Optically levitated nanodiamonds with nitrogen-vacancy centers promise a high-quality hybrid spinoptomechanical system. However, the trapped nanodiamond absorbs energy form laser beams and causes thermal damage in vacuum. It is proposed here to solve the problem by trapping a composite particle (a nanodiamond core coated with a less absorptive silica shell) at the center of strongly focused doughnut-shaped laser beams. Systematical study on the trapping stability, heat absorption, and oscillation frequency concludes that the azimuthally polarized Gaussian beam and the linearly polarized Laguerre-Gaussian beam LG 03 are the optimal choices. With our proposal, particles with strong absorption coefficients can be trapped without obvious heating and, thus, the spin-optomechanical system based on levitated nanodiamonds are made possible in high vacuum with the present experimental techniques.Introduction-. By trapping, detecting and manipulating nano-and micro-particles [1], optical tweezers are widely used in biophysics [2-4], colloidal sciences [5], chemistry, microfluidic dynamics [6], and fundamental physics [7][8][9][10][11][12][13][14][15]. Because of the wide applicability and high tunablity of the optically levitated systems, several schemes [16] were proposed to realize the ground-state cooling [17], to search for non-Newtonian gravity [18] and to detect gravitational wave [19]. Particularly, it brings about more interesting phenomena and novel applications [20,21] when the trapped particles have internal degrees of freedom (such as spins or electric dipoles) and enter the quantum regime.Optically levitated nanodiamonds with nitrogen-vacancy (NV) centers [22][23][24][25][26] are one of the most promising candidates for implementing a spin-optomechanical hybrid system. In principle, this system can have both long spin coherence time and high quality factor of mechanical oscillation in vacuum. The electron spins of NV centers were shown to have long spin coherence time (in the order of 10 2 µs) even in nanodiamonds of diameter about 20 nm [27]. When trapped in high-vacuum, the dielectric particles are predicted to have ultra-high quality factor Q larger than 10 10 [16,18,28]. Researchers have trapped diamond particles and observed the signal from NV centers in liquid [29,30], in air [31] and very recently in vacuum with pressure down to ∼ kPa [24,25] and ∼ 100 Pa [26].Realizing high quality mechanical oscillation requires trapping the particles in high vacuum (e.g, 10 −6 Pa) to get Q ∼ 10 10 . However, the high-vacuum condition usually causes the thermal damage problem, and experimentally trapping a nanodiamond in high vacuum is still very challenging. Nanodiamonds will absorb energy from the trapping laser beams due to the intrinsic defects [26] and the inevitable imperfections or graphitization [32] on diamond surface. The absorbed energy can hardly be dissipated in a high-vacuum environment, and the nanodiamonds will be quickly heated up significantly [24][25][26], which is unfavorable to the defect centers...

We systematically investigate the bistable behavior and squeezing property of the librational mode of a levitated nonspherical nanoparticle trapped by laser beams. By expanding the librational potential to the forth order of the librational angle θ, we find that the nonlinear coefficient of this mode is dependent only on the size and material of nanoparticle, but independent of trapping potential shape. The bistability and hysteresis are displayed when the driving frequency is red-detuned to the librational mode. In the bluedetuned region, we have studied squeezing of the variance of librational mode in detail, which has potential application for measurement of angle and angular momentum.

We investigate how to apply a high-frequency driving field to the quantum control of a single particle in an open double-well system. The linear stability analysis points out that the stability depends on the external-field parameters and the loss (or gain) coefficients of the system, and the instability leads to transition of the Floquet quasi-energy from real to complex values and results in the decaying probabilities of the particle in the double-well. Combining the analytical solutions in the high-frequency approximation with the numerical calculations based on the accurate model, we exhibit quantum-dynamical behaviors of the particle such as the Floquet oscillation, coherent destruction of tunneling, quasi-noon-state population, partial tunneling of one-particle, and the decaying behavior of the probabilities, which are due to the competition and balance between the quantum coherence and the loss (or gain) effect. The results propose an experimental method for testing the quantum motions of the open system by adjusting the driving field.

We present theoretical and experimental investigations of higher order correlations of mechanical motion in the recently demonstrated optical tweezer phonon laser, consisting of a silica nanosphere trapped in vacuum by a tightly focused optical beam [Nat. Photonics 13, 402 (2019)10.1038/s41566-019-0395-5]. The nanoparticle phonon number probability distribution is modeled with the master equation formalism in order to study its evolution across the lasing threshold. Up to fourth-order equal-time correlation functions are then derived from the probability distribution. Subsequently, the master equation is transformed into a nonlinear quantum Langevin equation for the trapped particle’s position. This equation yields the non-equal-time correlations, also up to fourth order. Finally, we present experimental measurements of the phononic correlation functions, which are in good agreement with our theoretical predictions. We also compare the experimental data to existing analytical Ginzburg-Landau theory where we find only a partial match.

We systematically investigate the nonlinearity of librational and translational modes, and present a theoretical scheme for quantum ground state cooling of both librational and translational modes of an optically levitated nonspherical nanoparticle via cavity mode. By expanding the trapping potential to the fourth order of both the translational and librational freedom degrees, we obtain the inherent nonlinearity of them and their nonlinear coupling. Through stability analysis, bi‐ and multistability are presented in this system, when either the librational or the translational drive is red‐detuning. The system will be stabilized if and only if these two drives are both blue‐detuning. In order to obtain the quantum ground states of the motional modes of ellipsoidal nanoparticle, a cavity mode is utilized to cool the librational and translational modes. By optimizing the frequencies and amplitudes of drives and residual air pressure, the quantum ground states of the librational and translational modes can be realized at the same time.