Quantum networking of microwave photons using optical fibers

We describe an adiabatic state-transfer mechanism that allows for high-fidelity transfer of a microwave quantum state from one cavity to another through an optical fiber. The conversion from microwave frequency to optical frequency is enabled by an optomechanical transducer. The transfer process utilizes a combined dark state of the mechanical oscillator and fiber modes, making it robust against both mechanical and fiber loss. We anticipate this scheme being an enabling component of a hybrid quantum computing architecture consisting of superconducting qubits with optical interconnects.

Figure 1

Schematic of the system being modeled. We consider two coupled cavity optomechanical systems, denoted with labels 1 and 2. Each system consists of two cavities, one with a microwave resonant frequency, denoted with red, and cavity operator ${\widehat{a}}_{mw,j}$, and one with an optical frequency, denoted with blue, and cavity operator ${\widehat{a}}_{o,j}$. The cavities are coupled via a common mechanical oscillator with mechanical frequency ${\omega }_m$ and operator ${\widehat{b}}_{m,j}$. This system is then coupled to a second identical cavity optomechanical system via an optical fiber, with operator $\widehat{f}$, that is connected with each optical cavity. This setup allows one to adiabatically transfer a quantum state stored in microwave cavity 1, denoted as ${|\psi \rangle }_1$, to microwave cavity 2 through the mechanical oscillators, optical cavities, and fiber. The adiabatic passage uses a dark state with minimal excitation in the mechanical and fiber modes, making it robust against loss in those modes.

Figure 2

Plot of the state-transfer fidelity for a coherent state $|\alpha ,s\rangle =|1,0\rangle$ (black, top), a squeezed-coherent state $|\alpha ,s\rangle =|1,0.4\rangle$ (red, middle), and a qubit state $\alpha |0\rangle +\beta |1\rangle$ (blue, bottom). Both optical and microwave cavity loss rates are varied equally as specified by the $x$ axis. We set the fiber and optomechanical loss rates to ${\kappa }_f/g={\gamma }_m/g=0.002$, the total time to $gT/2=25$, and the thermal population to $N_{th}=10$.

Figure 3

Plot of the state-transfer fidelity for a coherent state $|\alpha ,s\rangle =|1,0\rangle$ (black, top), a squeezed-coherent state $|\alpha ,s\rangle =|1,0.4\rangle$ (red, middle), and a qubit state $\alpha |0\rangle +\beta |1\rangle$ (blue, bottom). Both fiber and mechanical oscillator loss rates are varied equally as specified by the $x$ axis. We set the optical and microwave loss rates to ${\kappa }_o/g={\kappa }_{mw}/g=0.002$, the total time to $gT/2=25$, and the thermal population to $N_{th}=10$.

Figure 4

Plot of the state-transfer fidelity for a coherent state $|\alpha ,s\rangle =|1,0\rangle$ (black, top), a squeezed-coherent state $|\alpha ,s\rangle =|1,0.4\rangle$ (red, middle), and a qubit state $\alpha |0\rangle +\beta |1\rangle$ (blue, bottom). Here we study the effects of adiabaticity by varying $g$ (solid curves) and $T$ (dashed curves). We set the optical and microwave loss rates to ${\kappa }_o/g={\kappa }_{mw}/g={\kappa }_f/g={\gamma }_m/g=0.05$ for the dashed curves and ${\kappa }_{o}T={\kappa }_{mw}T={\kappa }_{f}T={\gamma }_{m}T=0.05$ for the solid curves. The thermal population is set to $N_{th}=10$. As seen in the figure, only when $gT/2\gtrsim 10$ can we achieve high-transfer fidelity state transfer. This is expected due to requirements for adiabaticity. However, while it is always better to increase the optomechanical coupling rate $g$, one cannot increase $T$ indefinitely as eventually photon loss becomes an issue leading to an optimal transfer time.