Spatial Characterization Of Two-Photon States - GAP-Optique

Abstract
The matrix notation, introduced here to describe the two-photon mode
function, reduces the calculation time for several features of the state. In
particular, this notation allows to calculate the purity of different parts of
the state analytically. This analytical solution reveals the effect of each spdc
parameter on the internal correlations, and shows the necessary conditions to
suppress the correlations, or to maximize them.
The description of the oam transfer mechanism shows that the pump oam
is totally transfer to the generated photons. But if only a portion of the generated
photons is detected their oam may not be equal to the pump’s oam. The
experiments described in the thesis show that the amount of oam transfer in
the noncollinear case is tailored by the parameters of the spdc. The analysis
of the spdc case can be extended to other nonlinear processes, such as Raman
transitions, where the specific characteristics of the process determine the
correlations and the oam transfer mechanism.
The results of this thesis contribute to a full description of the correlations
inside the two-photon state. Such a description allows to use the correlations
as a tool to modify the spatial state of the photons. This spatial information,
translated into oam modes, provides a multidimensional and continuum degree
of freedom, useful for certain tasks where the polarization, discrete and bidimensional,
is not enough. To make such future applications possible, it will be
necessary to optimize the tools for the detection of oam states at the single
photon level [15, 16].
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