Two Photon Sagnac Source

[Erik Ayer]

TL;DR Summary

This is referenced by John Cramer as a source of photons with variable entanglement and coherence

In this paper, Cramer references a Sagnac source and mentions it has a half wave plate to vary the entangement vs. coherence by rotating the plate. Look just below figure 1:

https://arxiv.org/pdf/1409.5098.pdf
What is this setup? My guess is that the half wave plate is right before the nonlinear optic and changes the polarization of the incoming photons somehow. I think that normally to pump BBO, the beam is in a specific polarization state (diagonal?), so what would the half wave plate be doing?

Also, it seems likely that the entanglement mentioned is momentum entanglement, but could possibly be polarization. Conversely, what aspect of coherence is being changed? If momentum, what does that physically do? I'm wondering whether the two cones of downconverted light are altered in some way, or is the coherence referring to whether the phases of photons being downconverted are less or more random?

 

[DrChinese]

Please refer to the following paper, which explains the setup in greater detail.

https://arxiv.org/abs/0706.2877
See Figure 3. In this setup, the polarized outputs (H+V and V+H) of the crystals are recombined so the path taken cannot be determined. Since they are now indistinguishable, there are in a superposition which results in polarization entanglement. They are able to achieve a high production level of entangled pairs using this configuration, and it supports tuning of the output wavelength of the photons by a few percent (which was fairly novel).

As to the half wave plate you are asking about (HWP1 in the paper): This appears to me to be used for something entirely different than in the Cramer/Herbert paper. Here, it is to make an adjustment to get the polarizations lined up correctly for re-entry to the PBS. In your reference, it is to control the amount of entanglement. It can do double duty as both, that makes sense, but in the earlier paper they are attempting to maximize entanglement and nothing else.

The outputs of the PPKTP crystal are parallel, i.e. in a straight line. Not like the outputs of BBo crystals which are conic.

 

[Erik Ayer]

Interesting! You mention that the output of ppKTP is a straight line, so the downconverted light is a beam? If so, the coherence that can be maximized at the expense of entanglement is not spatial coherence, correct? By that, I mean spatial coherence would be light all going in the same direction as in a laser or possibly after diffracting from a single slit. Would coherence then refer to the phase of the downconverted light?

It seems clear that the entanglement is polarization rather than momentum, again since the ppKTP is outputting a beam rather than cones.

 

[DrChinese]

Interesting! You mention that the output of ppKTP is a straight line, so the downconverted light is a beam? If so, the coherence that can be maximized at the expense of entanglement is not spatial coherence, correct? By that, I mean spatial coherence would be light all going in the same direction as in a laser or possibly after diffracting from a single slit. Would coherence then refer to the phase of the downconverted light?

It seems clear that the entanglement is polarization rather than momentum, again since the ppKTP is outputting a beam rather than cones.

I can't answer your question about coherence in this situation.

The polarization entanglement occurs when the output beams are recombined. That seems a bit strange, as at first blush they would seem to be entangled when they exit the crystal. I believe they are entangled as to wavelength (when exiting the crystal) as there is a conservation rule at play. And they might also be polarization entangled at that point; but to be useful (for the intended purpose) they need to be separated somehow without learning their polarization. Ultimately that is why there are 2 output beams rather than a single one, and why they are recombined.

I am not that familiar with these type crystals, so perhaps another here can fill in some gaps.

 

[Erik Ayer]

I was thinking about this yesterday and wondering whether the coherence is related to the outputs being polarization entangled vs. having one output always be horizontally polarized and the other vertical. In that case, "coherent" would mean always the same value.

In Young's double slit experiment, light first went through a single slit so it was "spatially" coherent - always coming from the same place (x-coordinate). What I'm kind of wondering is whether there are different types or meanings of coherence, such as phase coherence, or polarization coherence like above. If the two output were polarization coherent, then there would be no superposition of the phase before measurement/interaction and therefore, no entanglement. Likewise a spatially coherent light source couldn't be in superposition from two different locations (or more), so two photons couldn't then be entangled.

What I'm really trying to wrap my meatball around is the concept of entanglement vs. coherence. It seems like, just maybe, I'm getting a sliver of understanding.

As for the Sagnac source, I looked aroung the net a bit at ppKTP and found that the downconverted light isn't all colinear. At least not always, possibly. Maybe the colinear part in the Sagnac source is the degenerate case. It makes me wonder whether a set of BBO crystals, all cut for colinear downconversion, could do the same thing.

 

[DrChinese]

Likewise a spatially coherent light source couldn't be in superposition from two different locations (or more), so two photons couldn't then be entangled.

What I'm really trying to wrap my meatball around is the concept of entanglement vs. coherence. It seems like, just maybe, I'm getting a sliver of understanding.

When it comes to coherence (and entanglement), my understanding is close to a sliver.

The general rule is that entangled light will not be coherent - essentially those are complementary properties. For example, such light will not yield an interference pattern if run through a double slit setup. But there is enough more to the story, that I will defer to others who would wish to weigh in.