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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical trapping and cooling of glass microspheres

Mark G. Raizen, Simon Kheifets, Tongcang Li

Published Oct 3, 2012• 1 citation

Abstract

We report on experiments studying the Brownian motion of an optically trapped bead in air, and observe for the first time the short-time regime of ballistic motion. Einstein predicted this effect in 1907, but said the experiment would be impossible in practice. Our measurements were enabled by our development of a new detection system that is capable of real-time tracking of the motion of a trapped bead on unprecedented short time scales and correspondingly small length scales. We used the data to measure the average kinetic energy of a Brownian particle, and find good agreement with the energy equipartition theorem of statistical mechanics. Measurement of the instantaneous velocity also allows us to stably trap beads in vacuum, using active feedback to control and cool the center of mass motion to mK temperatures in three dimensions. The system of an optically trapped bead in vacuum can serve as a testing ground for macroscopic quantum superpositions and the role of decoherence. In the opposite extreme, a trapped bead in a fluid can be used to test basic questions in statistical mechanics, and fluid dynamics on the smallest scales.

DOI: 10.1117/12.928885

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Optically trapped nanoparticles have recently emerged as exciting candidates for tests of quantum mechanics at the macroscale and as versatile platforms for ultrasensitive metrology. Recent experiments have demonstrated parametric feedback cooling, nonequilibrium physics, and temperature detection, all in the classical regime. Here we provide the first quantum model for trapped nanoparticle cooling and force sensing. In contrast to existing theories, our work indicates that the nanomechanical ground state may be prepared without using an optical resonator; that the cooling mechanism corresponds to nonlinear friction; and that the energy loss during cooling is nonexponential in time. Our results show excellent agreement with experimental data in the classical limit, and constitute an underlying theoretical framework for experiments aiming at ground state preparation. Our theory also addresses the optimization of, and the fundamental quantum limit to, force sensing, thus providing theoretical direction to ongoing searches for ultra-weak forces using levitated nanoparticles.

Abstract Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence [1-4]. Quantum control of mechanical motion has been achieved by engineering the radiation pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator [5-8]. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states [9]. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects [10,11], since their trapping potential is fully controllable. In this work, we optically levitate a femto-gram dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its center-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 43%. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales [12,13].