  The development of hybrid quantum systems is central to the advancement of
emerging quantum technologies, including quantum information science and
quantum-assisted sensing. The recent demonstration of high quality
single-crystal diamond resonators has led to significant interest in a hybrid
system consisting of nitrogen-vacancy center spins that interact with the
resonant phonon modes of a macroscopic mechanical resonator through crystal
strain. However, the nitrogen-vacancy spin-strain interaction has not been well
characterized. Here, we demonstrate dynamic, strain-mediated coupling of the
mechanical motion of a diamond cantilever to the spin of an embedded
nitrogen-vacancy center. Via quantum control of the spin, we quantitatively
characterize the axial and transverse strain sensitivities of the
nitrogen-vacancy ground state spin. The nitrogen-vacancy center is an atomic
scale sensor and we demonstrate spin-based strain imaging with a strain
sensitivity of 3 10^(-6) strain Hz^(-1/2). Finally, we show how this
spin-resonator system could enable coherent spin-phonon interactions in the
quantum regime.
