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 five-dimensional cooling of a levitated nanoparticle. We cool the three center-of-mass motion modes and two 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.

We theoretically investigate the rigid body dynamics of an optically levitated nanodumbbell under parametric feedback cooling and provide a simplified model for describing the motion. Differing from previous studies, the spin of the nanoparticle about its symmetry axis is considered non-negligible. Simulations reveal that standard parametric feedback cooling can extract energy from two of the five rotational degrees of freedom when the nanoparticle is levitated using a linearly polarized laser beam. The dynamics after feedback cooling are characterized by a normal mode describing precession about the laser polarization axis together with spin about the nanoparticle's symmetry axis. Cooling the remaining mode requires an asymmetry in the two librational frequencies associated with motion about the polarization axis as well as information about the two frequencies of rotation about the polarization axis. Introducing an asymmetric potential allows full cooling of the librational coordinates if the frequencies of both are used in the feedback modulation and is an avenue for entering the librational quantum regime. The asymmetry in the potential needs to be large enough for practical cooling times as the cooling rate of the system depends non-linearly on the degree of asymmetry, a condition that is easily achieved experimentally.

This paper aims to correct the expression for the rate at which laser shot noise energy is delivered to a particle in levitated optomechanics. While previous articles have the same overall form and dependencies, the proportionality constants are either incorrect or misleading. The rate at which energy is delivered to an optically trapped particle's respective degrees of freedom depends on the radiation pattern of scattered light as well as the direction of laser propagation. For linearly polarized light in the Rayleigh regime, this leads the translational shot noise heating rate to be proportional to 1/10 of the total rate in the laser polarization direction, 7/10 in the laser propagation direction, and 2/10 in the direction perpendicular to both. Analytical expressions for the shot noise heating rate are provided in the Rayleigh limit as well as numerical calculations for particles in the Mie regime for silica and diamond. For completeness, expressions for the rotational shot noise heating for a symmetric top-like particle for linear, elliptically, and unpolarized light is also provided.

Forces and torques exerted on dielectric disks trapped in a Gaussian standing wave are analyzed theoretically for disks of radius 2 μm with indices of refraction n = 1.45 and n = 2.0 as well as disks of radius 200 nm with n = 1.45. Calculations of the forces and torques were conducted both analytically and numerically using a discrete-dipole approximation method. Besides harmonic terms, third-order rotranslational coupling terms in the potential energy can be significant and a necessary consideration when describing the dynamics of disks outside of the Rayleigh limit. The coupling terms are a result of the finite extension of the disk coupling to both the Gaussian and standing-wave geometry of the beam. The resulting dynamics of the degrees of freedom most affected by the coupling terms exhibit several sidebands as evidenced in the power spectral densities. Simulations show that for Gaussian beam waists of 2-4 μm the disk remains stably trapped.

A proposal for cooling the translational motion of optically levitated magnetic nanoparticles is presented. The theoretical cooling scheme involves the sympathetic cooling of a ferromagnetic YIG nanosphere with a spin-polarized atomic gas. The particle–atom cloud coupling is mediated through the magnetic dipole–dipole interaction. When the particle and atom oscillations are small compared to their separation, the interaction potential becomes dominantly linear, which allows the particle to exchange energy with the N atoms. While the atoms are continuously Doppler cooled, energy is able to be removed from the nanoparticle’s motion as it exchanges energy with the atoms. The rate at which energy is removed from the nanoparticle’s motion was studied for three species of atoms (Dy, Cr, Rb) by simulating the full N + 1 equations of motion and was found to depend on system parameters with scalings that are consistent with a simplified model. The nanoparticle’s damping rate due to sympathetic cooling is competitive with and has the potential to exceed commonly employed cooling methods.

We observe the coupled dynamics of both translational motion and torsional vibration for a levitated nanodumbbell at high vacuum. We also report cooling multiple degrees of freedom of the levitated nanodumbbell.

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