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Entanglement and interference in a nutshell

  1. Oct 13, 2007 #1
    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.
    Last edited: Oct 13, 2007
  2. jcsd
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