Bright and Dark States of Two Distant Macrospins Strongly Coupled by Phonons

Abstract

We study the collective dynamics of two distant magnets coherently coupled by acoustic phonons that are transmitted through a nonmagnetic spacer. By tuning the ferromagnetic resonances of the two magnets to an acoustic resonance of the intermediate, we control a coherent three-level system. We show that the parity of the phonon mode governs the indirect coupling between the magnets: the resonances with odd (even) phonon modes correspond to out-of-phase (in-phase) lattice displacements at the interfaces, leading to bright (dark) states in response to uniform microwave magnetic fields, respectively. The experimental sample is a trilayer garnet consisting of two thin magnetic films epitaxially grown on both sides of a half-millimeter-thick nonmagnetic single crystal. In spite of the relatively weak magnetoelastic interaction, the long lifetimes of the magnon and phonon modes are the key to unveil strong coupling over a macroscopic distance, establishing the value of garnets as a platform to study multipartite hybridization processes at microwave frequencies.

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Plain Language Summary

Quantum processing requires the coherent transfer of state information between distant quantum bits. Transfer by direct coupling is limited to distances where their wave functions overlap. Indirect coupling via a slowly decaying third-party waveform—a tripartite hybridization with vanishing direct coupling elements—promises an enhancement of the maximum separation and thus the size of quantum bit arrays. Here, we demonstrate control of the collective dynamics of two distant magnets mediated by the lattice vibrations, or phonons, in a monolithic device—an important step toward the development of integrated solutions.

In our experiment, two thin ferromagnets sit on either side of a 0.5-mm-thick crystal and communicate with one another by acting as “speakers” and “microphones” for sound waves in the crystal. The system can be brought into tripartite hybridization by carefully tuning the two ferromagnetic resonance frequencies to an acoustic resonance of the whole crystal. There, the entire system of magnetization and lattice can oscillate only coherently.

Illumination of the bound and antibound magnetic states by an external microwave field leads to bright or dark collective modes depending on the sign of the indirect mutual coupling. The phononic system uniquely allows for switching its polarity by shifting parity of the phonon-mode index, which decides if the lattice displacement at the position of the two magnets is out of phase or in phase.

The long lifetimes of magnons and phonons inside insulating garnets are key to unveiling this remote strong coupling between macrospins at room temperature. At low temperatures, we envisage quantum information exchange and distant entanglement of magnons, phonons, and microwave photons. Our work marries the fields of magnonics and phononics, profiting from the best of both worlds.