Coherent optical two-photon resonance tomographic imaging in three dimensions

Magnetic resonance imaging is a three-dimensional imaging technique, where a gradient of the magnetic field is used to interrogate spin resonances with spatial resolution. The application of this technique to probe the coherence of atoms with good three-dimensional resolution is a challenging application. We propose and demonstrate an optical method to probe spin resonances via a two-photon Raman transition, reconstructing the 3D-structure of an atomic ensemble's coherence, which is itself subject to external fields. Our method relies on a single time-and-space resolved heterodyne measurement, allowing the reconstruction of a complex 3D coherence profile. Owing to the optical interface, we reach a tomographic image resolution of 14 x 14 x 36 & mu;m(3). The technique allows to probe any transparent medium with a resonance structure and provides a robust diagnostic tool for atom-based quantum information protocols. As such, it is a viable technique for application to magnetometry, electrometry, and imaging of electromagnetic fields. Achieving micrometric resolution in 3D magnetic resonance imaging is a standing challenge, and carries the potential of probing atomic coherences. The authors propose an optical method to probe spin resonances and reconstruct the 3D structure of an atomic ensemble's coherence based on a single measurement of a two-photon Raman transition.