Remote magnon-phonon entanglement in the waveguide-magnomechanics

TL;DR

The paper addresses the challenge of generating remote magnon–phonon entanglement across spatially separated magnon modes by coupling them to a common waveguide and to local phonon modes in a magnomechanical setting. It develops a linearized, open-system framework using covariance matrices and logarithmic negativity to quantify a spectrum of entanglement types, from two-mode to genuine four-mode cases, and shows that waveguide-mediated dissipative magnon–magnon interactions can outperform coherent couplings for distant entanglement. Key results include stable remote two-mode entanglement between a distant magnon and a local phonon, robust multimode entanglement with a single phonon entangling to N magnons (and vice versa), and genuine four-mode entanglement in a two-magnon–two-phonon system, with entanglement strengths enhanced by dissipative coupling and optimized magnomechanical coupling g. The findings offer an experimentally feasible route to scalable remote entanglement in hybrid quantum systems, with implications for quantum networks and multiplexed quantum information processing across magnonic platforms and beyond.

Abstract

Generating long-distance quantum entanglement is crucial for advancing quantum information processing. In this work, we propose a protocol for generating remote magnon-phonon entanglement in a hybrid waveguide-magnomechanical system, where multiple spatially separated magnon modes couple to a common waveguide while interacting with their respective phonon modes. By applying tailored pulsed drives and engineering the magnon-phonon interactions, our scheme enables the creation of diverse long-distance and dynamically stable entanglement. Beyond basic magnon-phonon two-mode entanglement, it supports genuine multimode entanglement between a single phonon and multiple magnons, bipartite entanglement between a single magnon and multiple phonons, as well as genuine four-mode entanglement involving two magnons and two phonons. Moreover, we show that dissipative magnon-magnon interactions mediated by traveling photons can generate substantially stronger long-distance entanglement than coherent couplings. Our work provides an experimentally feasible scheme for the remote generation of magnon-phonon entanglement.

Figures (6)

• Figure 1: Schematic diagram: $N$ small YIG spheres (magnon modes) are coupled to a common waveguide, and the effective interactions between magnon modes $m_j$ and $m_l$ are mediated by traveling photons propagating in the waveguide. Moreover, the magnon mode $m_j$ in each YIG sphere is driven by a strong control field with Rabi frequency $\Omega_j$. The upper left inset illustrates the magnetostrictive mechanism, where dynamic magnon magnetization (represented by vertical black arrows) induces mechanical deformation in the YIG sphere, thereby coupling to its phonon mode $b_j$. The right panel schematically depicts the mode couplings: magnon mode $m_j$ couples to its phonon mode with strength $g_j$, while $\varphi_{jk}$ denotes the quantum traveling phase between magnon modes $m_j$ and $m_k$, which determines the form of the corresponding interaction.
• Figure 2: (a) Time evolution of the LN quantifying bipartite entanglement between modes $m_2$ and $b_1$, denoted as $E_{m_2|b_1}(t)$, under varying driving-enhanced magnomechanical coupling strength $g$ and quantum phase $\varphi$. (b) LN $E_{m_2|b_1}$ at a fixed time $\tau$ as a function of $g$ under different values of $\varphi$. (c) $E_{m_2|b_1}(\tau)$ as a function of temperature $T$ for different $\varphi$. (d) $E_{m_2|b_1}(\tau)$ in the coupling strength $g$ and decay rate $\kappa$ parameter space. (e) $E_{m_2|b_1}(\tau)$ in the parameter space spanned by magnon detunings $\Delta_1$ and $\Delta_2$. For (b)-(e), the evolution time is set to $\tau=3~\mu$s. The temperature is $T=10$ mK, except for (c). $\kappa/2\pi=3$ MHz except for (d). $\varphi=\pi$ for (d) and (e). $\Delta_1/2\pi=\Delta_2/2\pi=-10$ MHz for (a)-(d). Other parameters are set as $\omega_b/2\pi=10$ MHz, $\epsilon/2\pi=10$ GHz, $\kappa_b/2\pi=100$ Hz, $\gamma/2\pi=1$ MHz, and $g_2=0$.
• Figure 3: [(a), (b)] Schematic diagrams illustrating the entanglement between a single phonon mode and $N$ magnon modes, and between a single magnon mode and $N$ phonon modes, respectively. [(c), (d)] Time evolution of the LNs $E(t)$ under different phases for the models shown in (a) and (b), respectively. [(e), (f)] Dependence of the steady-state LNs $E_{b_1|M}(\tau)$ and $E_{m_1|B}(\tau)$ on the number of modes $N$, corresponding to the models in (a) and (b), respectively. Here, $g/2\pi=2~\mathrm{MHz}$ and $N=4$ for (c) and (d), while $\tau=4~\mu\mathrm{s}$ for (e) and (f). Moreover, $\Delta=-\omega_b$, and all remaining parameters are identical to those used in Fig. \ref{['MPent']}(a).
• Figure 4: [(a), (b)] The time evolution of the LNs $E(t)$ associated with the genuine four-mode entanglement is shown, with $g/2\pi=2$ MHz. [(c), (d)] Dependence of the various LNs $E(\tau)$ at fixed time $\tau=3~\mu$s on the coupling strength $g$. Here, $\Delta=-\omega_b$, and the remaining parameters are identical to those in Fig. \ref{['MPent']}(a).
• Figure 5: [(a), (b)] Time evolution of the LNs $E(t)$ for various bipartitions with $N=4$ and $N=5$, respectively. The coupling strength is set to $g/2\pi=2$ MHz. (c) LNs $E_{m_1|M}$ and $E_{m_1|m_2}$ evaluated at time $\tau=4~\mu$s as a function of the number of YIGs $N$. Here, the other parameters are set to $\varphi=\pi$, $\Delta=-\omega_b$, $\omega_b/2\pi=10$ MHz, $\epsilon/2\pi=10$ GHz, $\kappa_b/2\pi=100$ Hz, $\kappa/2\pi=3$ MHz, $\gamma/2\pi=1$ MHz, and $T=10$ mK.