Chiral spin-phonon bound states and spin-spin interactions with phononic lattices

Designing unconventional interactions between single phonons and spins is fascinating for its applications in quantum phononics. Here, we propose a reliable scheme for coupling spins and phonons in phononic dimer and trimer lattices, with the combination of solid-state defects and diamond phononic (optomechanical) crystals. The dimer and trimer lattices used are an array of coupled phononic cavities with spatially modulated hopping rates. We predict a series of unconventional sound-matter interaction phenomena in this hybrid quantum system. In the dimer lattice, we show the formation of chiral spin-phonon bound states and topology-dependent phononic collective radiation. While in the trimer lattice, chiral bound states still exist and the spin relaxation is sublattice-dependent. The chiral bound states existed in both types of lattices are robust to large amount of disorder, which can mediate chiral and robust spin-spin interactions. This work provides a promising platform for phonon-based quantum information processing and quantum simulation.