Optically Levitated Nanodumbbell Torsion Balance and GHz Nanomechanical Rotor

Levitated optomechanics has great potential in precision measurements, thermodynamics, macroscopic quantum mechanics, and quantum sensing. Here we synthesize and optically levitate silica nanodumbbells in high vacuum. With a linearly polarized laser, we observe the torsional vibration of an optically levitated nanodumbbell. This levitated nanodumbbell torsion balance is a novel analog of the Cavendish torsion balance, and provides rare opportunities to observe the Casimir torque and probe the quantum nature of gravity as proposed recently. With a circularly polarized laser, we drive a 170-nm-diameter nanodumbbell to rotate beyond 1 GHz, which is the fastest nanomechanical rotor realized to date. Smaller silica nanodumbbells can sustain higher rotation frequencies. Such ultrafast rotation may be used to study material properties and probe vacuum friction.

Figure 1

(a) A simplified diagram of the original Cavendish torsion balance that has two lead spheres suspended by a copper silvered torsion wire. (b) A nanodumbbell levitated by a linearly polarized optical tweezer in vacuum. The linearly polarized optical tweezer provides the restoring torque that confines the orientation of the nanodumbbell. $x_T$, $y_T$, $z_T$ are Cartesian coordinates of the trapping laser. $x_T$ is parallel to the electric field $\mathbf{E}$ of the incoming linearly polarized laser, and $z_T$ is parallel to the wave vector $\mathbf{k}$ of the laser. $x_N$ is parallel to the long axis of the nanodumbbell. The angle between $x_T$ and $x_N$ is $\theta$. (c) A simplified diagram for detecting the center-of-mass (c.m.) motion, the torsional (TOR) vibration, and the rotation (ROT) of a levitated nanodumbbell. The nanodumbbell is trapped at the focus of the lenses. The laser beam is initially linearly polarized. A quarter-wave ($\lambda /4$) plate is used to control its polarization. BS: non-polarizing beam splitter; PBS: polarizing beam splitter; $\lambda /2$: half-wave plate. Inset: A nanodumbbell with diameter $D$ and length $L$ created by attaching two identical nanospheres.

Figure 2

(a),(b): SEM images of silica nanodumbbells with two different sizes. The scale bar is 200 nm in (a) and 100 nm in (b). (c) Measured power spectrum densities (PSD) of the torsional vibration (labeled “Tor”) and the translational vibrations (labeled “$X$,” “$Y$,” “$Z$”) of a 170-nm-diameter nanodumbbell optically levitated at $5\times {10}^{-4}$ torr. (d) Measured PSD of the translational vibrations of the nanodumbbell levitated at 10 torr. The black curves are Lorentz fits.

Figure 3

(a) The ratio of air damping coefficients for translational motions perpendicular or parallel to its long axis ($x_N$ axis) as a function of the aspect ratio ($L/D$) of a nanodumbbell. (b) Calculated normalized drag torque of the rotation of a levitated nanodumbbell around $z_N$ axis as a function of the aspect ratio. (c) Effective susceptibilities of a silica nanodumbbell parallel (${\chi }_x$) or perpendicular (${\chi }_y$) to its long axis. (d) Calculated torque detection sensitivity of a levitated nanodumbbell with $D=170\mathrm{nm}$ or $D=50\mathrm{nm}$ as a function of air pressure. We assume $L/D=1.9$ in the calculations. The optical tweezer is assumed to be a focused 500 mW, 1550 nm laser with a waist of 820 nm.

Figure 4

(a) A nanodumbbell levitated by a circularly polarized laser will rotate. (b) Measured PSD of the rotation signal of a nanodumbbell. It has a sharp peak near 2.2 GHz. (c) Measured rotation frequency of the nanodumbbell as a function of pressure. (d) Calculated stress distribution of a nanodumbbell ($D=170\mathrm{nm}$, $L/D=1.9$) rotating at 1.2 GHz. (e) Calculated ultimate rotation frequency as a function of the diameter of the nanodumbbell when $L/D=1.9$. (f) Calculated ultimate rotation frequency as a function of the aspect ratio of the nanodumbbell when $D=100\mathrm{nm}$. The ultimate tensile strength is assumed to be 20 GPa (red solid line) or 10 GPa (blue dashed line).