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

Abstract

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 molecule or quantum dot. Exact determination of the number of such emitters in an imaging volume is essential for a number of applications; however, in a commonly employed intensity-based microscopy it is not possible to distinguish individual emitters 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 photons 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 emitters, including Raman and infrared emitters, which makes it a truly universal way to achieve super-resolution optical imaging. The scaling laws of this new approach are presented by the Cramer-Rao Lower Bounds and define the extent this technique can be used for quantum optical imaging with nanoscopic resolution.