En route to nanoscopic quantum optical imaging: counting emitters with photon-number-resolving detectors.

The fundamental understanding of biological pathways requires minimally invasive nanoscopic optical resolution imaging. Many approaches to high-resolution imaging rely on localization of single emitters, such as fluorescent molecules or quantum dots. Additionally, the exact determination of the number of such emitters in an imaging volume is essential for a number of applications; however, in standard intensity-based microscopy it is not possible to determine the number of individual emitters within a diffraction limited spot without initial knowledge of system parameters. Here we explore how quantum measurements of the emitted photons using photon number resolving detectors can be used to address this challenging task. In the proposed new approach, the problem of counting emitters reduces to the task of determining differences between the emitted photon distribution and the Poisson limit. We show that quantum measurements of the number of photons emitted from an ensemble of emitters enable the determination of both the number of emitters and the probability of emission. This method can be applied for any type of single-photon emitters. The scaling laws of this new approach are presented by the Cramer-Rao Lower Bounds, and this technique has great potential in quantum optical imaging with nanoscopic resolution.