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

Color centers, like the NV center in diamond, have emerged as an essential platform for quantum sensing and quantum networking. Bulk-mode acoustic waves in a crystalline material exert lattice strain through the thickness of the sample, enabling quantum control or hybrid coupling between color centers and a resonator. 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 summation of the X-ray diffraction through the diamond provides both a qualitative measurement of the bulk strain's modal distribution as well as a quantitative measurement of the amplitude. Also, we strain-driven Rabi procession of the NV center spin ensemble provides an additional quantitative measurement of the strain amplitude. As a result, we directly measure the NV spin-strain coupling parameter b by correlating these two sets of measurements at the same spatial position and applied microwave power. Our results demonstrate a unique technique for directly imaging AC lattice strain in nanomechanical structures and provide a direct measurement of a fundamental constant for the NV center defect spin Hamiltonian.