Hi Folks,I am currently reading Brian Greene's 'The Fabric of the

[xts]

The angular direction of the incoming photons, combined with their phase, is surely what gives rise to the interference pattern in the first place? The image at D0 surely reflects the intensity of the photons in that particular direction - which intensity is determined by diffraction at the slits, hence interference from the slits?

No.
The distribution of photons at D0 plane depends solely on angular direction of the photon leaving the crystal. Their phase (as well as other parameters, like polarisation) are ignored by this experiment. And those photons have an uniform (or rather blobby) angular distribution.

Where there was no coherence before, suddenly there is coherence, simply by virtue of retroactive detection of the idler photons? Is that the idea?

Exactly.
Incoherent light is a mixture of photons having some property (in our case angular direction) of different values. We may make it coherent by selecting only those photons, which have desired value of this parameter. It does not matter if we perform the selection first or retroactively.

Young did that inserting a single slit between source and dual-slit. QE does this retroactively/off-line/on-line by selecting only those hits, which correspond to proper outcome of the counterpart photon, which has always its angle correlated to our one.

 

[moving-finger]

The distribution of photons at D0 plane depends solely on angular direction of the photon leaving the crystal. Their phase (as well as other parameters, like polarisation) are ignored by this experiment. And those photons have an uniform (or rather blobby) angular distribution.

Are you saying there can be no interference pattern whatsoever observed at D0?

For any photon to leave the crystal and be detected at D0 (for any given position of D0), the photon must have a specific angle of emission. The configuration of D0 plus the two "points of emission" on the crystal defines an angle of emission and surely allows for an interference pattern?

Incoherent light is a mixture of photons having some property (in our case angular direction) of different values. We may make it coherent by selecting only those photons, which have desired value of this parameter. It does not matter if we perform the selection first or retroactively.

For any given position of crystal and D0, the angular direction to D0 is well-defined - whether we detect idler photons or not - hence interference should be observed (or not observed), whether we detect idler photons or not.

What difference does it make in this setup whether we detect idler photons or not?

 

[xts]

For any photon to leave the crystal and be detected at D0 (for any given position of D0), the photon must have a specific angle of emission.

True. (Actually not quite true - remember about uncertainity principle - but for our experiment it is allowable assumption)

The configuration of D0 plus the two "points of emission" on the crystal defines an angle of emission and surely allows for an interference pattern?

False. You forgot about lens in the middle, which do not project the image of the slits, but is focused at infinity - projects the angle. Slits are close to each other comparing to detector size, so it may be considered to be a point-like source, emittin angularily distributed light, which is then projected on a screen D0 plane) by out-of-focus lens.

For any given position of crystal and D0, the angular direction to D0 is well-defined - whether we detect idler photons or not - hence interference should be observed (or not observed), whether we detect idler photons or not.

False! You forgot about lens.
True! It is never observed. There is no interference pattern on D0 plane. The pattern appears not on the screen, but on computer printouts, as resulting from combination of the observed blob with selection strategy, making it fringed.

 

[Cthugha]

Just a comment: If you are really interested in this kind of experiments, have a look at Walborn et al., "Spatial correlations in parametric down-conversion", Physics Reports 495, 116 (2010).
Also available freely at arxiv:http://arxiv.org/abs/1010.1236"

This discusses these experiments in depth (see e.g. the part on conditional interference), but it is a rather long review article and you need to examine some of the math involved yourself to get a feeling for the possible regimes of single photon interference and conditional interference, so it takes some endurance to get something out of this paper.