Entanglement distribution among distinct mechanical nodes in a quantum network

Abstract

We propose two schemes to achieve remote entanglement distribution between two mechanical nodes with a significant frequency mismatch, based on optomechanical systems. The first scheme utilizes the physical mechanism to redistribute the quantum entanglement initially established in a dispersively-coupled optomechanical system with a megahertz mechanical resonance to a distant optomechanical system which embodies the tripleresonant interaction induced by the scattering of gigahertz mechanical phonon. We also provide a fast optical pulse protocol to realize the long-distance entanglement distribution from the optomechanical system supporting the gigahertz mechanical mode to the megahertz mechanical mode included in a distant optomechanical system. Specifically, these two schemes respectively demonstrate the megahertz-to-gigahertz and gigahertz-tomegahertz entanglement distribution in the quantum network of optical photons and phonons. This work may facilitate the application of various mechanical systems in hybrid quantum network-based quantum technologies and fundamental physical research.

Figures (6)

• Figure 1: Schematic diagrams of the ($\mathrm{a}$) hybrid system and ($\mathrm{b}$) physical mechanism to realize the remote megahertz-to-gigahertz mechanical entanglement distribution. Inset 1: Entanglement generation process. The down-conversion sideband ($\omega_l-\omega_b$) of the optical cavity mode ($c$) can couple to the WGM ($a_1$) via the mediation of optical waveguide. Inset 2: Entanglement distribution process. The optical WGM ($a_2$) is resonantly pumped by a laser to activate the beam-splitter type interaction.
• Figure 2: Density plot of steady-state (a) $E_{a_1b}$ and (b) $E_{mb}$ versus the detunings $\tilde{\Delta}_c$ and $\Delta_1$; (c) $E_{a_1b}$ and (d) $E_{mb}$ versus the detuning $\tilde{\Delta}_c$ and the coupling efficiency $\eta$. Note that we take $\eta=1$ in ($\mathrm{a}$) and ($\mathrm{b}$), and $\Delta_1/\omega_b=-1$ in ($\mathrm{c}$) and ($\mathrm{d}$). See main text for other plotting parameters.
• Figure 3: Density plot of bipartite entanglement ($\mathrm{a}$) $E_{cb}$, ($\mathrm{b}$) $E_{a_1b}$ and ($\mathrm{c}$) $E_{mb}$; and quantum excitations ($\mathrm{d}$) $\delta n_{b}$, ($\mathrm{e}$) $\delta n_{a_1}$ and ($\mathrm{f}$) $\delta n_{m}$ versus the environmental temperatures $T_1$ and $T_2$. Note that here we take $\eta=0.9$, $\tilde{\Delta}_c/\omega_b=0.75$, and $\Delta_1/\omega_b=-1$. The other parameters are the same as those used in Fig. \ref{['fig2']}.
• Figure 4: Schematic diagrams of the ($\mathrm{a}$) physical mechanism and ($\mathrm{b}$) hybrid system to realize the remote gigahertz-to-megahertz mechanical entanglement distribution. Inset 1: Entanglement preparation process. A blue-detuned optical pulse is used to activate the quantum entanglement between the optical output temporal mode ($\tilde{C}_1^{\mathrm{out}}$) and the gigahertz mechanical node ($b_1$). Inset 2: Entanglement distribution process. After the long-distance propagation in optical waveguide, the quantum entanglement can be further distributed to megahertz mechanical node ($b_2$) via the beam-splitter interaction activated by the red-detuned pulse.
• Figure 5: Sketch of the transmission loss model.