Imaging properties of an 'interaction-free' microscope

Abstract

The possibility of measuring the state of a quantum system by the non-observance of a result due to the existence of that state leads to setups that allow optical imaging with much less photons interacting with an object than is classically necessary. In 1981 Dicke considered "interaction-free" quantum measurements by analyzing the change of an atomic wave function by the non-scattering of a photon by the atom. Elitzur and Vaidman (EV) extended these results to the detection of an object via the change in the interference of a photon even though there is no direct interaction between the object and the photon, an "interaction-free" measurement (IFM). At most the efficiency of the EV scheme is that half of the photons entering the system leads to an IF measurement. This scheme has been first realized by Kwiat, et al. in 1995 and led to the suggestion, and later, the implementation of an "interaction-free" imaging setup.
High photon flux usually limits the applicability of current optical setups to image biological or photosensitive objects. The possibility of low-photon flux imaging necessitates characterizing such an implementation. In this paper we simulate the behavior of photons in a computer from first principles with the observed quantum mechanical behavior as they are detected on a screen from a lens. We obtain the point spread function (PSF) of a lens in a low photon, "interaction-free" regime through simulation.