Acoustic diamond resonators with ultrasmall mode volumes

Quantum acoustodynamics (QAD) is a rapidly developing field of research, offering possibilities to realize and study macroscopic quantum-mechanical systems in a new range of frequencies and implement transducers and new types of memories for hybrid quantum devices. Here we propose a novel design for a versatile diamond QAD cavity operating at gigahertz (GHz) frequencies, exhibiting effective mode volumes of about 10^-4λ³. Our phononic crystal waveguide cavity implements a nonresonant analog of the optical lightning-rod effect to localize the energy of an acoustic mode into a deeply subwavelength volume. We demonstrate that this confinement can readily enhance the orbit-strain interaction with embedded nitrogen-vacancy (NV) centers towards the highcooperativity regime and enable efficient resonant cooling of the acoustic vibrations towards the ground state using a single NV. This architecture can be readily translated towards setup with multiple cavities in one- or two-dimensional phononic crystals and the underlying nonresonant localization mechanism will pave the way to further enhance optoacoustic coupling in phoxonic crystal cavities.