Optical tomography can reveal the intrinsic structure of complex objects with high accuracy. Cold atoms are an excellent model physical system for designing new protocols. By combining the gradient echo memory protocol with spatial homodyne detection, our experiment achieved micron-level resolution and excellent shot-noise limited sensitivity for interrogating atomic coherence. We also demonstrated three-dimensional imaging of an external magnetic field, and plan to extend the scheme to ultra-sensitive three-dimensional imaging of microwave fields using Rydberg atoms. Our work pushes the boundaries of quantum sensing for weak fields and unexplored three-dimensional tomographic imaging. The method may also be applied to hot atoms or solid-state probes, such as color centers, or ions, embedded in an interrogated medium.
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