Microresonators enhancing long-distance dynamical entanglement generation in chiral quantum networks

Chiral quantum networks provide a promising route for realizing quantum information processing and quantum communication. Here we describe how two distant quantum nodes of chiral quantum network become dynamically entangled by a photon transfer through a common one-dimensional chiral waveguide. We harness the directional asymmetry in chirally coupled single-mode ring resonators to generate an entangled state between two atoms. We report a concurrence of up to 0.969, a huge improvement over 0.736, which was suggested and analyzed in great detail in Gonzalez-Ballestero et al. [Phys. Rev. B 92, 155304 (2015)]. This significant enhancement is achieved by introducing microresonators which serve as an efficient photonic interface between light and matter. The robustness of our protocol to experimental imperfections such as fluctuations in internodal distance, imperfect chirality, various detunings, and atomic spontaneous decay is demonstrated. Our proposal can be utilized for long-distance entanglement generation in quantum networks, which is a key ingredient for many applications in quantum computing and quantum information processing.

Figure 1

Model of a chiral quantum network. Each node of the network comprises one qubit coupled to a single-mode microtoroidal resonator. Information is transferred between the nodes via a photon in the chiral waveguide.

Figure 2

(a) Optimal entanglement generation for $g_1\approx 0.126{\gamma }_R$, $g_2\approx 0.277{\gamma }_R$. Various fidelities comparing the state with $|{\mathrm{\Psi }}^{\pm }\rangle$ and $|ge\rangle$ are also plotted. (b) Maximum concurrence $C_{\max }$ against $g_1$ and $g_2$. (c) Maximum transfer fidelity ${\mathcal{F}}_{3,\max }$ against $g_1$ and $g_2$.

Figure 3

Analytical approximation of concurrence in the long-time regime. Numerical solution was obtained by simulating the master equation in Eq. (3), using the same parameters as in Eq. (10) and neglecting atomic decays (${\mathrm{\Gamma }}_1={\mathrm{\Gamma }}_2=0$). Optimal entanglement generation for $g_1\approx 0.126{\gamma }_R$, $g_2\approx 0.277{\gamma }_R$. Good approximation is obtained for ${\gamma }_{R}t\gtrsim 10$, which includes the maxima.

Figure 4

(a) Variation of $C_{\text{max}}$ with internodal distance $D$. (b) Variation of $C_{\text{max}}$ at $D=0.5\lambda$ with chirality $\chi$ (defined in main text). (c) $C_{\text{max}}$ against $D$ and $\chi$. In (a) and (b), the cavity-atom couplings are set at the optimal values $g_1=0.126{\gamma }_R$, $g_2=0.277{\gamma }_R$.

Figure 5

Effect of random detunings on concurrence $C_{\text{max}}$. (a) Independent detunings on cavity and atom separately. (b) Effect of combined detuning on both cavity and atom, averaged over 20 runs. The cavity-atom couplings are set at the optimal values $g_1=0.126{\gamma }_R$, $g_2=0.277{\gamma }_R$.

Figure 6

Effect of atomic losses on concurrence. For the $C_0$ curve, the cavity-atom couplings are set at the optimal values $g_1=0.126{\gamma }_R$, $g_2=0.277{\gamma }_R$. For the $C_{\text{opt}}$ curve, separate optimization is done for different $\mathrm{\Gamma }$.

Figure 7

Further enhancement in entanglement generation when ${\gamma }_{R1}\ne {\gamma }_{R2}$. (a) Optimal conditions for ${\gamma }_{R1}\ne {\gamma }_{R2}$ without cavity: ${\gamma }_{R2}=3.88{\gamma }_{R1}$. The solid blue curve is the result obtained in Ref. [31]. (b) Optimal conditions for ${\gamma }_{R1}\ne {\gamma }_{R2}$ with cavity: ${\gamma }_{R2}=4.82{\gamma }_{R1}$, $g_1=2.21{\gamma }_{R1}$, $g_2=2.11{\gamma }_{R1}$.

Figure 8

Nonchiral scheme for entanglement generation, with ${\gamma }_L={\gamma }_R$. (a) Concurrence and various fidelities comparing the state with $|{\mathrm{\Psi }}^{\pm }\rangle$ and $|ge\rangle$. (b) Maximum concurrence $C_{\text{max}}$ against $g_1$ and $g_2$. (c) $C_{\text{max}}$ against internodal distance $D$. In (a) and (c), the optimal parameters $g_1=0.00410{\gamma }_R,g_2=0.00170{\gamma }_R$ are used.