Dancing in the Light: Nearly 200 years ago, the botanist Robert Brown noted that pollen particles floating on a liquid displayed a random motion, jittering under the microscope as if the particles were alive. In 1905, Albert Einstein described this Brownian motion in terms of statistical thermodynamics. Now, Li et al. (p. 1673 , published online 20 May) use a single, optically trapped silica bead to probe the dynamics of Brownian motion, measuring the predicted instantaneous velocity of the particle and verifying the short-time-scale behavior predicted a century ago. As well as testing fundamental principles of physics, the technique also has practical implications for cooling particles to ultralow temperatures.

Microscale resonators cooled so that their vibrational motion approaches the quantum limit enable the study of quantum effects in macroscopic systems. An approach that could probe the interface between quantum mechanics and general relativity is now demonstrated by using lasers to suspend a glass microsphere in a vacuum. Cooling of micromechanical resonators towards the quantum mechanical ground state in their centre-of-mass motion has advanced rapidly in recent years1,2,3,4,5,6,7,8. This work is an important step towards the creation of ‘Schrödinger cats’, quantum superpositions of macroscopic observables, and the study of their destruction by decoherence. Here we report optical trapping of glass microspheres in vacuum with high oscillation frequencies, and cooling of the centre-of-mass motion from room temperature to a minimum temperature of about 1.5 mK. This new system eliminates the physical contact inherent to clamped cantilevers, and can allow ground-state cooling from room temperature9,10,11,12,13,14,15. More importantly, the optical trap can be switched off, allowing a microsphere to undergo free-fall in vacuum after cooling15. This is ideal for studying the gravitational state reduction16,17,18,19, a manifestation of the apparent conflict between general relativity and quantum mechanics16,20. A cooled optically trapped object in vacuum can also be used to search for non-Newtonian gravity forces at small scales21, measure the impact of a single air molecule14 and even produce Schrödinger cats of living organisms9.

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.

We demonstrate both theoretically and experimentally nonparaxial Mathieu and Weber accelerating beams, generalizing the concept of previously found accelerating beams. We show that such beams bend into large angles along circular, elliptical, or parabolic trajectories but still retain nondiffracting and self-healing capabilities. The circular nonparaxial accelerating beams can be considered as a special case of the Mathieu accelerating beams, while an Airy beam is only a special case of the Weber beams at the paraxial limit. Not only do generalized nonparaxial accelerating beams open up many possibilities of beam engineering for applications, but the fundamental concept developed here can be applied to other linear wave systems in nature, ranging from electromagnetic and elastic waves to matter waves.

The conductance of metallic graphene nanoribbons (GNRs) with single defects and weak disorder at their edges is investigated in a tight-binding model. We find that a single edge defect will induce quasilocalized states and consequently cause zero-conductance dips. The center energies and breadths of such dips are strongly dependent on the geometry of GNRs. Armchair GNRs are more sensitive to a vacancy than zigzag GNRs, but are less sensitive to a weak scatter. More importantly, we find that with a weak disorder, zigzag GNRs will change from metallic to semiconducting due to Anderson localization. However, a weak disorder only slightly affects the conductance of armchair GNRs.