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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Signal<br />
purity<br />
1<br />
0<br />
(a)<br />
0.1 3<br />
2.3. Correlations between signal and idler<br />
(b)<br />
0.1 Pump waist 3<br />
(c)<br />
0.1<br />
Emission<br />
angle<br />
Figure 2.7: The effect of the emission angle on the signal purity changes depending<br />
on the filters used in space and frequency. When both filters have a finite size like in<br />
(a), the purity increases with the angle of emission, and has a maximum for a fixed<br />
value of the pump beam waist. When the frequency filters are infinitely narrow like<br />
in (b), the dependence of the purity on the angle of emission disappears. When using<br />
narrow filters in space, as in (c), the purity is equal to 1 for a certain pump beam<br />
waist that changes with the angle of emission. The parameters used to generate this<br />
figure are listed in table 2.2.<br />
Table 2.2: The parameters used in figures 2.6 and 2.7<br />
Parameter Figure 2.6 Figure 2.7(a) Figure 2.7(b) Figure 2.7(c)<br />
Crystal liio3 liio3 liio3 liio3<br />
L 1 mm 1 mm 1 mm 1 mm<br />
ρ0 0 ◦ 0 ◦ 0 ◦ 0 ◦<br />
T0 → ∞ → ∞ → ∞ → ∞<br />
wp 400 µm 400 µm 400 µm 400 µm<br />
λp 405 nm 405 nm 405 nm 405 nm<br />
∆λp → 0 → 0 → 0 → 0<br />
ws variable → ∞ 400 µm 400 µm<br />
λ 0 s 810 nm 810 nm 810 nm 810 nm<br />
∆λs 0, 1, 10 nm → ∞ 10 nm → 0 10 nm<br />
ϕs 10 ◦ 5, 10, 20 ◦ 5, 10, 20 ◦ 5, 10, 20 ◦<br />
various values of the emission angle ϕs = ϕi, in degenerate type-i spdc configurations<br />
described by the parameters listed in the second, third and fourth<br />
columns of table 2.2.<br />
Figure 2.7 (a) shows the case of finite spatial and temporal filters. The<br />
purity of the signal photon is always smaller than one, increases with the emission<br />
angle, and has a maximum for a given value of the pump beam waist. For<br />
a very narrow band frequency filter with a ws = wi = 400 µm spatial filter,<br />
figure 2.7 (b) shows how the correlation between the photons is minimal for<br />
small pump beams. The emission angle for this particular crystal length is<br />
irrelevant. Finally, figure 2.7 (c) considers a frequency filter ∆λs = ∆λi = 10<br />
nm with infinitely narrow spatial filters. In this case, maximal purity appears<br />
for each emission angle at a particular value of the pump beam waist.<br />
Conclusion<br />
<strong>Two</strong> photons with two degrees of freedom compose the two-photon state generated<br />
in spdc. The correlations between all four elements affect the state of<br />
single photons or two-photon states with one degree of freedom. Using the pu-<br />
3mm<br />
5º<br />
10º<br />
20º<br />
27