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

Bulk-mode acoustic waves in a crystalline material exert lattice strain through the thickness of the sample, which couples to the spin Hamiltonian of defect-based qubits such as the nitrogen-vacancy (NV) center defect in diamond. This mechanism has been previously harnessed for unconventional quantum spin control, spin decoherence protection, and quantum sensing. Bulk-mode acoustic wave devices are also important in the microelectronics industry as microwave filters. A key challenge in both applications is a lack of appropriate operando microscopy tools for quantifying and visualizing gigahertz-frequency dynamic strain. In this work, we directly image acoustic strain within NV center-coupled diamond thin-film bulk acoustic wave resonators using stroboscopic scanning hard X-ray diffraction microscopy at the Advanced Photon Source. The far-field scattering patterns of the nano-focused X-ray diffraction encode strain information entirely through the illuminated thickness of the resonator. These patterns have a real-space spatial variation that is consistent with the bulk strain's expected modal distribution and a momentum-space angular variation from which the strain amplitude can be quantitatively deduced. We also perform optical measurements of strain-driven Rabi precession of the NV center spin ensemble, providing an additional quantitative measurement of the strain amplitude. As a result, we directly measure the NV spin-stress coupling parameter $b = 2.73(2)$ MHz/GPa by correlating these measurements at the same spatial position and applied microwave power. Our results demonstrate a unique technique for directly imaging AC lattice strain in micromechanical structures and provide a direct measurement of a fundamental constant for the NV center defect spin Hamiltonian.