentrations of each sample, diluted independently in response to variable input flow. Then, the diluted samples flow into the combinatorial dilution module to generate a full set of seven combinations from the three samples. First, we investigated the performance of the initial concentration controller by computational simulation (CFD-ACE ? ). The simulated output concentrations are extremely close to the expected theoretical values. Further, a PDMS-based initial concentration controller was fabricated, and its linearity and independency were tested with fluorescent dye. Then, we designed, simulated, and tested a combinatorial dilution device integrated with the initial concentration controller. Finally, as proof-of-concept, we performed a simple combinatorial cytotoxicity test with three drugs (Mitomycin C, Doxorubicin, and 5-FU) for MCF-7 cancer cells.

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