Spatial Characterization Of Two-Photon States - GAP-Optique

CHAPTER 6
Summary
This thesis characterizes the correlations in two-photon quantum states, both
between photons, and between the spatial and frequency degrees of freedom.
The photon pairs are generated by spontaneous parametric down-conversion
spdc, or by the excitation of Raman transitions in cold atomic ensembles.
Special attention is given to the entanglement of the photon pair in the spatial
degree of freedom, associated to the orbital angular momentum oam. The
main contributions or the thesis are:
A novel matrix formalism to describe the two-photon mode function.
This formalism makes it possible to analytically calculate several features
of the down-converted photons, and reduces the numerical calculation time of
other features, as shown in chapter 1 and reference [41].
Analytical expressions for the purity of the subsystems formed by
a single photon in space and frequency, or by a spatial two-photon
state. These expressions quantify the correlations in the two-photon state,
and make the effect of the various parameters of the spdc process on these
correlations explicit. The thesis presents a set of conditions to suppress or
enhance the correlations between the photons, or between degrees of freedom
in the two-photon state. With these conditions, it is possible to design spdc
sources with specific levels of correlations, for example, sources that generate
pure heralded single photons, or alternatively, maximally entangled states; as
shown in chapter 2 and in references [41, 45].
A selection rule for oam transfer. This selection rule explains several
contradictory measurements of the oam transfer from the pump beam to the
signal and idler photons in spdc. We showed that the oam content of the
pump is completely transferred to the photons emitted in all directions. This
selection rule always holds if all possible emission directions are considered,
for example in collinear configurations, but not necessarily if only a part of
all emission directions is detected. These conditions for the validity of the
selection rule give clear guidelines for the design of sources for protocols that
exploit the multidimensionality of oam, as shown in chapter 3 and references
[71, 72].
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