Entanglement and interference in a nutshell

[bruce2g]

I've been discussing about entanglement and interference on this forum for a while -- whether a single entangled beam can interfere, and why coincidence counting produces interference. I think I finally figured out intuitively how all this works. I know that some people are probably sick of this topic (myself perhaps included -- I have a couple of previous threads here and here), so I'd like to share what I think I've figured out, and then hopefully move on to something new.

I was reading Sneaking a Look at God's Cards by Giancarlo Ghirardi, and it turns out that Einstein and Bohr touched on a similar issue in their famous debates. Einstein would propose an apparatus for measuring a photon's path in a two-slit interference, and then Bohr would show that the mechanism would minutely alter each photon's effective starting position, and this would be enough to destroy the interference.

The variation in path plays a role in SPDC pair creation. When you use a SPDC crystal to create an entangled pair, the signal photon can be emitted from anywhere on a relatively large ring on the surface of the crystal (there's a separate ring for each wavelength). If the signal photon is emitted from the left side of the crystal, for example, then it is closer to the left slit, and its path to the left slit is shorter than its path to the right slit. On the other hand, photons emitted from the right part of the crystal have a shorter path to the right slit. Thus each signal photon starts out with a different phase difference between the left and right slit, and so you cannot see any interference since, as Bohr pointed out to Einstein, each photon has a different phase and so no clear interference pattern will emerge.

Apparently, if you run the signal beam through a pinhole, so that all the photons have the same path lengths to the slits, then you should see interference. However, the pinhole effectively measures the photon's position, and this will break the entanglement with the idler.

Coincidence counting corrects this in the following manner: the idler photon is detected at a specific point in space (the detector is typically fairly small). So any signal photons coincident with that idler will also go through a mirror point on the way to the slits. So, coincidence counting acts as a virtual 'pinhole' to select signal photons that will reach the slits with the same phase between the two slits, and the interference is restored.

I know there's more to the story -- e.g., the idler cannot be detected in a place that provides which-path information. Anyhow, I'd appreciate it if someone could let me know if I've oversimplified too much or if this makes sense.

 

[Evalesco]

That's a really interesting explanation of how entanglement and interference work together! It makes sense that running the signal beam through a pinhole would restore the interference, as all of the photons would have the same path lengths to the slits. I'm also intrigued by the role coincidence counting plays in correcting this issue. It's fascinating how it essentially acts as a virtual 'pinhole' for selecting signal photons that will reach the slits with the same phase between the two slits. Overall, your explanation is quite detailed and seems to make perfect sense!

 

[denian]

First of all, it's great that you've been exploring the topic of entanglement and interference and have come to some intuitive understanding. It's a complex and fascinating area of research that continues to puzzle and challenge scientists.

In a nutshell, entanglement refers to the phenomenon where two or more particles become connected in such a way that the state of one particle affects the state of the other, even when they are separated by large distances. This has been demonstrated through various experiments, including the famous EPR (Einstein-Podolsky-Rosen) experiment.

Interference, on the other hand, refers to the phenomenon where two or more waves overlap and interact with each other, either constructively or destructively. This can be seen in the classic double-slit experiment, where a single beam of light can create an interference pattern when passed through two slits.

Now, when it comes to entangled particles interfering, there are a few key points to consider. First, as you mentioned, the path variation plays a crucial role. This is because the path difference between the two slits determines the interference pattern, and when entangled particles have different path lengths, they cannot produce a clear interference pattern.

However, when coincidence counting is used, it effectively selects particles that have the same path length to the slits, thus restoring the interference pattern. This is because the idler photon's detection acts as a "virtual pinhole" that only allows particles with the same path length to reach the slits.

It's important to note that this is not a measurement of the particle's position, as that would break the entanglement. Instead, it's a way of selecting particles with the same path length without directly measuring their position.

Overall, your understanding of the topic seems to be on the right track. However, as you mentioned, there are still many complexities and nuances to consider when it comes to entanglement and interference. Keep exploring and learning, and who knows, you may come up with even more insights and breakthroughs in this fascinating area of research.