Imaging moving atoms by holographically reconstructing the dragged slow light

The propagation of light in moving media is dragged by atomic motion. The light-drag effect can be dramatically enhanced by reducing the group velocity with electro-magnetically induced transparency (EIT). We develop a systematic procedure to accurately reconstruct the complex wavefront of the slow light with single-shot measurements, enabling precise, photon shot-noise limited spectroscopic measurements of atomic response across EIT even in presence of generic atomic number fluctuations. Applying the technique to an expanding cloud of cold atoms, we demonstrate simultaneous inference of the atomic density distribution and the velocity field from the complex imaging data. This inline imaging technique may assist a wide range of cold atom experiments to access spectroscopic and phase space information with in situ and minimally destructive measurements.