Optical trapping describes the interaction between light and matter to manipulate micro-objects through momentum transfer. In the case of 3D trapping with a single beam, this is termed optical tweezers. Optical tweezers are a powerful and noninvasive tool for manipulating small objects, and have become indispensable in many fields, including physics, biology, soft condensed matter, among others. In the early days, optical trapping was typically accomplished with a single Gaussian beam. In recent years, we have witnessed rapid progress in the use of structured light beams with customized phase, amplitude, and polarization in optical trapping. Unusual beam properties, such as phase singularities on-axis and propagation invariant nature, have opened up novel capabilities to the study of micromanipulation in liquid, air, and vacuum. We summarize the recent advances in the field of optical trapping using structured light beams.

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Optical trapping with structured light: a review

The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering1. Today, the increasing demand for applied quantum technologies requires adaptation of this level of control to individual quantum systems2,3. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback4. Successful implementations thus far include experiments on the level of optical and atomic systems5–7. Here we demonstrate real-time optimal control of the quantum trajectory8 of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3 times the zero-point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of 0.56 ± 0.02 quanta, realizing quantum ground-state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems. Optimal quantum control of an optically trapped nanoparticle in its ground state is demonstrated at room temperature, using Kalman filtering to track its quantum trajectory in real time.

Real-time optimal quantum control of mechanical motion at room temperature

Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence1–3. Quantum control of mechanical motion has been achieved by engineering the radiation–pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator4–7. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states8. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects9,10, since their trapping potential is fully controllable. Here we optically levitate a femtogram (10−15 grams) 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 centre-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 0.43. 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 scales11. Quantum control of an optically levitated nanoparticle with a mass of just one femtogram is demonstrated in a cryogenic environment by feedback-cooling the motion of the particle to the quantum ground state.

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Quantum control of a nanoparticle optically levitated in cryogenic free space.

Since their invention in 1986 by Arthur Ashkin and colleagues, optical tweezers have become an essential tool in several fields of physics, spectroscopy, biology, nanotechnology, and thermodynamics. In this tutorial, we provide a primer on how to calibrate optical tweezers and how to use them for advanced applications. After a brief general introduction on optical tweezers, we focus on describing and comparing the various available calibration techniques. Then, we discuss some cutting-edge applications of optical tweezers in a liquid medium, namely, to study single-molecule and single-cell mechanics, microrheology, colloidal interactions, statistical physics, and transport phenomena. Finally, we consider optical tweezers in vacuum, where the absence of a viscous medium offers vastly different dynamics and presents new challenges. We conclude with some perspectives for the field and the future applications of optical tweezers. This tutorial provides both a step-by-step guide ideal for non-specialists entering the field and a comprehensive manual of advanced techniques useful for expert practitioners. All of the examples are complemented by the sample data and software necessary to reproduce them.

Optical tweezers — from calibration to applications: a tutorial

The control of levitated nano- and micro-objects in vacuum—which capitalizes on scientific achievements in the fields of atomic physics, control theory, and optomechanics—is of considerable interes...

Levitodynamics: Levitation and control of microscopic objects in vacuum

Quantum control of complex objects in the regime of large size and mass provides opportunities for sensing applications and tests of fundamental physics. The realization of such extreme quantum states of matter remains a major challenge. We demonstrate a quantum interface that combines optical trapping of solids with cavity-mediated light-matter interaction. Precise control over the frequency and position of the trap laser with respect to the optical cavity allowed us to laser-cool an optically trapped nanoparticle into its quantum ground state of motion from room temperature. The particle comprises 108 atoms, similar to current Bose-Einstein condensates, with the density of a solid object. Our cooling technique, in combination with optical trap manipulation, may enable otherwise unachievable superposition states involving large masses.

https://science.sciencemag.org/content/sci/early/2020/01/29/science.aba3993.full.pdf

Cooling of a levitated nanoparticle to the motional quantum ground state.

We report quantum ground state cooling of a levitated nanoparticle in a room temperature environment. Using coherent scattering into an optical cavity we cool the center of mass motion of a $143$ nm diameter silica particle by more than $7$ orders of magnitude to $n_x=0.43\pm0.03$ phonons along the cavity axis, corresponding to a temperature of $12~\mu$K. We infer a heating rate of $\Gamma_x/2\pi = 21\pm 3$ kHz, which results in a coherence time of $7.6~\mu$s -- or $15$ coherent oscillations -- while the particle is optically trapped at a pressure of $10^{-6}$ mbar. The inferred optomechanical coupling rate of $g_x/2\pi = 71$ kHz places the system well into the regime of strong cooperativity ($C \approx 5$). We expect that a combination of ultra-high vacuum with free-fall dynamics will allow to further expand the spatio-temporal coherence of such nanoparticles by several orders of magnitude, thereby opening up new opportunities for macrosopic quantum experiments.

Kahan Dare

Papers

Cooling of a levitated nanoparticle to the motional quantum ground state.

Motional Quantum Ground State of a Levitated Nanoparticle from Room Temperature

Cooling of a levitated nanoparticle to the motional quantum ground state