Robustness of continuous-variable entanglement via geometrical nonlinearity

We propose a scheme to generate robust stationary continuous-variable entanglement in optomechanical systems, based on geometrical nonlinearity that occurs for large mechanical displacements. Such nonlinearity is often used to correct the dynamics of the systems in the strong-coupling regime. It appears that geometrical nonlinearity enhances the entanglement and shifts its maximum towards high detuning values. Using the experimental parameters, we find that such a scheme generates a very robust entanglement against thermal decoherence even at room temperature. Our results show that geometrical nonlinearity affects entanglement as the optomechanical quantum interface.

Figure 1

Linear regime obtained with the physical parameters in Table 1. (a) Logarithmic negativity $E_{\mathcal{N}}$ versus normalized detuning $\frac{\Delta }{{\Omega }_m}$. The entanglement is maximal around the blue detuning $\frac{\Delta }{{\Omega }_m}=-1$. (b) Logarithmic negativity $E_{\mathcal{N}}$ versus intracavity field with high input power $P_0=10\text{mW}$. The entanglement is enhanced for high input power.

Figure 2

Plots of the input power $P_0=10\text{mW}$ and the others parameters are those in Table 1. (a) Logarithmic negativity versus the normalized detuning for different values of geometrical nonlinearity. The increase of nonlinear parameter enhances the entanglement and shifts its maximum value towards high detuning values (compare the gray dash-dotted line and the solid black line). (b) Logarithmic negativity versus the geometrical nonlinearity for $\frac{\Delta }{{\Omega }_m}=-0.5$. This shows the robustness of the entanglement in the presence of geometrical nonlinearity.

Figure 3

Plot of the logarithmic negativity versus the mean bath occupation for different values of the nonlinear parameter with an input power $P_0=10\text{mW}$. This shows the robustness of entanglement against thermal decoherence depending on the nonlinear term. For $\beta =0.6$ this robustness persists to $n_{th}=2500$ (gray dash-dotted line).