Heisenberg scaling of imaging resolution by coherent enhancement

Classical imaging works by scattering photons from an object to be imaged, and achieves resolution scaling as $1/\sqrt{t}$, with $t$ the imaging time. By contrast, the laws of quantum mechanics allow one to utilize quantum coherence to obtain imaging resolution that can scale as quickly as $1/t$ -- the so-called "Heisenberg limit." However, ambiguities in the obtained signal often preclude taking full advantage of this quantum enhancement, while imaging techniques designed to be unambiguous often lose this optimal Heisenberg scaling. Here, we demonstrate an imaging technique which combines unambiguous detection of the target with Heisenberg scaling of the resolution. We also demonstrate a binary search algorithm which can efficiently locate a coherent target using the technique, resolving a target trapped ion to within 0.3% of the $1/e^2$ diameter of the excitation beam.