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.