Optically levitated nano-objects in vacuum are amongst the highest-quality mechanical oscillators, and thus of great interest for force sensing, cavity quantum optomechanics, and nanothermodynamic studies. These precision applications require exquisite control. Here, we present full control over the rotational and translational dynamics of an optically levitated silicon nanorod. We trap its centre-ofmass and align it along the linear polarization of the laser field. The rod can be set into rotation at a predefined frequency by exploiting the radiation pressure exerted by elliptically polarized light. The rotational motion of the rod dynamically modifies the optical potential, which allows tuning of the rotational frequency over hundreds of Kilohertz. Through nanofabrication, we can tailor all of the trapping frequencies and the optical torque, achieving reproducible dynamics which are stable over months, and analytically predict the motion with great accuracy. This first demonstration of full ro-translational control of nanoparticles in vacuum opens up the fields of rotational optomechanics, rotational ground state cooling and the study of rotational thermodynamics in the underdamped regime.

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 a remarkable frequency stability f r/Δf r of 7.7 × 1011. While the dynamics of this periodically driven rotor generally can be chaotic, we derive and verify that stable limit cycles exist over a surprisingly wide parameter range. This robustness should enable, in principle, measurements of external torques with sensitivities better than 0.25 zNm, even at room temperature. We show that in a dilute gas, real-time phase measurements on the locked nanorod transduce pressure values with a sensitivity of 0.3%.

We study the interaction of dielectric rods and disks with the laser field of a high finesse cavity. The quantum master equation for the coupled particle-cavity dynamics, including Rayleigh scattering, is derived for particle sizes comparable to the laser wavelength. We demonstrate that such anisotropic nanoparticles can be captured from free flight at velocities higher than those required to capture dielectric spheres of the same volume, and that efficient ro-translational cavity cooling into the deep quantum regime is achievable.

Whether quantum physics is universally valid is an open question with far-reaching implications. Intense research is therefore invested into testing the quantum superposition principle with ever heavier and more complex objects. Here we propose a radically new, experimentally viable route towards studies at the quantum-to-classical borderline by probing the orientational quantum revivals of a nanoscale rigid rotor. The proposed interference experiment testifies a macroscopic superposition of all possible orientations. It requires no diffraction grating, uses only a single levitated particle, and works with moderate motional temperatures under realistic environmental conditions. The first exploitation of quantum rotations of a massive object opens the door to new tests of quantum physics with submicron particles and to quantum gyroscopic torque sensors, holding the potential to improve state-of-the-art devices by many orders of magnitude.

Optical control of nanoscale objects has recently developed into a thriving field of research with far-reaching promises for precision measurements, fundamental quantum physics and studies on single-particle thermodynamics. Here, we demonstrate the optical manipulation of silicon nanorods in high vacuum. Initially, we sculpture these particles into a silicon substrate with a tailored geometry to facilitate their launch into high vacuum by laser-induced mechanical cleavage. We manipulate and trace their center-of-mass and rotational motion through the interaction with an intense intracavity field. Our experiments show that the anisotropy of the nanorotors leads to optical forces that are three times stronger than on silicon nanospheres of the same mass. The optical torque experienced by the spinning rods will enable cooling of the rotational motion and torsional optomechanics in a dissipation-free environment.

We introduce and discuss the one-dimensional Lévy crystal as a probable candidate for an experimentally accessible realization of space-fractional quantum mechanics (SFQM) in a condensed-matter environment. The discretization of the space-fractional Schrödinger equation with the help of shifted Grünwald-Letnikov derivatives delivers a straightforward route to define the Lévy crystal of order αε(1,2]. As key ingredients for its experimental identification we study the dispersion relation as well as the density of states for arbitrary αε(1,2]. It is demonstrated that in the limit of small wave numbers all interesting properties of continuous-space SFQM are recovered, while for α→2 the well-established nearest-neighbor one-dimensional tight-binding chain arises.

We show how charged levitated nano-and micro-particles can be cooled by interfacing them with an RLC circuit. All-electrical levitation and cooling is applicable to a wide range of particle sizes and materials, and will enable state-ofthe-art force sensing within an electrically networked system. Exploring the cooling limits in the presence of realistic noise we find that the quantum regime of particle motion can be reached in cryogenic environments both for passive resistive cooling and for an active feedback scheme, paving the way to levitated quantum electromechanics. arXiv:1802.05928v3 [quant-ph]

Motivated by trapping and cooling experiments with non-spherical nanoparticles, we discuss how their combined rotational and translational quantum state is affected by the interaction with a gaseous environment. Based on the quantum master equation in terms of orientation-dependent scattering amplitudes, we evaluate the localization rate for gas collisions off an anisotropic van der Waals-type potential and for photon scattering off an anisotropic dielectric. We also show how pure angular momentum diffusion arises from these open quantum dynamics in the limit of weak anisotropies.