Tongcang Li

Measurement of the Instantaneous Velocity of a Brownian Particle

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. An optically trapped silica bead in solution is used to probe assumptions underlying statistical theories of Brownian motion. 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.

Millikelvin cooling of an optically trapped microsphere in vacuum

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 ‘Schrodinger 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 Schrodinger cats of living organisms9.

Nonparaxial Mathieu and Weber accelerating beams.

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.

Generation of linear and nonlinear nonparaxial accelerating beams

We study linear and nonlinear self-accelerating beams propagating along circular trajectories beyond the paraxial approximation. Such nonparaxial accelerating beams are exact solutions of the Helmholtz equation, preserving their shapes during propagation even under nonlinearity. We generate experimentally and observe directly these large-angle bending beams in colloidal suspensions of polystyrene nanoparticles.

Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial

The propagation of microwaves through a chiral metamaterial based on a magnetic dimer is experimentally studied. As proposed by our previous theoretical model, two resonance peaks are obtained in the transmission spectrum; these originate from the hybridization effect of magnetic resonance modes in this system. Optical activity is also observed in the transmission wave. The polarization state dramatically changes around the resonance frequency: the transmitted wave becomes elliptically polarized with its major polarization axis approximately perpendicular to that of the linear incident wave. This coupled magnetic dimer system provides a practical method to optically design tunable active medium and device.

Generation of Acoustic Self-bending and Bottle Beams by Phase Engineering

Directing acoustic waves along curved paths is critical for applications such as ultrasound imaging, surgery and acoustic cloaking. Metamaterials can direct waves by spatially varying the material properties through which the wave propagates. However, this approach is not always feasible, particularly for acoustic applications. Here we demonstrate the generation of acoustic bottle beams in homogeneous space without using metamaterials. Instead, the sound energy flows through a three-dimensional curved shell in air leaving a close-to-zero pressure region in the middle, exhibiting the capability of circumventing obstacles. By designing the initial phase, we develop a general recipe for creating self-bending wave packets, which can set acoustic beams propagating along arbitrary prescribed convex trajectories. The measured acoustic pulling force experienced by a rigid ball placed inside such a beam confirms the pressure field of the bottle. The demonstrated acoustic bottle and self-bending beams have potential applications in medical ultrasound imaging, therapeutic ultrasound, as well as acoustic levitations and isolations.

Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss.

Beyond Brownian Motion On long time scales, the random Brownian motion of particles diffusing in a liquid is well described by theories developed by Einstein and others, but the instantaneous or short time scale behavior has been much harder to observe or analyze. Kheifets et al. (p. 1493) combined ultrasensitive position detection with sufficient data collection to probe the Brownian motion of microbeads in fluids on time scales that are shorter than the characteristic bead-fluid interaction time. The motions of Brownian particles are tracked and evaluated on short time scales where solvent effects play a role. Measurement of the instantaneous velocity of Brownian motion of suspended particles in liquid probes the microscopic foundations of statistical mechanics in soft condensed matter. However, instantaneous velocity has eluded experimental observation for more than a century since Einstein’s prediction of the small length and time scales involved. We report shot-noise–limited, high-bandwidth measurements of Brownian motion of micrometer-sized beads suspended in water and acetone by an optical tweezer. We observe the hydrodynamic instantaneous velocity of Brownian motion in a liquid, which follows a modified energy equipartition theorem that accounts for the kinetic energy of the fluid displaced by the moving bead. We also observe an anticorrelated thermal force, which is conventionally assumed to be uncorrelated.

Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling

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.

Brownian motion at short time scales

Brownian motion has played important roles in many different fields of science since its origin was first explained by Albert Einstein in 1905. Einsteins theory of Brownian motion, however, is only applicable at long time scales. At short time scales, Brownian motion of a suspended particle is not completely random, due to the inertia of the particle and the surrounding fluid. Moreover, the thermal force exerted on a particle suspended in a liquid is not a white noise, but is colored. Recent experimental developments in optical trapping and detection have made this new regime of Brownian motion accessible. This review summarizes related theories and recent experiments on Brownian motion at short time scales, with a focus on the measurement of the instantaneous velocity of a Brownian particle in a gas and the observation of the transition from ballistic to diffusive Brownian motion in a liquid.

Optomechanics of levitated dielectric particles

We review recent works on optomechanics of optically trapped microspheres and nanoparticles in vacuum, which provide an ideal system for studying macroscopic quantum mechanics and ultrasensitive force detection. An optically trapped particle in vacuum has an ultrahigh mechanical quality factor as it is well-isolated from the thermal environment. Its oscillation frequency can be tuned in real time by changing the power of the trapping laser. Furthermore, an optically trapped particle in vacuum may rotate freely, a unique property that does not exist in clamped mechanical oscillators. In this review, we will introduce the current status of optical trapping of dielectric particles in air and vacuum, Brownian motion of an optically trapped particle at room temperature, Feedback cooling and cavity cooling of the Brownian motion. We will also discuss about using optically trapped dielectric particles for studying macroscopic quantum mechanics and ultrasensitive force detection. Applications range from creating macroscopic Schrodingers cat state, testing objective collapse models of quantum wavefunctions, measuring Casimir force, searching short-range non-Newtonian gravity, to detect gravitational waves.