Another double slit question

Fiziqs

I realize that the people here must be sick of answering stupid questions about the double slit experiment, and different ways of setting it up, but if I may, I have a question about what you would expect to see if the double slit experiment were set up in a slightly different manner, and why.

First, I am assuming that in the classic double slit experiment we need only put a detector at one slit in order to destroy the interference pattern. But this leaves me with a question. Is it the fact that we then know which slit the particle went through that destroys the interference pattern, or is it the fact that we interacted with the probability wave that destroyed the interference pattern? In other words, could we destroy the probability wave without knowing which slit the particle went through.

So my question is, what if, instead of setting up the double slit experiment in the way that I usually see it portrayed, with something that looks like a laser pointed at a wall with two slits in it, but instead we set it up with a light positioned in the center of a box with a pair of slits on each of the six opposing walls, and a screen positioned behind each pair of slits. I assume that absent any detectors we would expect to see an interference pattern on all six of the screens. But what if we then put a detector on just one of the twelve slits? Would that one detector be sufficient to destroy the interference pattern on all six of the screens? Or would it only destroy the interference pattern on the screen positioned behind the wall with the detector?

What would you expect to see with such a setup, and why?

Thanks to everyone for considering my question.

vanhees71

I'm never sick about answering (or at least trying to answer) such questions.

I always find these ideas on which-way information vs. the observation of an interference pattern quite vague. One should clearly specify the experiment and analyse it. Then most of the quibbles with quantum theory vanish usually in a natural way.

One must also state clearly which interpretation of quantumt theory one follows. I'm using the minimal statistical interpretation.

Now let's consider the usual double-slit experiment. Let's use single photons of a well-defined linear polarization and frequency. Hitting the double slit without any device to determine through which of the slits the photon has gone with very many of such prepared photons, you'll find the double-slit interference pattern on the detection screen.

Now the question is, how you can (at least in principle) gain "which-way information" for each single photon with certainty. This is only possible by somehow "tagging" each photon with the information through which slit it might have come. This can be easily achieved by, e.g., putting quarter-wave plates into the slits. Such a quarter-wave plate transforms the linear-polarization state into an elliptically polarized state. If we choose the orientation of the quarter-wave plates to be [itex]45^{\circ}[/itex] in the one slit and [itex]-45^{\circ}[/itex] in the other, with the angle measured relative to the polarization direction of the incoming photon, then any photon, coming through slit 1 becomes left-circular (helicity -1) and any photon coming through slit 2 becomes right-singular (helicity +1) polarized. These polarization states are completely disinguishable, because the corresponding state kets are orthogonal to each other. Now, orthogonal states can never interfere, and thus you won't see any two-slit interference pattern anymore, because the two ways a photon can run to hit the screen are now completely distinguishable, because this information is inherent in any photon behind the double slit. Thus the possibibilities cannot interfere anymore, and thus you don't see an interference pattern.

There are very clever setups of this kind, using entangles photon pairs, where you can choose, whether you want to see the interference pattern or not by looking on subensembles of the complete ensemble after the whole experiment has been performed and the data on the position of each photon hitting the screen are fixed. Thus you can "erase" the which-way information for a subensemble of the whole ensemble such that the subensemble shows the interference pattern again. See this publication for details:

S. P. Walborn, M. O. Terra Cunha, S. Pádua, C. H. Monken, Double-slit quantum eraser, Phys. Rev. A 65, 033818 (2002)
http://link.aps.org/abstract/PRA/v65/e033818

It's also nicely described on the following website:

http://grad.physics.sunysb.edu/~amarch/

Concerning your alternative setup, I don't see how the six double-slit experiments should be correlated. By just putting a light source into the box, for sure they are not related in any way.

mfb

You would destroy the interference pattern where you destroy coherency between the two slits - at the side of your detector only.

Fiziqs

If I may bother you further, what is the mechanism by which the detector introduces decoherence between the two slits?

In the classic double slit experiment, with a detector at both slits, how do the detectors introduce decoherence?

Dumb question I know.

mfb

The detectors interact with the wave function "in some way" (enough to cause decoherence, i.e. a phase shift which cannot be predicted).

Fiziqs

Now when you say "in some way", do you mean that it depends upon the method being used, or do you mean that we really don't know exactly how the detector interacts with the wave to cause decoherence?

mfb

It interacts according to the laws of physics, which are well-known for usual detectors.
It depends on the precise quantum-mechanical state of the detector (which we usually do not know), and the used method of course.