Entangling a nanomechanical resonator and a superconducting microwave cavity

We propose a scheme able to entangle at the steady state a nanomechanical resonator with a microwave cavity mode of a driven superconducting coplanar waveguide. The nanomechanical resonator is capacitively coupled with the central conductor of the waveguide and stationary entanglement is achievable up to temperatures of tens of milliKelvin.

Figure 1

Schematic representation of the capacitive coupling between a nanomechanical resonator and a superconducting coplanar microwave cavity. (a) Plan view of the device; the dark region is etched away and the resulting cantilever is metalized to form one plate of a capacitor. (b) Equivalent circuit.

Figure 2

(Color online) Zero-temperature logarithmic negativity for (a) driving on the blue sideband and (b) driving on the red sideband. $\overline{\kappa }=\kappa \times {10}^{-6}{\mathrm{s}}^{-1}$, ${\overline{\gamma }}_m={\gamma }_m\times {10}^{-6}{\mathrm{s}}^{-1}$.

Figure 3

(Color online) (a) Typical temperature, $T$ (mK) dependence of the logarithmic negativity (in this case, driving on the blue sideband with $\kappa ={\gamma }_m=5\times {10}^4{\mathrm{s}}^{-1}$). (b) $T_c$ (mK) as a function of damping for driving on the blue sideband. (c) $T_c$ (mK) as a function of damping for driving on the red sideband. $\overline{\kappa }=\kappa \times {10}^{-6}{\mathrm{s}}^{-1}$, ${\overline{\gamma }}_m={\gamma }_m\times {10}^{-6}{\mathrm{s}}^{-1}$.