Quantum router of silicon-vacancy centers via a diamond waveguide

Abstract

As a key component of quantum networks, the quantum router distributes quantum information among different quantum nodes. The silicon-vacancy (SiV) center in diamond offers a promising platform for quantum technology due to its strong strain-induced coupling with phonons. However, the development of a practical quantum router faces the challenges of achieving long-range entanglement and suppressing decoherence. Here, we propose a non-Markovian quantum router based on a diamond waveguide embedded with an array of SiV centers as the quantum nodes. Unlike conventional channel-switching methods, our design enables parallel quantum-state transfer from a single input node to multiple target nodes, analogous to a classical WiFi router. We demonstrate that persistent entanglement and suppressed decoherence of the SiV centers over long distances are achievable when bound states are present in the energy spectrum of the total system formed by the SiV centers and the phonon waveguide. Our scheme enriches the implementation of quantum routing and prompts the development of solid-state quantum networks.

Figures (6)

• Figure 1: (a) Schematic of $N$ SiV centers embedded in a one-dimensional phonon waveguide. (b) In a magnetic field, the SiV center is seen as a four-level system, whose sublevels are $\ket{i}$ ($i=1,\ldots,4$). Transition between sublevels with different orbital degrees of freedom of $\ket{1}\leftrightarrow \ket{3}$ or $\ket{2} \leftrightarrow \ket{4}$ has transition frequency $\omega_{0}$. At zero magnetic field, there are two orbital branches in the ground state of SiV center, which can be viewed as a two-level system denoted by $\ket{1}$ and $\ket{3}$.
• Figure 2: (a) Energy spectrum of the total system obtained by numerically solving Eq. \ref{['Y']}. (b) Time evolution of the concurrence $C(t)$ obtained by numerically solving Eq. \ref{['c']} for different values of $\omega_0$. The orange, blue, and purple curves correspond to the cases with two, one, and zero bound states, respectively. The red dotted lines represent the analytical results of Eq. \ref{['c2']}, showing a good agreement with the numerical results. (c) Evolution of concurrence $C(t)$ when a random fluctuation $\chi$ is added on the frequency $\omega_0=\Delta$ of the SiV centers. The red and green dashed lines are the average values obtained by averaging over 100 random configurations when $\chi=[-0.5\Delta,0.5\Delta]$ and $[-\Delta,5\Delta]$. The purple and orange regions are their respective variations. The blue solid lines are the fluctuation-free results. We use $\omega_c=7\Delta$, $S=100\,\mathrm{nm} ^2$, $d/2\pi \approx 4\,\mathrm{PHz}$, $\delta x\equiv |x_1-x_2|=10\,\mathrm{nm}$, $v \approx 1 \times 10^4 \, \text{m/s}$, and $N=2$.
• Figure 3: Evolution of the state-transfer fidelity obtained from numerical solutions of Eq. \ref{['c']} for different values of $\omega_0$. The purple, green, and red curves denote the results with zero, one, and two bound states, respectively. The gray dots denote analytical results of Eq. \ref{['c2']}, which show a good agreement with the numerical results. The parameters are the same as those in Fig. \ref{['F2']}.
• Figure 4: (a) Energy spectrum, (b) long-time concurrence $C(\infty)$, and (c) long-time state-transfer fidelity $F(\infty)$ as a function of the inter-SiV distance $\delta x$ when $\omega_0=\Delta$. In (b) and (c), the green curves indicate the maximum and minimum values derived from Eq. \ref{['c2']} and the red dots denote the numerical results obtained from Eq. \ref{['c']}. The green regions cover the values of $C(\infty)$ and $F(\infty)$ during their persistent oscillation. Other parameters are the same as Fig. \ref{['F2']}.
• Figure 5: (a) Energy spectrum of total system. (b) Time evolution of bipartite entanglement $C_{12}(t)$ and $C_{13}(t)$. (c) Time evolution of the fidelity $F_{12}(t)$ and $F_{13}(t)$. In (b) and (c), the cyan dashed curves correspond to results from Eq. \ref{['c']}, while the red solid curves are derived from Eq. \ref{['c3']}, both for the case with three bound states when $\omega_0=\Delta$. For comparison, the black dashed lines from Eq. \ref{['c3']} show the case without bound states when $\omega_0=2\Delta$. The parameters are the same as in Fig. \ref{['F2']} except for $\delta x = 10.5\mathrm{nm}$.