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Bulk-mode acoustic waves in a crystalline material exert lattice strainthrough the thickness of the sample, which couples to the spin Hamiltonian ofdefect-based qubits such as the nitrogen-vacancy (NV) center defect in diamond.This mechanism has been previously harnessed for unconventional quantum spincontrol, spin decoherence protection, and quantum sensing. Bulk-mode acousticwave devices are also important in the microelectronics industry as microwavefilters. A key challenge in both applications is a lack of appropriate operandomicroscopy tools for quantifying and visualizing gigahertz-frequency dynamicstrain. In this work, we directly image acoustic strain within NVcenter-coupled diamond thin-film bulk acoustic wave resonators usingstroboscopic scanning hard X-ray diffraction microscopy at the Advanced PhotonSource. The far-field scattering patterns of the nano-focused X-ray diffractionencode strain information entirely through the illuminated thickness of theresonator. These patterns have a real-space spatial variation that isconsistent with the bulk strain's expected modal distribution and amomentum-space angular variation from which the strain amplitude can bequantitatively deduced. We also perform optical measurements of strain-drivenRabi precession of the NV center spin ensemble, providing an additionalquantitative measurement of the strain amplitude. As a result, we directlymeasure the NV spin-stress coupling parameter $b = 2.73(2)$ MHz/GPa bycorrelating these measurements at the same spatial position and appliedmicrowave power. Our results demonstrate a unique technique for directlyimaging AC lattice strain in micromechanical structures and provide a directmeasurement of a fundamental constant for the NV center defect spinHamiltonian.

Stroboscopic X-ray Diffraction Microscopy of Dynamic Strain in Diamond  Thin-film Bulk Acoustic Resonators for Quantum Control of Nitrogen Vacancy  Centers