• Andreev process
• correlated electron pair
• entanglement
• ghost diffraction
• ghost imaging
• ghost interference
• transfer matrix

The thesis work is set in the framework of quantum imaging, an area of quantum optics that exploits quantum correlations (such as quantum entanglement) to reconstruct images of object, with resolution or other characteristics that exceed the limits of classical optics.
Recently, several experiments demonstrated the possibility of implementing ghost imaging and ghost diffraction schemes with photonic fields.
The goal of this thesis is to analyze diffraction effects and to reconstruct images in the case of electronic sources.
The basic idea is to observe ghost diffraction effects exploiting the quantum correlation of a Cooper pair emitted by a superconductive source in such a way that one electron goes in opposite direction with respect to the other. This idea originates from a formal analogy with systems having biphotonic correlated sources (twin-beams).
After a brief review of the relevant experiments about ghost imaging, ghost interference and electron field emission, an effective model for the emission of Cooper pairs in the vacuum is introduced. This model exploits the matrix element formalism; a perturbation approach is exploited in the hypothesis of weak coupling.
The dynamics of the system in the presence of an object (e.g. a single- or double-slit aperture) is studied, focusing on the non equilibrium steady state and on the far field limit.
A gedanken-experiment is proposed in different configurations, aiming to reconstruct the image or the diffraction pattern through coincidence counting measurements of particles from different directions. The fundamental aspect is that one moves only the second detector, the one that detects particles that do not ``see'' the object, while the other is held fix.
The first obtained result is just formal: various contributions, depending on the parameters of the system, are isolated and analyzed one by one. Then, some limit cases are discussed.The first one is the one with a planar infinite source. The ghost diffraction/interference effect is verified by numerical simulations and the direct analytic calculation of the point-like case, both showing patterns similar to that of classical optics, with the exception of the object-second detector distance being the relevant one. The result is totally analogous to the photonic case.The second setup is the one with a space-limited spherical-symmetric superconductive source. Interference fringes are not observed; instead, in case of not too small objects, one can reconstruct the image of the aperture. The specific cases of single and double slits are discussed.