  Surface acoustic waves (SAWs) are a versatile tool for coherently interfacing
with a variety of solid-state quantum systems spanning microwave to optical
frequencies, including superconducting qubits, spins, and quantum emitters.
Here, we demonstrate SAW cavity optomechanics with quantum emitters in 2D
materials, specifically monolayer WSe$_2$, on a planar lithium niobate SAW
resonator driven by superconducting electronics. Using steady-state
photoluminescence spectroscopy and time-resolved single-photon counting, we map
the temporal dynamics of modulated 2D emitters under coupling to different SAW
cavity modes, showing energy-level splitting consistent with deformation
potential coupling of 30 meV/%. We leverage the large anisotropic strain from
the SAW to modulate the excitonic fine-structure splitting on a nanosecond
timescale, which may find applications for on-demand entangled photon-pair
generation from 2D materials. Cavity optomechanics with SAWs and 2D quantum
emitters provides opportunities for compact sensors and quantum
electro-optomechanics in a multi-functional integrated platform that combines
phononic, optical, and superconducting electronic quantum systems.
