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Optomechanics, the study of the mechanical interaction of light with matter, has proven to be a fruitful area of research that has yielded many notable achievements, including the direct detection of gravitational waves in kilometer-scale optical interferometers. Light has been used to cool and demonstrate quantum control over the mechanical degrees of freedom of individual ions and atoms, and more recently has facilitated the observation of quantum ``mechanics'' in objects of larger mass, even at the kg-scale. Levitated optomechanics, where an object can be suspended by radiation pressure and largely decoupled from its environment, has recently established itself as a rich field of study, with many notable results relevant for precision measurement, quantum information science, and foundational tests of quantum mechanics and fundamental physics. This article provides a survey of several current activities in field along with a tutorial describing associated key concepts and methods, both from an experimental and theoretical approach. It is intended as a resource for junior researchers who are new to this growing field as well as beginning graduate students. The tutorial is concluded with a perspective on both promising emerging experimental platforms and anticipated future theoretical developments., Comment: 50 pages, 19 figures, submitted to Advances in Optics and Photonics

A levitated non-spherical nanoparticle in a vacuum is ideal for studying quantum rotations and is an extremely sensitive torque and force detector. It has been proposed to probe fundamental particle-surface interactions such as the Casimir torque and the rotational quantum vacuum friction, which require it to be driven to rotate near a surface at sub-micrometer separations. Here, we optically levitate a silica nanodumbbell in a vacuum at about 430 nm away from a sapphire surface and drive it to rotate at GHz frequencies. The relative linear speed between the tip of the nanodumbbell and the surface reaches 1.4 km/s at a sub-micrometer separation. The rotating nanodumbbell near the surface demonstrates a torque sensitivity of $(5.0 \pm 1.1) \times 10^{-26} {\rm NmHz}^{-1/2}$ at room temperature. Moreover, we levitate a nanodumbbell near a gold nanograting and use it to probe the near-field intensity distribution beyond the optical diffraction limit. Our numerical simulation shows it is promising to detect the Casimir torque between a nanodumbbell and a nanograting., 4 figures

Paramagnetic ions and radicals play essential roles in biology and medicine, but detecting these species requires a highly sensitive and ambient-operable sensor. Optically addressable spin color centers in 3D semiconductors have been used for detecting paramagnetic spins as they are sensitive to the spin magnetic noise. However, the distance between spin color centers and target spins is limited due to the difficulty of creating high-quality spin defects near the surface of 3D materials. Here, we show that spin qubits in hexagonal boron nitride (hBN), a layered van der Waals (vdW) material, can serve as a promising sensor for nanoscale detection of paramagnetic spins in liquids. We first create shallow spin defects in close proximity to the hBN surface, which sustain high-contrast optically detected magnetic resonance (ODMR) in liquids. Then we demonstrate sensing spin noise of paramagnetic ions in water based on spin relaxation measurements. Finally, we show that paramagnetic ions can reduce the contrast of spin-dependent fluorescence, enabling efficient detection by continuous wave ODMR. Our results demonstrate the potential of ultrathin hBN quantum sensors for chemical and biological applications., Comment: 4 figures

Van der Waals layered materials are a focus of materials research as they support strong quantum effects and can easily form heterostructures. Electron spins in van der Waals materials played crucial roles in many recent breakthroughs, including topological insulators, two-dimensional (2D) magnets, and spin liquids. However, nuclear spins in van der Waals materials remain an unexplored quantum resource. Here we report the first demonstration of optical polarization and coherent control of nuclear spins in a van der Waals material at room temperature. We use negatively-charged boron vacancy ($V_B^-$) spin defects in hexagonal boron nitride to polarize nearby nitrogen nuclear spins. Remarkably, we observe the Rabi frequency of nuclear spins at the excited-state level anti-crossing of $V_B^-$ defects to be 350 times larger than that of an isolated nucleus, and demonstrate fast coherent control of nuclear spins. We also detect strong electron-mediated nuclear-nuclear spin coupling that is 5 orders of magnitude larger than the direct nuclear spin dipolar coupling, enabling multi-qubit operations. Nitrogen nuclear spins in a triangle lattice will be suitable for large-scale quantum simulation. Our work opens a new frontier with nuclear spins in van der Waals materials for quantum information science and technology.

Realizing a large-scale fully controllable quantum system is a challenging task in current physical research and has broad applications. Ultracold atom and molecule arrays in optical tweezers in vacuum have been used for quantum simulation, quantum metrology and quantum computing. Recently, quantum ground state cooling of the center-of-mass motion of a single optically levitated nanoparticle in vacuum was demonstrated, providing unprecedented opportunities for studying macroscopic quantum mechanics and precision measurements. In this work, we create a reconfigurable optically-levitated nanoparticle array in vacuum. Our optically-levitated nanoparticle array allows full control of individual nanoparticles to form an arbitrary pattern and detect their motion. As a concrete example, we choose two nanoparticles without rotation signals from an array to synthesize a nanodumbbell in-situ by merging them into one trap. The nanodumbbell synthesized in-situ can rotate beyond 1 GHz. Our work provides a new platform for studying macroscopic many-body physics., Comment: 6 pages, 4 figures

The dynamics of three interacting objects has been investigated extensively in Newtonian gravitational physics (often termed the three-body problem), and is important for many quantum systems, including nuclei, Efimov states, and frustrated spin systems. However, the dynamics of three macroscopic objects interacting through quantum vacuum fluctuations (virtual photons) is still an unexplored frontier. Here, we report the first observation of Casimir interactions between three isolated macroscopic objects. We propose and demonstrate a three terminal switchable architecture exploiting opto-mechanical Casimir interactions that can lay the foundations of a Casimir transistor. Beyond the paradigm of Casimir forces between two objects in different geometries, our Casimir transistor represents an important development for control of three-body virtual photon interactions and will have potential applications in sensing and information processing with the Casimir effect., Comment: 7 pages, 4 figures

Optically active spin defects in van der Waals materials are promising platforms for modern quantum technologies. Here we investigate the coherent dynamics of strongly interacting ensembles of negatively charged boron-vacancy ($\mathrm{V}_{\mathrm{B}}^-$) centers in hexagonal boron nitride (hBN) with varying defect density. By employing advanced dynamical decoupling sequences to selectively isolate different dephasing sources, we observe more than 5-fold improvement in the measured coherence times across all hBN samples. Crucially, we identify that the many-body interaction within the $\mathrm{V}_{\mathrm{B}}^-$ ensemble plays a substantial role in the coherent dynamics, which is then used to directly estimate the concentration of $\mathrm{V}_{\mathrm{B}}^-$. We find that at high ion implantation dosage, only a small portion of the created boron vacancy defects are in the desired negatively charged state. Finally, we investigate the spin response of $\mathrm{V}_{\mathrm{B}}^-$ to the local charged defects induced electric field signals, and estimate its ground state transverse electric field susceptibility. Our results provide new insights on the spin and charge properties of $\mathrm{V}_{\mathrm{B}}^-$, which are important for future use of defects in hBN as quantum sensors and simulators., Comment: 8+8+4 pages, 4+5+1 figures

Optically levitated nonspherical particles in vacuum are excellent candidates for torque sensing, rotational quantum mechanics, high-frequency gravitational wave detection, and multiple other applications. Many potential applications, such as detecting the Casimir torque near a birefringent surface, require simultaneous cooling of both the center-of-mass motion and the torsional vibration (or rotation) of a nonspherical nanoparticle. Here we report the first 5D cooling of a levitated nanoparticle. We cool the 3 center-of-mass motion modes and 2 torsional vibration modes of a levitated nanodumbbell in a linearly-polarized laser simultaneously. The only uncooled rigid-body degree of freedom is the rotation of the nanodumbbell around its long axis. This free rotation mode does not couple to the optical tweezers directly. Surprisingly, we observe that it strongly affects the torsional vibrations of the nanodumbbell. This work deepens our understanding of the nonlinear dynamics and rotation coupling of a levitated nanoparticle and paves the way towards full quantum control of its motion., Comment: 5 pages, 4 figures

In this paper, results of quantum calculations are presented for feedback cooling of an optically trapped nanoparticle in the laser-shot-noise-dominant regime. We numerically investigate the system using both parametric and force feedback cooling schemes. For the same measurement efficiency, the cooling limit from the force feedback is lower than that from the parametric feedback. We also develop a set of semi-classical equations for feedback cooling that accurately match the quantum results. It is demonstrated, by rescaling the semi-classical equations, that the cooling dynamics is uniquely determined by the parameter set: the feedback strength, the measurement efficiency and the change of occupation number over one oscillation period due to the shot noise. The minimum occupation number is determined by the measurement efficiency and the change of occupation number over one period.

Spontaneous symmetry breaking is a universal concept throughout science. For instance, the Landau-Ginzburg paradigm of translational symmetry breaking underlies the classification of nearly all quantum phases of matter and explains the emergence of crystals, insulators, and superconductors. Usually, the consequences of translational invariance are studied in large systems to suppress edge effects which cause undesired symmetry breaking. While this approach works for investigating global properties, studies of local observables and their correlations require access and control of the individual constituents. Periodic boundary conditions, on the other hand, could allow for translational symmetry in small systems where single particle control is achievable. Here, we crystallize up to fifteen 40Ca+ ions in a microscopic ring with inherent periodic boundary conditions. We show the ring's translational symmetry is preserved at millikelvin temperatures by delocalizing the Doppler laser cooled ions. This establishes an upper bound for undesired symmetry breaking at a level where quantum control becomes feasible. These findings pave the way towards studying quantum many-body physics with translational symmetry at the single particle level in a variety of disciplines from simulation of Hawking radiation to exploration of quantum phase transitions., 15 pages, 4 figures

The question whether quantum mechanics is complete and the nature of the transition between quantum mechanics and classical mechanics have intrigued physicists for decades. There have been many experimental breakthroughs in creating larger and larger quantum superposition and entangled states since Erwin Schr��dinger proposed his famous thought experiment of putting a cat in a superposition of both alive and dead states in 1935. Remarkably, recent developments in quantum optomechanics and electromechanics may lead to the realization of quantum superposition of living microbes soon. Recent evidence also suggests that quantum coherence may play an important role in several biological processes. In this review, we first give a brief introduction to basic concepts in quantum mechanics and the Schr��dinger's cat thought experiment. We then review developments in creating quantum superposition and entangled states and the realization of quantum teleportation. Non-trivial quantum effects in photosynthetic light harvesting and avian magnetoreception are also discussed. At last, we review recent proposals to realize quantum superposition, entanglement and state teleportation of microorganisms, such as viruses and bacteria., review article for Contemporary Physics, 28 pages

We present a design of an r.f. trap using planar electrodes with the goal to trap on the order of 100 ions in a small ring structure of diameters ranging between 100 $\mu$m and 200 $\mu$m. In order to minimize the influence of trap electrode imperfections due to the fabrication, we aim at trapping the ions around 400 $\mu$m above the trap electrodes. In view of experiments to create freely rotating crystals near the ground state, we numerically study factors breaking the rotational symmetry such as external stray electric fields, local charging of the trap electrodes, and fabrication imperfections. We conclude that these imperfections can be controlled sufficiently well under state-of-the-art experimental conditions to allow for freely rotating ion rings even at energies comparable to the ground state energy of the rotational degree-of-freedom., Comment: 8 pages, 11 figures; submitted to Physical Review A

This is a reply to the comment from Patrick Bruno (arXiv:1211.4792) on our paper (Phys. Rev. Lett. 109, 163001 (2012)).

Brownian motion has played important roles in many different fields of science since its origin was first explained by Albert Einstein in 1905. Einstein's 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., Comment: review paper, 14 pages, 13 figures, 92 references

We propose to study the Brownian motion of a classical microsphere submerged in superfluid $^4$He using the recent laser technology as a direct investigation of the thermal fluctuations of quasiparticles in the quantum fluid. By calculating the temperature dependence of both the friction coefficient and the strength of the random force, we show that the resonant mode of the fluctuational motion can be fully resolved by the present technology. Contrary to the previous work, it is found that the roton contribution is not negligible, and it even becomes dominant when the temperature is above 0.76\,K., 4 pages, 4 figures

In this paper, we calculate the relationships both between the width of the tunnel barrier and the spin-polarization(SP) of the electronic current when it is injected from a ferromagnetic metal into a semiconductor through a tunnel barrier and between the bias and SP. The results agree with the latest experimental results. We found that a moderate bias and tunnel barrier width allow a giant SP and there is little spin injection at very low bias.