We propose a technique to obtain sub-wavelength resolution using photons from uncorrelated single photon sources. The method employs N photons of wavelength λ spontaneously emitted from N atoms and subsequently detected by N detectors. We demonstrate that for certain detector positions the N-th order correlation function as a function of the first detector position is a pure sinusoidal oscillation with a fringe spacing of λ/N and a contrast of 100%. The result corresponds to an N-fold increase in resolution compared to classical microscopy. Our technique is also capable of imaging a distinct physical object with sub-Rayleigh resolution.
In this paper we study the resolution of images illuminated by sources composed of
N+1 photons in which one non-degenerate photon is entangled with
N degenerate photons. The
N degenerate photons illuminate an object and are collected by an
N photon detector. The signal from the
N photon detector is measured in coincidence with the non-degenerate photon giving rise to a ghost image. We discuss the case of three photons in various configurations and generalize to
N+1. Using the Rayleigh criterion, we find that the system may give an improvement in resolution by a factor of
N compared to using a classical source. For the case that the
N-photon number detector is a point detector, a coherent image is obtained. If the
N-photon detector is a bucket detector, the image is incoherent. The visibility of the image in both cases is 1. In the opposite case in which the non-degenerate photon is scattered by the object, then, using an
N-photon point detector may reduce the Airy disk by a factor of
N.
It has been recently shown that an interferometric measurement may allow for subwavelength resolution of incoherent light. Whereas this holds for noiseless detectors, one could expect that the resolution is in practice limited by the signal-to-noise ratio. Here I present a qualitative assessment of the ultimate resolution limits that can be achieved using noisy detectors. My analysis indeed indicates that the signal-to-noise ratio represents a fundamental limit to quantum imaging, and the reduced resolution scales with the square root of the signal-to-noise ratio. For example, a signal-to-ratio of
20dB is needed to resolve one order of magnitude below the wavelength.