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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2. Correlations and entanglement<br />
Filters<br />
0nm<br />
1nm<br />
10nm<br />
→∞<br />
0.1 Collection mode 1mm<br />
<strong>Spatial</strong><br />
purity<br />
Figure 2.3: The spatial purity increases by filtering the state in space or frequency.<br />
For the parameters chosen here, the bandwidth of the generated photons is smaller<br />
than 10 nm, making 10 nm filters equivalent to infinitely broad ones. The parameters<br />
used to generate this figure are listed in table 2.1.<br />
<strong>Spatial</strong><br />
purity<br />
1<br />
0<br />
0.1<br />
Pump<br />
waist<br />
30m 462m Emission<br />
angle<br />
1mm 0.1 Collection mode 1mm<br />
1<br />
0.2<br />
1º<br />
5º<br />
(a) (b) (c)<br />
0º<br />
0.1 1mm<br />
Pump<br />
waist<br />
20m 500m Figure 2.4: For the values reported in reference [6], figure (a) shows that the purity<br />
is smaller than 1. This fact is in agreement with the implicit spatio-temporal<br />
correlations reported in the reference. For the values reported in references [46] and<br />
[31], figures (b) and (c) show that the purity has its maximum value. There was no<br />
evidence of spatio-temporal correlations in the results reported in these references.<br />
In all three cases, it is possible to modify the value of the purity by tailoring the spdc<br />
parameters. The parameters used to generate this figure are listed in table 2.1.<br />
10 nm interference filters.<br />
For the noncollinear configuration in reference [31], the highly focused pump<br />
beam is responsible for the lack of correlations. The figure shows that for lessfocused<br />
pump beams the purity decreases as the correlations between space<br />
and frequency become more important.<br />
The correlations between frequency and space in the two-photon state discussed<br />
in this section, suggest that a complete description of the correlations<br />
between the generated photons, should take into account both degrees of freedom,<br />
as the next section discusses.<br />
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