Cavity optomechanics with ultrahigh-$Q$ crystalline microresonators

We present the observation of optomechanical coupling in crystalline whispering-gallery-mode (WGM) resonators. The high purity of the material enables optical quality factors in excess of ${10}^{10}$ and finesse exceeding ${10}^6$, as well as mechanical quality factors greater than ${10}^5$. Ultrasensitive displacement measurements reveal mechanical radial modes at frequencies up to $20$ $\mathrm{MHz}$, corresponding to unprecedentedly high sideband factors ($>$$100$). In combination with the weak intrinsic mechanical damping this renders crystalline WGM microresonators promising for experiments in the classical and quantum regime of optomechanics.

Figure 1

(a) Transmission on resonance vs coupling parameter ${\tau }_0/{\tau }_{\mathrm{ex}}$ while approaching a tapered fiber to a CaF${}_2$ cavity. The data (blue circles) show that ideal coupling behavior (red line) is possible up to a coupling factor ${\tau }_0/{\tau }_{\mathrm{ex}}\approx 8$. (b) Measurement of the resonance linewidth of a different cavity (radius $2\hspace{0.5em}\mathrm{mm}$) with calibration peaks at 2 $\mathrm{MHz}$ detuning and Lorentzian fit (red line). The left inset shows a diamond-turned resonator made of CaF${}_2$. (c) Ringdown measurements (blue circles) of the same resonator and exponential fit (red line). The measured lifetime of $\tau =3.35$ $\mu$s corresponds to an intrinsic quality factor of $Q_0=1.18\times {10}^{10}$.

Figure 2

Displacement spectral density (SD) of a mechanical mode of a cylindrical cavity. (a) Cavity free-standing at atmospheric pressure. The blue lines are data (with calibration [8] peak), the red lines are Lorentzian fits. The inset shows the typical displacement pattern of a mode in this frequency range. (b) The quality factor of the same mechanical mode measured at low pressure and with optimized clamping increased to 114 300. The inset illustrates the mounting of the resonator. It is clamped by four tungsten tips, three sidewise (red shaded), and one from below.

Figure 3

(a) Photocurrent spectral density normalized to equivalent mechanical displacement fluctuations at a Fourier frequency of $14.5\hspace{0.5em}\mathrm{MHz}$. Three spectra were measured with a Nd:YAG laser coupled to a ${\mathrm{CaF}}_2$ microdisk waxed on a metal holder (configuration 1), the same disk clamped between two tungsten tips (configuration 2), and a fiber loop cavity (FLC). The disk exhibits several orders of mechanical radial breathing modes (RBMs) up to 20 MHz (second to fourth order are shown). (b) For the case of central clamping, measurement and simulation of first- to fourth-order RBM frequencies show excellent agreement. The increase in modal displacement at the support tip for higher-order RBMs explains the measured dependence of $Q_{\mathrm{m}}$ on the RBM order (from $Q_{\mathrm{m}}=2500$ to $Q_{\mathrm{m}}=40$). The color code represents radial displacement (arbitrary units).