Imaging quantistico di profili rifrattivi non uniformi

The technological exploitation of quantum states and quantum correlations, aiming to overcome the limits of conventional systems, is one of the most active research frontier nowadays. Quantum metrology, in particular aims at the improvement of the resolution or the sensitivity of measurements, beating fundamental limits found in the classical framework. In the quantum optical domain several examples of promising quantum enhanced measurement techniques have been developed: for particle tracking in optical tweezers, sub-shot-noise wide field microscopy, quantum correlated imaging and spectroscopy, beam displacement measurement, remote detection and ranging. One of the most remarkable achievement has been the sensitivity enhancement of the most sophisticated optical instruments currently available, i.e. large scale interferometers for gravitational waves detection. The most fundamental limit to the sensitivity in every optical measurement, when classical states of light are considered, is the ¿Shot Noise Limit¿ (SNL) which scales as the inverse square root of the mean number of photons used. SNL becomes a serious limitation, not only when extremely high sensitivity is required (e.g. in gravitational wave detectors), but also when the energy that can be used is constrained. For instance, in biological and biochemical investigation, probing delicate systems with few photons would be extraordinarily important. In addition, there are systems that are sensitive to the single photon, like retina photo-transduction, photosynthesis or atomic systems. However, quantum mechanics allows the existence of states with strong degree of cooperation among photons, such as entanglement, squeezing and single photon states, which can be produced and manipulated experimentally. Such quantum correlation can be used to surpass the SNL. In my thesis work I have applied quantum metrology techniques to the detection of objects with a non-uniform refractive spatial profile, a problem not yet treated in literature. Classical techniques in this context are commonly used for detection of turbulence or flows, and can be also applied for example to biological imaging of quasi transparent sample and in Gradient index optics (GRIN) lenses testing. A sensible improvement to the classical accuracy can be found using the "Twin Beam State" (TWB). Such state is the result of "Parametric Down Conversion" (PDC), a process in which photons from a pump beam interacting with a nonlinear crystal, are converted into pairs of photons perfectly correlated, due to conservation of energy and momentum. The idea is to use one of the created beams to probe the sample and the other as a reference. Such a scheme allows to exploit the quantum correlation of the two beams to reduce the fluctuations. In particular exploiting the multimode spatial correlation, naturally produced in the PDC process, allows a 2D reconstruction of complex spatial profiles, thus enabling an enhanced imaging. TWB have already been used and proved effective for absorption imaging and interferometry measurements. When dealing with a refractive index gradient both a deflection and a phase shift of the beam must be taken into account and in my work I modelled such an interaction and found that a TWB scheme allows to improve on the SNL. The model developed in the thesis is meant to be followed by a first experimental demonstration of such enhanced measurement scheme. A similar model can be also used to describe wave front