Coherent optical two-photon resonance tomographic imaging in three dimensions

Three-dimensional imaging is one of the crucial tools of modern sciences, that allows non-invasive inspection of physical objects. We propose and demonstrate a method to reconstruct a three-dimensional structure of coherence stored in an atomic ensemble. Our method relies on time-and-space resolved heterodyne measurement that allows the reconstruction of a complex three-dimensional profile of the coherence with a single measurement of the light emitted from the ensemble. Our tomographic technique provides a robust diagnostic tool for various atom-based quantum information protocols and could be applied to three-dimensional magnetometry, electrometry and imaging of electromagnetic fields.