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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5.3. <strong>Spatial</strong> entanglement<br />
5.20 is satisfied when L = 333 µm; therefore, the amount of entanglement is<br />
constant. If the length of the cloud increases even more, the position for the<br />
maxima and the minima get inverted. When<br />
<br />
L > R 1 + 2R2<br />
w2 −1/2<br />
p<br />
(5.23)<br />
the entanglement is maximum for transverse emitting configurations ϕ = 90 ◦ , 270 ◦ ,<br />
and minimum for collinear configurations ϕ = 0 ◦ , 180 ◦ . This variation is possible<br />
in Raman transitions where the transversal size of the cloud is comparable<br />
to the longitudinal size.<br />
Another parameter that plays a role in the variation of the amount of<br />
entanglement is the Stokes spatial filter ws. The right side of figure 5.5 shows<br />
the effect of changing the filtering over the amount of entanglement. Very<br />
narrow spatial filters (ws → ∞) diminish both the amount of entanglement<br />
and its azimuthal variability.<br />
Conclusion<br />
As in spdc, the geometrical configuration of the Raman transitions determines<br />
the oam content and the spatial correlations of the generated Stokes and anti-<br />
Stokes photons. The size and shape of the cloud defines the emission angles<br />
for which the correlations are maximum and minimum.<br />
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