# Questions about Delayed-Choice Quantum Eraser

Dear Cecil,

I was reading about Scully and Druhl’s delayed-choice quantum eraser in Brian Greene’s Fabric of the Cosmos today and I had a couple of questions that maybe you can help me with.

As I understand the idea, in one type of this of experiment a photon is fired(?) to a beam splitter the photon then has a 50% probability of going to one two down-converters which then separates the photon into two different photons. The signal photon continues on to a reflective surface and then to a screen while the idler photon then goes to a detector. Since we know which way the original photon went at the beam splitter there is no interference pattern shown at the screen.

In another version of the experiment instead of the idler photon going directly to the detector another beam splitter is added which gives the idler photon a 50% chance of going to a detector (d1) or to another beam splitter which gives the photon a 50% chance of going two different detectors (d2, d3). If the idler photon is detected at d1 (or d4 if went the other way at the first beam splitter) there is no interference pattern at the screen for the signal that corresponds to the idler photon detected at d1 (or d4). However, if the idler photon is detected at d2 or d3 there will be an interference pattern since it cannot be determined where the original photon went at the first beam splitter.

Now for my questions.

1. If there are no idler photon detectors will there only be an interference pattern?

2. What if idler photon detectors are there but are not setup to detect idler photons (there are turned off) will there only be an interference pattern?

3. What if the idler photon detectors are far enough away from the beam splitter that the signal photon will hit the screen before the idler photon reaches any detector, will there be an interference pattern? What if the detectors are tuned off after the signal photon has hit the screen but before the idler photon reaches the detector, will there be an interference pattern?

4. What if more beam splitters are added so that no idler photon detector will show which way the original photon went at the first beam splitter, will there only be an interference pattern? If detectors are added that will determine the which way the original photon went at the beam splitter will there be an interference pattern? What if the new detectors are are left turned “off”? What if they are set turned “off” but will turn on after the signal photon hits the screen but before the idler photon will reaches the new detectors, will there be an interference pattern?

I hope this makes sense and thank you.

Bumped for another chance.

OK, I’ll give this a shot. This is kind of complicated, though.

First, let me describe the experiment a little more completely, as I understand it. I think you’re describing the same setup I’ve seen, but the measurements are a little more complicated than you think. The setup has five photon detectors: the four you’re calling d1,d2,d3,d4, and the detector that you’re calling the “screen” where the interference pattern is generated. However, this pattern is not something you can see in the way you would see a normal two-slit interference pattern. The reason is that this is a conditional interference pattern; the signal-photon intensity pattern will have the characteristic interference bands only if the idler photon is detected at d2 or d3. However, which of d1,d2,d3,d4 detects the idler photon, for a particular trial, is completely random. So what you actually see if you project the signal photons onto a screen is the superposition of the four signals: the two interference patterns (idler detected at d2 or d3) and the two noninterference patterns (idler detected at d1 or d4). (You might think that you could still see an interference pattern in the noise, but in fact the d2 and d3 patterns conspire to be perfectly out of phase, so that their superposition has no interference bands.)

The way you “see” interference bands in this experiment is to make coincidence measurements and plot the statistics: For example, “How often did I see a signal photon at point x on the screen when I also saw a photon at detector d2?” The d2 and d3 coincidence measurements show interference fringes; the d1 and d4 coincidence measurements do not.

This setup makes your questions 1 and 2 moot; the interference patterns only emerge when conditioned on the results of d1-d4, so if these are not present, there aren’t any interference patterns to see, just as there aren’t any patterns to see in the basic experiment except conditionally. As for question 3, an experiment has actually been performed this way. The results do not depend on the relative path length (down-converter to screen vs. down-converter to d1-d4), as you might expect since these measurements in principle can have spacelike separation.

I’m afraid I don’t understand what you mean in question 4. Are you suggesting replacing the two first beam splitters (not the one splitting the beam between d2,d3, but the other two) with mirrors so that the idler photon detection never gives which-path information? This will still not give visible interference fringes, because (as above) the d2 and d3 fringes are out of phase.

Quantum-mechanically, one way of thinking of what’s happening is to understand interference as a sum of different complex phases (in this case, resulting from differing path lengths for two photon paths). If the quantum state of a photon taking one path is α|Φ> and the quantum state of the photon taking the other path is β|Φ> (where |Φ> is a quantum state and a and b are complex phases) then the two states can interfere if the photon is allowed to “take both paths”; the resulting state is ( α+β )|Φ>. If a and b depend on position then you can get interference fringes.

However, this depends on the two quantum states resulting from the two paths being the same up to a complex phase. In the quantum-eraser experiment this is not the case. The state of the photon if it takes one path is α|Φ>|1> (the |1> indicating an idler photon on the upper trajectory, headed toward d1); if it takes the other path the state is β|Φ>|2>, with an idler photon on the lower trajectory, headed toward d4. These two quantum states (|Φ>|1> and |Φ>|2>) are orthogonal, so there will be no interference fringes.

Hope this makes sense.

I’m reading the same book, The Fabric of the Cosmos by Brian Greene… and today I read about the exact same experiment… and found this thread when doing a search to see if another question had already been answered here. It’s not that old a thread, so I hope nobody objects to my reviving it.

A scenario is described where the idle photon detectors (d 1-4) are all ten light years away, but the screen is in a much more convenient place (say, ferinstance, at 7-11). Greene says that “if a practical joker” should sabotage the two distant detectors that could pick up a photon from either path (d2 and d3) nearly 10 years later, there wouldn’t be any interference pattern revealed.

Now, I get that this means you wouldn’t be able to tell the difference between photons that do have which-path info and which ones don’t - this is not really a case of the future changing the past. But Greene doesn’t say what would happen if the same trickster were to only sabotage d1 and d4, which do have which-path info, several years after the experiment began - several years after that image appeared on the screen at 7-11 - it seems to me that you would see an interference pattern, and would be forced to conclude that something would go wrong with d1 and d4.

Have I got that right?
Can talk of future effecting past be avoided by saying that d1 and d4 are, after all, in the same slice of now as the screen on 7-11 at readout?
I really do wanna understand this stuff as well as I can without picking up another degree or 2, so any thoughts or further reading would be very welcome.

Here’s the issue: The “interference patterns” in quantum eraser experiments (delayed or not) are conditional interference patterns. They only appear statistically, when you compare the results at the “screen” with the measurements of the detectors d1-d4. To summarize:

You will never “see” an interference pattern in this experiment. (Here by “see” I mean just staring at the screen, not paying attention to the measurements at d1-d4.)

You can see interference patterns by looking at the screen only when a photon has been detected at (for example) d2; but when you just stare at the screen (so that you see the photons associated with detections at d1, d2, d3, and d4), the interference patterns cancel out perfectly, as they must to preserve causality. Once the idler photon is created in perfect quantum correlation with the signal photon you cannot ever see an interference pattern without either performing a coherent erasure of the idler photon (which requires bringing it together with the signal photon again) or looking at conditional statistics.