Spatial Characterization Of Two-Photon States - GAP-Optique

Abstract
In the same way that electronics is based on measuring and controlling the state
of electrons, the technological applications of quantum optics will be based
on our ability to generate and characterize photonic states. The generation
of photonic states is traditionally associated to nonlinear optics, where the
interaction of a beam and a nonlinear material results in the generation of
multi-photon states. The most common process is spontaneous parametric
down-conversion (spdc), which is used as a source of pairs of photons not only
for quantum optics applications but also for quantum information and quantum
cryptography [1, 2].
The popularity of spdc lies in the relative simplicity of its experimental realization,
and in the variety of quantum features that down-converted photons
exhibit. For instance, a pair of photons generated via spdc can be entangled
in polarization [3, 4], frequency [5, 6], or in the equivalent degrees of freedom of
orbital angular momentum, space, and transverse momentum [7, 8, 9, 10, 11].
Standard spdc applications focus on a single degree of freedom, wasting the
entanglement in other degrees of freedom and the correlations between them.
Among the few configurations using more than one degree of freedom are hyperentanglement
[12, 13], spatial entanglement distillation using polarization
[14], or control of the joined spectrum using the pump’s spatial properties [6].
This thesis describes the spatial properties of the two-photon state generated
via spdc, considering the different parameters of the process, and the
correlations between space and frequency. To achieve this goal, I use the purity
to quantify the correlations between the photons, and between the degrees
of freedom. Additionally, I study the spatial correlations by describing the
transfer of orbital angular momentum (oam) from the pump to the signal and
idler photons, taking into account the pump, the detection system and other
parameters of the process.
This thesis is composed of six chapters. Chapter 1 introduces the mode
function, used throughout the thesis to describe the two-photon state in space
and frequency. Chapter 2 describes the correlations between degrees of freedom
or photons in the two-photon state, using the purity to quantify such correlations.
Chapter 3 explains the mechanism of the oam transfer from pump
to signal and idler photons. Chapter 4 describes the effect of different spdc
parameters on the oam transfer in noncollinear configurations, both theoretically
and experimentally. In analogy with the downconverted case, chapter 5
discusses the two-photon state generated via Raman transition, by describing
its mode function, the correlations between different parts of the state, and the
oam transfer in the process. Finally, chapter 6 summarizes the main results
presented by this thesis.
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