Does downconversion cause pump photon wavefunction collapse?

[Erik Ayer]

TL;DR Summary

When a photon is downconverted, does its path collapse?

I saw a paper on an experiment where a pump beam first went through a double-slit, then was downconverted with BBO. Recently a friend with a PhD in quantum physics said the downconversion will cause the pump's wavefunction to collapse and the implication for this experiment is that the pump photon would then have only gone through one slit or the other rather that a superposition of both, and hence there would be no interference. That depends on how close the BBO was to the slit and whether the light had overlapped and interfered by then.

If the wavefunction does collapse at downconversion, the this experiment would be kind of stupid. With the BBO immediately following the double slit, there would be no interference. If the BBO was placed where the light from the slits overlapped, there would be interference but it would be the pump beam's interference rather than the downconverted light.

More generally, if a pump beam with some finite cross section is downconverted, when that happens does it happen at a specific position within that cross section? Initially every photon is in a superposition across the entire beam (and the double-slit experiment works and stuff), but I'm wondering whether the two photons from downconversion then come from a specific point within the intersection of the beam and the BBO rather than be in superposition of having downconverted across the whole cross section.

 

[charters]

Check out Wang, Zou, Mandel's induced coherence experiment - less well known than something like the DCQE, but in my opinion one of the coolest quantum optics experiments. It shows it is possible to prepare a beam in a superposition of having been downconverted by two different BBOs. Like any interferometer, it requires the right, special alignment of the features (here the BBOs), so generically the two paths through two different BBOs won't interfere, in which case where you place the collapse is arbitrary and interpretation dependent. But there is definitely at least this one circumstance where the downconversion does not spatially collapse the beam.

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.44.4614

 

[Erik Ayer]

I couldn't access that paper, but found another one that covers several experiments including that one: https://arxiv.org/pdf/1410.6649.pdf. So yeah, it looks like these show that, at least in some cases, downconversion doesn't collapse the path photons took.

A while back I read a book which made the claim that, if an interaction didn't leave a macroscopic effect, it wouldn't cause wave function collapse. A photon going through a beam splitter wouldn't leave a macroscopic change, so its wavefunction would take both paths. For downconversion, the full term is spontaneous parametric down conversion where "parameteric" means there is not change to the non-linear medium. "No change" is a superset of "no macroscopic change," so it would seem like SPDC would not cause the path a pump photon took to collapse. However, a friend with a PhD in quantum physics disagreed.

 

[Aidyan]

A while back I read a book which made the claim that, if an interaction didn't leave a macroscopic effect, it wouldn't cause wave function collapse. A photon going through a beam splitter wouldn't leave a macroscopic change, so its wavefunction would take both paths. For downconversion, the full term is spontaneous parametric down conversion where "parameteric" means there is not change to the non-linear medium. "No change" is a superset of "no macroscopic change," so it would seem like SPDC would not cause the path a pump photon took to collapse. However, a friend with a PhD in quantum physics disagreed.

These are interesting questions I was wondering about too. So, according to this point of view also a simple polarizer, a polarization rotator, any transparent medium such as a prism or a filter do not 'collapse' the wavefunction either(?) Seems plausible to me, but, at least as far I could see, the literature leaves these questions open or does not address it. I'm also wondering if deep down that leads to the good old measurement problem, which still has not found a definite resolution.

At any rate, a PhD is not a guarantee, especially if someone is not a specialists in the field. Nowadays quantum optics can be a quite complicate science, not to speak about the conceptual foundations of QP where there is a plethora of misunderstandings also among physicists.

 

[PeterDonis]

a friend with a PhD in quantum physics disagreed

Have you pointed him at the paper you linked to?

 

[Erik Ayer]

Yeah, I'll share this link will him soon, like tomorrow. From that link, it's pretty clear that there is interference after downconversion, which kind of fits with the hypothesis that when there isn't a macroscopic effect, superposition remains intact.

 

[DrChinese]

I couldn't access that paper, but found another one that covers several experiments including that one: https://arxiv.org/pdf/1410.6649.pdf. So yeah, it looks like these show that, at least in some cases, downconversion doesn't collapse the path photons took.

A while back I read a book which made the claim that, if an interaction didn't leave a macroscopic effect, it wouldn't cause wave function collapse. A photon going through a beam splitter wouldn't leave a macroscopic change, so its wavefunction would take both paths. For downconversion, the full term is spontaneous parametric down conversion where "parameteric" means there is not change to the non-linear medium. "No change" is a superset of "no macroscopic change," so it would seem like SPDC would not cause the path a pump photon took to collapse. However, a friend with a PhD in quantum physics disagreed.

Great reference. You are tackling a very complex area, good luck. I will make a couple of comments, keep in mind that these are general around PDC and there are many nuances as you drill in.

a. Particles (photons) can be entangled on one or more bases. And there can theoretically be collapse on one basis without collapse on another.

b. I don't think of PDC entangled pairs as having an exact source position. And I certainly don't think of the creation of such a pair as implying there was collapse of the input photon. In fact quite the opposite, there can't be such a collapse: in Type I parametric down conversion (some variations anyway), as there are 2 crystals oriented perpendicularly. It is the superposition of these that create polarization entanglement. So the "source" is both crystals (and neither crystal) in the sense that it must be indistinguishable.

 

[Erik Ayer]

That is a really good point about Type-I downconversion, thank you!

The way I'm kind of thinking about this, and please smack me if I'm way off base, is that initially, a photon's wave function spans the cross-section of the entire beam. If it hits a brick, that wave function collapses to a point (or small area) such that it hit a specific part of the brick. For downconversion, again the pump photon spans the cross-section of the beam and if downconversion happens, the point where the two photons emerge also spans the beam (from this thread, I don't think the position of the pump photon collapses at downconversion in the way it does when it hits the brick).

From figure 2 in the link, it would follow that a pump photon hits BS(sub)p and goes into superposition between the upper and lower paths. If downconversion occurs, then two photons are emitted from NL(sub)1 in superposition with two photons being emitted by NL(sub)2, but there is no possibility of one photon from each. Due to the superposition of the pair being from NL1 and NL2, there can be interference.

 

[vanhees71]

I couldn't access that paper, but found another one that covers several experiments including that one: https://arxiv.org/pdf/1410.6649.pdf. So yeah, it looks like these show that, at least in some cases, downconversion doesn't collapse the path photons took.

A while back I read a book which made the claim that, if an interaction didn't leave a macroscopic effect, it wouldn't cause wave function collapse. A photon going through a beam splitter wouldn't leave a macroscopic change, so its wavefunction would take both paths. For downconversion, the full term is spontaneous parametric down conversion where "parameteric" means there is not change to the non-linear medium. "No change" is a superset of "no macroscopic change," so it would seem like SPDC would not cause the path a pump photon took to collapse. However, a friend with a PhD in quantum physics disagreed.

I already stumble over equation (5) in the above cited paper. The nice thing of the SPDC process is that it produces entangled two-photon states, i.e., described by something like
$$\hat{A}_p^{\dagger}=\frac{1}{2} [\hat{a}_{H}(\vec{k}) \hat{a}_{V}(\vec{k}') - \hat{a}_H(\vec{k}']\hat{a}_V(\vec{k}).$$
For a more thorough discussion, see

J. Garrison, R. Chiao, Quantum optics, Oxford University
Press, New York (2008).
https://dx.doi.org/10.1093/acprof:oso/9780198508861.001.0001
p. 400ff

This is a very nice book, doing everything correctly with field operators and not in the somewhat misleading way it's often described in experimental papers, as is stressed in the first sentence of the quoted paper, but I find it a bit strange in claiming (5) would describe the nice Bell states prepared by parametric downconversion (+some other elements like band filters etc. to bring the state of the real device closer to the idealized states quoted above).