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...
Hybrid spin-mechanical systems have great potentials in sensing, macroscopic quantum mechanics, and quantum information science. In order to induce strong coupling between an electron spin and the center-of-mass motion of a mechanical oscillator, a large magnetic gradient is usually required, which is difficult to achieve. Here we show that strong coupling between the electron spin of a nitrogen-vacancy (NV) center and the torsional vibration of an optically levitated nanodiamond can be achieved in a uniform magnetic field. Thanks to the uniform magnetic field, multiple spins can strongly couple to the torsional vibration at the same time. We propose to utilize this new coupling mechanism to realize the Lipkin-Meshkov-Glick (LMG) model by an ensemble of NV centers in a levitated nanodiamond. The quantum phase transition in the LMG model and finite number effects can be observed with this system. We also propose to generate torsional superposition states and realize torsional matter-wave interferometry with spin-torsional coupling.
Abstract. Closing the terrestrial water budget is necessary to providing consistent estimates of budget components for understanding water resources and changes over time. Given the lack of in-situ observations of budget components at anything but local scale, merging information from multiple data sources (e.g. in-situ observation, satellite remote sensing, land surface model and reanalysis) through data assimilation techniques that optimize the estimation of fluxes is a promising approach. In this study, a systematic method is developed to optimally combine multiple available data sources for precipitation (P), evapotranspiration (ET), runoff (R) and the total water storage change (TWSC) at 0.5° spatial resolution globally and to obtain water budget closure (i.e. to enforce P − ET − R − TWSC = 0) through a Constrained Kalman Filter (CKF) data assimilation technique. The resulting long-term (1984–2010), monthly, 0.5° resolution global terrestrial water cycle Climate Data Record (CDR) dataset is developed under the auspices of the National Aeronautics and Space Administration (NASA) Earth System Data Records (ESDRs) program. This dataset serves to bridge the gap between sparsely gauged regions and the regions with sufficient in-situ observations in investigating the temporal and spatial variability in the terrestrial hydrology at multiple scales. The CDR created in this study is validated against in-situ measurements like river discharge from the Global Runoff Data Centre (GRDC) and the United States Geological Survey (USGS) and ET from FLUXNET. The dataset is shown to be reliable and can serve the scientific community in understanding historical climate variability in water cycle fluxes and stores, benchmarking the current climate, and validating models.
We use the concept of entropy power to derive a one-parameter class of information-theoretic uncertainty relations for pairs of conjugate observables in an infinite-dimensional Hilbert space. This class constitutes an infinite tower of higher-order statistics uncertainty relations, which allows one in principle to determine the shape of the underlying information-distribution function by measuring the relevant entropy powers. We illustrate the capability of this class by discussing two examples: superpositions of vacuum and squeezed states and the Cauchy-type heavy-tailed wave function.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.