 |
| Figure 1: The delayed-choice quantum eraser experiment |
Suppose a series of photons are sent through a double-slit apparatus. As you may know, an interference pattern is formed on the back screen. Each photon's trajectory can be represented as a wave that passes through both slits and is finally absorbed at a particular position on the back screen (with a specific probability).
Adding a splitting crystal (BBO in Figure 1) immediately after the slits converts the photon into two entangled photons, each with half the energy of the original photon. One photon (called the signal photon) goes to the back screen (D0) which, after a series of such experiments, builds up a blob pattern that does not exhibit interference. Why not? Because the wave function depends on the location where the photon pairs were created (as represented by the green line apex at the upper slit or the red line apex at the lower slit) and thus on which slit the original photon went through. This constitutes "which-way" information which destroys interference.
So far so good. Now suppose the second photon (called the idler photon) is sent on a long journey - a much longer journey than the signal photon took to get to the back screen - and then, optionally, a beam splitter is placed in its path. This is the delayed-choice aspect of the experiment.
If the beam splitter is present (as in Figure 1), then the idler photon hits one side of the beam splitter according to which slit the original photon went through (i.e., the red path comes from the lower slit and hits the lower side of the beam splitter, the green path comes from the upper slit and hits the upper side of the beam splitter). Analogous to the double-slit interaction, this beam splitter interaction can be represented as a wave that is reflected by and also passes through the beam splitter. Subsequently detecting the photon on the lower side of the beam splitter (D1) or the upper side (D2) will tell you nothing about which side of the beam splitter the idler photon came from, and thus nothing about which slit the original photon went through. That is, the "which-way" information has been lost. This is the eraser aspect of the experiment.
Given that the "which-way" information is erased when the beam splitter is present, what kind of pattern do you predict will be seen on the back screen (i.e., by the signal photons at D0)?
To see the answer, go back to the second paragraph of this post. What pattern was exhibited on the back screen then? A blob pattern that did not exhibit interference, and the same answer remains true here. The rest of the setup with the idler photon makes no difference at all. There is no mysterious "backwards-in-time" effect that changes the pattern (as is sometimes suggested), since the pattern is the same regardless of what subsequently occurred elsewhere.
 |
| Figure 2: D0 = D1 + D2 (with the beam splitter) |
Now that is not quite the end of the story. It is possible to match up the idler photon detected at one of the final detectors (D1 or D2) with its entangled signal photon partner on the back screen (using a mechanism called coincidence counting). If the beam splitter is in place and the signal photons are later highlighted according to which detector the idler photon partner was detected at, then an interference pattern is revealed for each highlighted group (see Figure 2).
So does this imply a "backwards in time" effect, albeit hidden? No, the two interference patterns are always encoded in the total signal photon pattern and can even be used to predict the probability of measuring the idler photon at D1 or D2. For example, suppose a signal photon was detected at D0 at the location indicated by the green bar in Figure 2. Note that there is a peak for D1 and a trough for D2. This predicts that the idler photon will, with near
 |
| Figure 3: D0 = D1 + D2 (without the beam splitter) |
certainty, be detected at D1. The correlation is due simply to the entanglement between the signal and idler photons which the measurement after the beam splitter verifies.
If the beam splitter were not present, then D1 and D2 would instead detect which slit the original photon passed through (i.e., the "which-way" information). So if the signal photons were highlighted according to which detector the idler photon partner was detected at, then a non-interference pattern would be revealed for each highlighted group (see Figure 3).
References:
A Delayed Choice Quantum Eraser - experiment by Kim et al., in 1999.
The Notorious Delayed-Choice Quantum Eraser - blog post by Sean Carroll
The delayed choice quantum eraser, debunked - blog post by Sabine Hossenfelder
Delayed-choice quantum eraser - Wikipedia
