An optically levitated nanoparticle in vacuum is a paradigm optomechanical system for sensing and studying macroscopic quantum mechanics. While its center-of-mass motion has been investigated intensively, its torsional vibration has only been studied theoretically in limited cases. Here we report the first experimental observation of the torsional vibration of an optically levitated nonspherical nanoparticle in vacuum. We achieve this by utilizing the coupling between the spin angular momentum of photons and the torsional vibration of a nonspherical nanoparticle whose polarizability is a tensor. The torsional vibration frequency can be one order of magnitude higher than its center-of-mass motion frequency, which is promising for ground state cooling. We propose a simple yet novel scheme to achieve ground state cooling of its torsional vibration with a linearly-polarized Gaussian cavity mode. A levitated nonspherical nanoparticle in vacuum will also be an ultrasensitive nanoscale torsion balance with a torque detection sensitivity on the order of 10 −29 N · m/ √ Hz under realistic conditions. An optically levitated dielectric particle in vacuum [1][2][3] is an ultrasensitive detector for force sensing [4,5], millicharge searching [6] and other applications [7,8]. It will provide a great platform to test fundamental theories such as objective collapse models [9, 10] and quantum gravity [11] when its mechanical motion can be cooled to the quantum regime [12,13]. Recently, feedback cooling of the center-of-mass (COM) motion of a levitated nanosphere to about 450 µK (about 63 phonons at 150 kHz) [14], and cavity cooling of the COM motion of a nanosphere to a few mK [15] were demonstrated. The vibration mode would have already been in ground state at 450 µK [14] if its frequency is above 10 MHz. Increasing the vibration frequency of the nanoparticle can be a key to achieve ground state cooling. However, this can not be achieved by simply increasing the intensity of the trapping laser, which induces heating and subsequently causes the loss of the nanoparticle [4,16]. Besides COM motion, a pioneering work has proposed to use multiple Laguerre-Gaussian (LG) cavity modes to achieve angular trapping of a dielectric rod and cool its torsional vibration (TOR) to the ground state [12]. This was later generalized to micro-windmills [17], which have better overlap with LG cavity modes. These intriguing proposals of torsional optomechanics, however, have not been realized experimentally yet.In this work, we report the first experimental observation of the torsional vibration of an optically levitated nonspherical nanoparticle in vacuum, and show that the torsional frequency can be one order of magnitude higher than the COM frequency at the same laser intensity. We explain our observation using a model of an ellipsoidal nanoparticle levitated by a linearly-polarized Gaussian beam. For an ellipsoid much smaller than the wavelength of the trapping laser, its polarizability is a tensor due to its geometry [18]. In a linearly polariz...

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 Schrödinger's cat state, testing objective collapse models of quantum wavefunctions, measuring Casimir force, searching short-range non-Newtonian gravity, to detecting gravitational waves.

Hybrid spin-mechanical systems have great potentials in sensing, macroscopic quantum mechanics, and quantum information science. In order to induce strong coupling between an electron spin and the center-of-mass motion of a mechanical oscillator, a large magnetic gradient is usually required, which is difficult to achieve. Here we show that strong coupling between the electron spin of a nitrogen-vacancy (NV) center and the torsional vibration of an optically levitated nanodiamond can be achieved in a uniform magnetic field. Thanks to the uniform magnetic field, multiple spins can strongly couple to the torsional vibration at the same time. We propose to utilize this new coupling mechanism to realize the Lipkin-Meshkov-Glick (LMG) model by an ensemble of NV centers in a levitated nanodiamond. The quantum phase transition in the LMG model and finite number effects can be observed with this system. We also propose to generate torsional superposition states and realize torsional matter-wave interferometry with spin-torsional coupling.

Searching topological states in artificial systems has recently become a rapidly growing field of research. Meanwhile, significant experimental progresses on observing topological phenomena have been made in superconducting circuits. However, topological insulator states have not yet been reported in this system. Here, for the first time, we experimentally realize a tunable dimerized spin chain model and observe the topological magnon insulator states in a superconducting qubit chain. Via parametric modulations of the qubit frequencies, we show that the qubit chain can be flexibly tuned into topologically trivial or nontrivial magnon insulator states. Based on monitoring the quantum dynamics of a single-qubit excitation in the chain, we not only measure the topological winding numbers, but also observe the topological magnon edge and defect states. Our experiment exhibits the great potential of tunable superconducting qubit chain as a versatile platform for exploring non-interacting and interacting symmetry-protected topological states. arXiv:1901.05683v2 [quant-ph]

Traditional quantum error-correcting codes are designed for the depolarizing channel modeled by generalized Pauli errors occurring with equal probability. Amplitude damping channels model, in general, the decay process of a multilevel atom or energy dissipation of a bosonic system at zero temperature. We discuss quantum errorcorrecting codes adapted to amplitude damping channels for higher dimensional systems (qudits). For multi-level atoms, we consider a natural kind of decay process, and for bosonic systems, we consider the qudit amplitude damping channel obtained by truncating the Fock basis of the bosonic modes to a certain maximum occupation number. We construct families of single-error-correcting quantum codes that can be used for both cases. Our codes have larger code dimensions than the previously known single-error-correcting codes of the same lengths. Additionally, we present families of multi-error correcting codes for these two channels, as well as generalizations of our construction technique to error-correcting codes for the qutrit V and Λ channels. Index Termsamplitude damping channel, quantum codes, qudit Part of this work was presented at the 2014 IEEE Symposium on Information Information Theory.Markus Grassl is with Universität Erlangen-Nürnberg and the Max