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