Spatial Characterization Of Two-Photon States - GAP-Optique

CHAPTER 2
Correlations and
entanglement
The two-photon system described in chapter 1 consists of two photons with two
degrees of freedom. Although the mode function deduced fully characterizes the
two-photon state, the degree of correlations between each of its parts (different
subsystems) are not explicit. In this chapter, I use the purity of a subsystem
state to indicate the presence of correlations between it and the rest of the
two-photon state, as shown in figure 2.1. This chapter has three sections.
Section 2.1 describes the main characteristics of the purity, and explains why
it can be used to characterize correlations in composed systems. Section 2.2
describes the spatial part of the two-photon state, and section 2.3 describes
the state of the signal photon. In both sections a discussion about the origin
of the correlations is followed by analytical and numerical calculations of the
purity. The calculations clarify the role of each spdc parameter in the internal
correlations of the two-photon state. By engineering the spdc process, it is
possible to tailor, and even to suppress correlations between different degrees
of freedom or between different photons. Chapter 3 considers the spatial part
of the two-photon state, after the correlations between space and frequency are
suppressed.
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