Complex-valued three-dimensional atomic spectroscopy with Gaussian-assisted inline holography - Xing Huang; Yuzhuo Wang; Jian Zhao; Saijun Wu (Physical Review Research)
When a laser-cooled atomic sample is optically excited, the envelope of coherent forward scattering can often be decomposed into a few complex Gaussian profiles. The convenience of Gaussian propagation helps address key challenges in digital holography. In this paper, we develop a Gaussian-decomposition-assisted approach to inline holography for single-shot, simultaneous measurements of absorption and phase-shift profiles of small atomic samples sparsely distributed in three dimensions. The samples' axial positions are resolved with micrometer resolution and their spectroscopy are extracted from complex-valued images recorded at various probe frequencies. The phase-angle readout is not only robust against transition saturation but also insensitive to atom-number and optical-pumping-induced interaction-strength fluctuations. Benefiting from such features, we achieve hundred-kHz-level single-shot resolution to the transition frequency of a ^{87}Rb D_{2} line, with merely hundreds of atoms. We further demonstrate single-shot three-dimensional field sensing by measuring local light shifts to the atomic array with micrometer spatial resolution.