Cooling and Control of a Cavity Optoelectromechanical System

We implement a cavity optoelectromechanical system integrating electrical actuation capabilities of nanoelectromechanical devices with ultrasensitive mechanical transduction achieved via intracavity optomechanical coupling. Electrical gradient forces as large as $0.40\mu \mathrm{N}$ are realized, with simultaneous mechanical transduction sensitivity of $1.5\times {10}^{-18}\mathrm{m}{\mathrm{Hz}}^{-1/2}$ representing a 3 orders of magnitude improvement over any nanoelectromechanical system to date. Optoelectromechanical feedback cooling is demonstrated, exhibiting strong squashing of the in-loop transduction signal. Out-of-loop transduction provides accurate temperature calibration even in the critical paradigm where measurement backaction induces optomechanical correlations.

Figure 1

Experimental schematic including electronic locking method for in-loop probe. The out-of-loop probe was thermally locked. FPC: fiber polarization controller. Inset: electric field distribution between electrodes. Apparatus was at room temperature ($300\mathrm{K}$) and atmospheric pressure.

Figure 2

Gradient force actuation of a COEMS. (a) Square root transduction spectra. Black curve: measured spectra; red (dark grey) curve: theoretical model including interference between the mechanical modes; light grey curve: Brownian motion spectra; dash-dotted line: transduction sensitivity. Insets: (from left to right) finite-element models of the lowest order crown ($j=1$), lowest order radial flexural ($j=2$), and second order crown ($j=3$) modes. Resolution bandwidth: ${\Gamma }_{\mathrm{RBW}}/2\pi =3\mathrm{kHz}$. (b) Square root peak transduction spectra as a function of rf drive amplitude. Green triangles: $j=1$, red circles: $j=2$, black squares: $j=3$.

Figure 3

Feedback cooling with varying feedback gain. (a) and (b): In- and out-of-loop transduction spectra. (c): In- ■ and out-of-loop ● temperature inferences. The solid red curve and dashed blue curve, respectively, denote the theoretical predictions of actual mechanical oscillator temperature and inferred in-loop temperature [27].