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 $14\times14\times36$ $μ\mathrm{m}^3$. 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.