Reversible Optical-to-Microwave Quantum Interface

We describe a reversible quantum interface between an optical and a microwave field using a hybrid device based on their common interaction with a micromechanical resonator in a superconducting circuit. We show that, by employing state-of-the-art optoelectromechanical devices, one can realize an effective source of (bright) two-mode squeezing with an optical idler (signal) and a microwave signal, which can be used for high-fidelity transfer of quantum states between optical and microwave fields by means of continuous variable teleportation.

Figure 1

Schematic description of the proposed optical-microwave interface. Alice mixes the optical cavity output with the input optical field she has to transfer, and communicates the results of her Bell measurements to Bob. The output state of the microwave field in Bob’s hands is a faithful copy of the optical input field state when the optical-microwave cavity outputs are strongly entangled by their common interaction with the mechanical resonator, and Bob correctly displaces its state conditioned to Alice’s measurement results. The scheme can be reversed by exchanging the roles of Alice and Bob: Bob performs the Bell measurements on microwave fields and the state of an input microwave field is teleported onto the optical output in Alice’s hands after communication of the measurement results and the conditional displacement.

Figure 2

$E_N$ at four different values of the normalized inverse of the bandwidth $ϵ=\tau {\omega }_m$ vs the normalized frequency ${\Omega }_w/{\omega }_m$, at fixed central frequency of the optical output mode ${\Omega }_c=-{\omega }_m$. The optical and microwave cavity detunings have been fixed at ${\Delta }_c=-{\Delta }_w=-{\omega }_m$, while the other parameters are ${\omega }_m/2\pi =10$ MHz, $Q\equiv {\omega }_m/{\gamma }_m=1.5\times {10}^5$, ${\omega }_w/2\pi =10\mathrm{GHz}$, ${\kappa }_w=0.04{\omega }_m$, $P_w=42\mathrm{mW}$, $m=10\mathrm{ng}$, $T=15\mathrm{mK}$, $d=100\mathrm{nm}$, $\mu =0.013$, where $d$ and $\mu$ are parameters of the equivalent capacitor defined in the Supplemental Material [22]. This set of parameters is analogous to that of Teufel et al. [19] for the MC and MR, except that we have considered a lower mechanical quality factor, and a heavier mass, in order to take into account the presence of the coating. We have then assumed an OC of length $L=1\mathrm{mm}$ and damping rate ${\kappa }_c=0.04{\omega }_m$, driven by a laser with wavelength ${\lambda }_{0c}=810\mathrm{nm}$ and power $P_c=3.4\mathrm{mW}$.

Figure 3

Teleportation fidelity $F$ at four different values of $ϵ=\tau {\omega }_m$ vs ${\Omega }_w/{\omega }_m$ and for the cat-state amplitude $\alpha =1$. The other parameters are as in Fig. 2.

Figure 4

Teleportation fidelity $F$ at four different values of $ϵ=\tau {\omega }_m$ vs the cat-state amplitude $\alpha$, at a fixed central frequency of the microwave output mode ${\Omega }_w={\omega }_m$ and fixed temperature $T=15\mathrm{mK}$. The other parameters are as in Fig. 2.