Optomechanical Transducers for Long-Distance Quantum Communication

We describe a new scheme to interconvert stationary and photonic qubits which is based on indirect qubit-light interactions mediated by a mechanical resonator. This approach does not rely on the specific optical response of the qubit and thereby enables optical quantum interfaces for a wide range of solid state spin and charge based systems. We discuss the implementation of state transfer protocols between distant nodes of a quantum network and show that high transfer fidelities can be achieved under realistic experimental conditions.

Figure 1

(a) A quantum network where spin or charge based qubits and photons are coupled by an optomechanical transducer (OMT). (b) At each node the OMT mediates coherent coupling between the qubit and photons in the fiber, but also adds noise and loss channels in form of mechanical dissipation (${\Gamma }_{\mathrm{th}}$) and intrinsic cavity decay (${\kappa }_0$). See text for details.

Figure 2

(a) Effective single-qubit decay $\Gamma$ as a function of $G$ and ${\omega }_q$ for the parameters ${\kappa }_f=0.05{\omega }_R$, ${\kappa }_0={\gamma }_m=0$, with cavity and resonator being in resonance (${\Delta }_c={\omega }_R$) at $G=1.5{\kappa }_f$. The dotted line indicates the control pulse shown in (c). (b) Pulse shapes for ${\Gamma }_{1,2}(t)$ which implement a perfect state transfer $v_2(t_f)\simeq 1$ as described in the text. (c) Control pulses for $G_{1,2}(t)$ which generate the ${\Gamma }_{1,2}(t)$ shown in (b). The dashed lines indicate the corresponding noise terms which appear in ${\mathcal{L}}_{\mathrm{noise}}$. The parameters used for this plot are ${\omega }_q^{1,2}={\omega }_R-1.5{\kappa }_f$, ${\Gamma }_{th}/{\kappa }_f=0.01$ and all others as in (a).

Figure 3

(a) State transfer fidelity obtained from a numerical simulation of Eq. (4) for the control pulses shown in Fig. 2 and ${\kappa }_0=0$. (b) The same plot for ${\Gamma }_{\mathrm{th}}=0$ but including an exponential loss of qubit coherence $\sim e^{-t/T_2}$ during the transfer. From these two plots we extract the numerical coefficients ${\mathcal{C}}_1\approx 4$, ${\mathcal{C}}_2\approx 1.4$, and ${\mathcal{C}}_3\approx 7.5$, which appear in the approximate expression of $\mathcal{F}$ given in Eq. (7).

Figure 4

Scalable quantum networks based on multimode OM transducers. At each node the three cavities are modeled by $H_c=\sum _{n=1}^3{\Delta }_n{c}_n^{†}{c}_n+J(c_s^{†}{c}_3+\mathrm{H}.\mathrm{c}.)$ where $J$ is the tunneling coupling of mode $c_3$ with $c_s=(c_1+c_2)/\sqrt{2}$. The driving field applied through the “control fiber” excites the asymmetric mode $c_a=(c_1-c_2)/\sqrt{2}$ such that for ${\Delta }_1={\Delta }_2$ we obtain $⟨c_1⟩=-⟨c_2⟩=\alpha$ and $⟨c_3⟩=0$. The motion of the resonator modulates ${\Delta }_1$ and induces a linearized OM coupling as given in Eq. (1) with the empty mode $c=(c_s+c_3)/\sqrt{2}$. Thereby, laser noise from the control fields does not affect the quantum channel and nodes can be selectively activated. The direction of the driving field is used to send photons into different directions to connect any two nodes of a large network.