GHz Rotation of an Optically Trapped Nanoparticle in Vacuum

We report on rotating an optically trapped silica nanoparticle in vacuum by transferring spin angular momentum of light to the particle’s mechanical angular momentum. At sufficiently low damping, realized at pressures below ${10}^{-5}\mathrm{mbar}$, we observe rotation frequencies of single 100 nm particles exceeding 1 GHz. We find that the steady-state rotation frequency scales linearly with the optical trapping power and inversely with pressure, consistent with theoretical considerations based on conservation of angular momentum. Rapidly changing the polarization of the trapping light allows us to extract the pressure-dependent response time of the particle’s rotational degree of freedom.

Figure 1

Simplified experimental setup. The polarization state of an initially linearly polarized laser beam can be set by a quarter-wave plate before entering a vacuum chamber. Inside the chamber, an optical trap for a nanoparticle is formed by focusing the beam with an aspheric lens (0.77 NA). The light is collected by an identical lens and equally split by a beam splitter (BS). One half of the power is utilized for center-of-mass (c.m.) detection of the particle. The other half is sent onto a half-wave plate followed by a polarizing beam splitter (PBS), which enables balanced detection of the particle rotation via a spectrum analyzer.

Figure 2

Rotation frequency as a function of pressure at a focal trapping power of 226(5) mW and for nearly left-circularly polarized (LCP) trapping light. (a) Measured power spectral density (PSD) of the rotation signal at a pressure of $1.1\times {10}^{-5}\mathrm{mbar}$ showing a signal at 1.31 GHz, which corresponds to a rotation frequency of ${\mathrm{\Omega }}_{\mathrm{rot}}/(2\pi )=655\mathrm{MHz}$. (b) Measured rotation frequency for varying gas pressure with a maximum rotation frequency of ${\mathrm{\Omega }}_{\mathrm{rot}}/(2\pi )=1.029(1)\mathrm{GHz}$ at a pressure of $7.2\times {10}^{-6}\mathrm{mbar}$. We attribute the deviation between theory and experiment below ${10}^{-3}\mathrm{mbar}$ to an underestimation of pressure by the used ion gauge.

Figure 3

(a) Power dependence of the rotation frequency at a pressure $p_{\mathrm{gas}}=1.0\times {10}^{-4}\mathrm{mbar}$. The polarization of the trapping light equals the one in Fig. 2 and corresponds to a quarter-wave plate angle of $-29°$, see arrow in (b). (b) Particle rotation frequency as a function of quarter-wave plate angle at a focal power of 226(5) mW. The wave plate angle determines the degree of linear vs circular polarization of the trapping light. A finite degree of circular polarization is necessary to induce rotation of the particle. The orange dashed line is a fit to ${\mathrm{\Omega }}_{\mathrm{rot}}=\mathrm{Re}[a\sqrt{(1-\cos b{)}^2{\sin }^2(2\varphi -{\varphi }_0)-{\sin }^2(b){\cos }^2(2\varphi -{\varphi }_0)}]$ [13]. The data in (a) and (b) have been recorded with different particles.

Figure 4

Measurement of system dynamics at a focal power $P=230(5)\mathrm{mW}$. (a) After a steplike change of the optical torque by a fast rotation of the quarter-wave plate [see Figs. 1 and 3] we measure the rotation frequency as a function of time at a fixed pressure. A fit (dashed line) of ${\mathrm{\Omega }}_{\mathrm{rot}}=c_1+c_2\exp (-t/t_{\mathrm{damp}})$, with $t_{\mathrm{damp}}$, $c_1$, and $c_2$ as free parameters, reveals the characteristic response time $t_{\mathrm{damp}}$ of our system. (b) Repeating the procedure described in (a) for different pressures results in a damping time which scales as $t_{\mathrm{damp}}\propto 1/p_{\mathrm{gas}}$ (dashed line).