Diploma thesis

3.3 Generating pure heralded single photons
We investigate different possibilities to generate pure heralded single photon states
with waveguided PDC. All plots and Schmidt decompositions, in this chapter and
the whole thesis, have been performed with consideration of the sinc term in the
two-photon state (Formula 3.22). All pump widths given in this section describe the
width of the pump intensity. This serves the purpose to make this data comparable
to units used in the laboratory.
3.3.1 Spectral filtering
The oldest and most straightforward method to create spectrally decorrelated photon
pairs is the application of spectral filtering. Most nonlinear crystals exhibit a
phasematching contour with a negative slope of -45 ◦ . This frequency distribution
can be modified by processing the photons through spectral filtering. In the experiment
a narrow spectral filter is placed in the beam path of the heralding photons
(see Figure 3.34). Filtering the signal arm would have the same effect, but in this
case a heralding detection event would not necessarily herald a signal photon. Its
partner may have been filtered.
Figure 3.34: Heralding filtered photons for higher purity
For simplicity we model the filter as a Gaussian function in frequency space.
Mathematically speaking we insert an additional filter function into our two-photonstate
3.23 and get:
� ∞ � ∞
|Ψs,i〉 = A
0
0
dωs dωi e − (ωi−ωf )2
2σ2 f e − (ωs+ωi−ωp)2 2σ2 ∆kL
p −γ(
e 2 )2
â † s (ωs) â †
i (ωi) |0〉 .
(3.55)
The effect of the filter function can be easily understood by an actual example
plotted in Figure 3.35. In the left picture a JSA with huge correlations is plotted.
The filter term, visualized in the second picture as the horizontal function, discards
a large part of the JSA and shapes it into a less correlated form. The result is
plotted in the figure to the right. The drawback of this method is the introduction
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