Optomechanical Entanglement between a Movable Mirror and a Cavity Field

We show how stationary entanglement between an optical cavity field mode and a macroscopic vibrating mirror can be generated by means of radiation pressure. We also show how the generated optomechanical entanglement can be quantified, and we suggest an experimental readout scheme to fully characterize the entangled state. Surprisingly, such optomechanical entanglement is shown to persist for environment temperatures above 20 K using state-of-the-art experimental parameters.

Figure 1

Plot of the logarithmic negativity $E_{\mathcal{N}}$ as a function of the normalized detuning $\Delta /w_m$ in the case of an optical cavity of length $L=1\mathrm{mm}$, driven by a laser with wavelength 810 nm and power $P=50\mathrm{mW}$. The mechanical oscillator has a frequency $w_m/2\pi =10\mathrm{MHz}$, a damping rate ${\gamma }_m/2\pi =100\mathrm{Hz}$, and its temperature is $T=400\mathrm{mK}$. The solid line refers to a mass $m=5\mathrm{ng}$ and finesse $\mathcal{F}=1.07\times {10}^4$, while the dashed line refers to a mass $m=50\mathrm{ng}$ and finesse $\mathcal{F}=3.4\times {10}^4$.

Figure 2

Plot of the logarithmic negativity $E_{\mathcal{N}}$ versus the mirror temperature. The solid line refers to a mass $m=5\mathrm{ng}$, detuning $\Delta =w_m$, and finesse $\mathcal{F}=1.07\times {10}^4$; the dashed line refers to a mass $m=50\mathrm{ng}$, $\Delta =w_m/2$, and finesse $\mathcal{F}=3.4\times {10}^4$. The other parameters are those of Fig. 1.

Figure 3

Schematic description of the proposed experiment, including the second Fabry-Perot cavity on the right for the detection of the mechanical motion.