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 existing in both types of lattices are robust to a 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.