Optomechanical Down-Conversion

Abstract

To demonstrate optomechanical down-conversion we follow the scheme described in Sect. 2.3.6. We set the detuning $\Delta \approx \omega _m$ for the pump beam and increase the pump power until breaking the rotating wave approximation. For our parameters the limit for $g\gtrsim \omega _m$ is at a power level of $P\gtrsim 15$ mW (this takes into account a typical coupling efficiency of ${\sim }75\,\%$ of the pump beam to the cavity mode). Our optomechanical cavity comprises a micromechanical resonator, made of a $150\times 50\times 1$ $\upmu$m$^3$ SiN beam with a high reflectivity (${>}99.991\,\%$) dielectric mirror pad in its center (diameter 50 $\upmu$m) as one of the end mirrors of a Fabry-Pérot cavity of length $L=25$ mm and linewidth $\kappa =464$ kHz. Its mechanical resonance frequency is $\omega _m/2\pi \approx 950$ kHz, its mechanical quality factor $Q\approx 6{,}700$ and the effective mass $m_{eff}=55$ ng (see Sect. 3.10). Due to the lower reflectivity of the second cavity mirror (99.91$\,\%$) we obtain a good approximation of a single-sided cavity of finesse $F\approx 6{,}300$. We use a Nd:YAG laser at $\lambda =1{,}064$ nm both for pumping the optomechanical cavity and for read-out of the mechanics. For this we split the laser beam into a faint ($\approx 15$ $\upmu$W) read-out and a strong (up to 4 mW) driving beam on a polarizing beam splitter (PBS), as is shown in Fig. 7.1 and described in detail in Sect. 3.4. In addition, the faint beam is phase modulated by an electro-optical modulator (EOM) to achieve Pound-Drever-Hall stabilization (cf. Sect. 3.3.1) of the pump laser frequency with respect to the optomechanical cavity by acting back on the laser. Frequency detuning of the driving beam with respect to the cavity frequency is achieved by acousto-optic modulation (AOM). Both beams are then recombined into the same spatial mode of the optomechanical cavity. Note, however that they always remain distinguishable due to their orthogonal polarization. The experiment is performed at room temperature in vacuum ($\sim 10^{-6}$ mbar).