Remote magnon-phonon entanglement in the waveguide-magnomechanics

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 magnomechanical 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 remote entanglement than coherent couplings. Our work provides an experimentally feasible scheme for the remote generation of magnon-phonon entanglement.

💡 Research Summary

The paper proposes a versatile protocol for generating long‑distance continuous‑variable entanglement between magnon and phonon modes in a hybrid waveguide‑magnomechanical architecture. The system consists of N yttrium‑iron‑garnet (YIG) spheres, each supporting a magnon mode (mj) and a mechanical vibration (phonon bj). All spheres are coupled to a common micro‑strip waveguide, which mediates both coherent and dissipative magnon‑magnon interactions via traveling microwave photons. The magnon‑phonon coupling within each sphere arises from magnetostrictive forces and can be enhanced by strong microwave drives (Ωj), leading to an effective linearized interaction strength gj.

The total Hamiltonian is split into three parts: (i) the free magnomechanical Hamiltonian Hs, (ii) the waveguide‑mediated magnon‑magnon interaction HI with complex coupling √κjκl e^{iϕjl}, and (iii) the external drive Hd. The phase ϕjl, determined by the propagation distance Lj l, controls the balance between coherent (∝ sin ϕ) and dissipative (∝ cos ϕ) coupling channels. After linearizing around the strong drive, the dynamics are described by a set of quantum Langevin equations that can be written compactly as \dot{u}(t)=A u(t)+ε_in(t), where u(t) contains the quadratures of all magnon and phonon modes, A is a 4N×4N drift matrix, and ε_in(t) represents Gaussian noise with diffusion matrix D.

Because the system remains Gaussian, its full quantum state is captured by the covariance matrix V(t), which obeys the Lyapunov equation \dot{V}=A V+V A^T+D. Starting from thermal states (mean occupations \bar n for magnons and \bar n_b for phonons), V(t) is obtained numerically. Entanglement is quantified using the logarithmic negativity (LN). For bipartite subsystems a 4×4 reduced covariance matrix is partially transposed, and the smallest symplectic eigenvalue yields the LN. The same procedure is extended to multipartite partitions (e.g., one‑to‑N, N‑to‑1, and two‑to‑two mode entanglement).

Key results are demonstrated through extensive simulations. First, for N=2 the authors show remote magnon‑phonon entanglement between m2 and b1. The LN reaches steady values of ≈0.2–0.3 when the traveling‑photon phase is set to ϕ=π, corresponding to purely dissipative magnon‑magnon coupling. This configuration is markedly more robust against thermal noise, maintaining LN≈0.04 even at 200 mK, whereas purely coherent coupling (ϕ=π/2) quickly loses entanglement with increasing temperature. The entanglement improves with larger enhanced coupling g (≈1.5–2 MHz) and higher magnon decay rate κ (≈3–4 MHz), and tolerates moderate detuning (Δ≈−ω_b).

Second, the protocol is generalized to multipartite scenarios. When all magnons share identical detuning Δ and decay κ, a single phonon can become entangled with N magnons (E_{b|m1…mN}) and, conversely, a single magnon can entangle with N phonons (E_{m|b1…bN}). Again, the dissipative phase ϕ=π yields the strongest LN, and the entanglement persists as N increases up to at least five, indicating scalability of the scheme for quantum networks that require many‑node correlations.

Third, genuine four‑mode entanglement is explored in a two‑magnon, two‑phonon configuration. By exploiting the same waveguide‑mediated dissipative channel, the authors obtain LN≈0.15 for the bipartition (m1 m2)|(b1 b2), confirming that the system can host true multipartite continuous‑variable entanglement beyond simple pairwise correlations.

All simulations employ experimentally realistic parameters: magnon frequencies ω_j/2π≈10 GHz, phonon frequency ω_b/2π≈10 MHz, magnon decay κ/2π≈3 MHz, phonon decay κ_b/2π≈100 Hz, intrinsic magnon loss γ/2π≈1 MHz, and bare magnetostrictive coupling ˜g_j tunable from 0 to 60 mHz. Strong drives amplify the effective magnon‑phonon coupling to the MHz regime, a range already demonstrated in recent YIG‑cavity experiments. Consequently, the authors argue that the proposed scheme is within current experimental reach.

A particularly insightful finding is that the dissipative magnon‑magnon interaction mediated by traveling photons can outperform coherent coupling in generating remote entanglement. This suggests a new design principle for quantum communication architectures: engineering loss channels (via phase control) to act as resources rather than liabilities. The work thus opens a pathway toward building distributed quantum networks where distant mechanical resonators (phonons) are entangled through magnetic excitations, offering a hybrid platform that combines the long coherence of magnons with the versatility of phononic quantum memories.