Quantum imaging by coherent enhancement

Conventional wisdom dictates that to image the position of fluorescent atoms or molecules, one should stimulate as much emission and collect as many photons as possible. That is, in this classical case, it has always been assumed that the coherence time of the system should be made short, and that the statistical scaling $\sim1/\sqrt{t}$ defines the resolution limit for imaging time $t$. However, here we show in contrast that given the same resources, a long coherence time permits a higher resolution image. In this quantum regime, we give a procedure for determining the position of a single two-level system, and demonstrate that the standard errors of our position estimates scale at the Heisenberg limit as $\sim 1/t$, a quadratic, and notably optimal, improvement over the classical case.