Brownian motion of particles affects many branches of science. We report on the Brownian motion of micrometer-sized beads of glass held in air by an optical tweezer, over a wide range of pressures, and we measured the instantaneous velocity of a Brownian particle. Our results provide direct verification of the energy equipartition theorem for a Brownian particle. For short times, the ballistic regime of Brownian motion was observed, in contrast to the usual diffusive regime. We discuss the applications of these methods toward cooling the center-of-mass motion of a bead in vacuum to the quantum ground motional state.

The apparent conflict between general relativity and quantum mechanics remains one of the unresolved mysteries of the physical world. According to recent theories, this conflict results in gravity-induced quantum state reduction of "Schr\"odinger cats", quantum superpositions of macroscopic observables. In recent years, great progress has been made in cooling micromechanical resonators towards their quantum mechanical ground state. This work is an important step towards the creation of Schr\"odinger cats in the laboratory, and the study of their destruction by decoherence. A direct test of the gravity-induced state reduction scenario may therefore be within reach. However, a recent analysis shows that for all systems reported to date, quantum superpositions are destroyed by environmental decoherence long before gravitational state reduction takes effect. Here we report optical trapping of glass microspheres in vacuum with high oscillation frequencies, and cooling of the center-of-mass motion from room temperature to a minimum temperature of 1.5 mK. This new system eliminates the physical contact inherent to clamped cantilevers, and can allow ground-state cooling from room temperature. After cooling, the optical trap can be switched off, allowing a microsphere to undergo free-fall in vacuum. During free-fall, light scattering and other sources of environmental decoherence are absent, so this system is ideal for studying gravitational state reduction. A cooled optically trapped object in vacuum can also be used to search for non-Newtonian gravity forces at small scales, measure the impact of a single air molecule, and even produce Schr\"odinger cats of living organisms.Comment: 18 pages, 4 figures, references update

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...

We propose a method to generate and detect large quantum superposition states and arbitrary Fock states for the oscillational mode of an optically levitated nanocrystal diamond. The nonlinear interaction required for the generation of non-Gaussian quantum states is enabled through the spin-mechanical coupling with a built-in nitrogen-vacancy center inside the nanodiamond. The proposed method allows the generation of large superpositions of nanoparticles with millions of atoms and the observation of the associated spatial quantum interference under reasonable experimental conditions.