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 (N-V) center defect in diamond. This mechanism has previously been 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 N-V 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 nanofocused 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 of the N-V center spin ensemble, providing an additional quantitative measurement of the strain amplitude. As a result, we directly measure one of the six N-V spin-stress coupling parameters, $b=2.73(2)$ 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 N-V center defect spin Hamiltonian.