NOON-state generation and superresolved interference in a double-slit experiment

Abstract

Maximally entangled NOON states are proposed to be generated with $N$ independent photons and a fixed double-slit in the Young's interference experiment. A strict condition is required that these photons have to be arranged in a straight line and separated from each other by certain equal distances. The initial product state turns into a NOON state of the photons at the double-slit, after $N$-photon postselected measurements. With a spatially random laser beam, we experimentally investigate the high-order correlation functions to imitate the behavior of the single-photon and $N$-photon wave packets of the NOON states. Since the $N$-photon wave packet is the product of $N$ single-photon wave packets, two methods are adopted to observe the superresolved fringes. The first method is to use the product of the second-order correlation functions. The second one is to measure the $2N\mathrm{th}$-order correlation functions. In the both cases, the superresolved fringes of up to fourth order are successfully observed.