Graduate Decoherence in the double slit experiment

[drl]

Dr. Chinese. Not very knowlegeable about Q.M. But in the use of polarized crystals the change in polarization of the crystals when they are crossed would also result in a change in their wave function to the degree in which they were turned, in turn, altering their interference pattern. I am still at sea using this logic that if detectors are placed at both slits, I would expect that the wave functions remain the same and the interference pattern should result which I was informed is not the case. Please Exlain

 

[Agrippa]

Generally, the types of interactions you describe (reflection/scattering/etc.) do not produce entanglement of light (or other particles).

Are you sure about this? Imagine my box contains a particle that's in a superposition of being on the left side of the box and of being on the right side of the box. Then I send my photon through. Does the photon not then enter into a superposition of reflecting from the left side of the box and reflecting from the right side of the box?

I would recommend reading up of entanglement of light via PDC (parametric down conversion).

PDC is method of entangling photon pairs. This is not what's happening in my set up. My box contains some matter (I was not thinking of photons). Photons are sent into the box, reflect off this matter, exit the box, and are then channeled toward a double slit apparatus. It is unclear to me how studying PDC is going to help me here.

 

[Agrippa]

Maybe it is better to answer this in a rather general manner. If you entangle some property of your photons with something else, you will find that this property will vary strongly each time you measure it and in principle a measurement on the entangled partner could at any time set your photon into a state, where your property of choice takes one of these values at random in each measurement run.

Sure, except that I'm not thinking of measuring the photon's entangled partners, since they're locked in a box that only the photons can penetrate. Instead, I'm using the double slit apparatus to measure the photons.

Now the question is, why the interference pattern disappears for some entangled states. For the typical double slit, there are two ways of destroying the pattern.

1) The two paths become distinguishable. You get this for example by placing optics that change the path of photons depending on their polarization. Or you may get this if you introduce a polarization shift that depends on which slit the photon takes. You may introduce optics that create some time delay for photons going through a certain slit and so on and so forth. Stuff like that is used in many complicated versions of the double slit. However, in the "vanilla" double slit, there are no markers like that. Unless your intended version of entanglement creates some initial asymmetry in the double slit experiment (such as left-circularly polarized photons go to the left slit, right-circularly polarized photons go to the right slit) or enables you to nail down the exact time of photon emission so precisely that the photon travel time differences from the slits to the screen positions become larger than this window, the entanglement will not have any influence with respect to this point.

I don't believe that such an asymmetry exists in my intended version. I've got photons (let's say infrared) that penetrate a box, reflect/scatter (and thereby entangle) with matter in that box, and then exit the box. After exiting the box I think no such asymmetries can exist since each exiting photon is then directed towards a single slit (with a width of one wave length of the photon), which then directs each photon toward the usual double-slit set up. So the two paths don't become distinguishable in the sense you describe (correct me if I'm wrong).

2) There is some varying initial relative phase shift at the slits. This does not give you which-way information, but it will change the interference pattern. The maximum of the interference pattern willl always be where the light fields from the two slits add up in phase. If you add a relative phase shift to the double slit, the positions of maxima and minima will move accordingly. If this phase variation is large, you end up with the superposition of many interference patterns, which sum up to no pattern at all. You can easily see this effect just by using the same light source and putting it close to a double slit and placing it far away afterwards. Putting it close will destroy the pattern. Putting it far away will preserve the pattern. This shows that the coherence measured is usually not a property of the light source. So how can you use entanglement to destroy the interference pattern in this way? If your entangled property results in such a relative phase shift between the paths to the slits, this will of course destroy your pattern. This is the case for momentum entanglement as different momenta result in different emission angles and therefore different path lengths between your point of emission and the two slits. Unless you have a similar kind of entanglement that results in such a phase shift, your double slit interference pattern will not change at all.

I'm puzzled as to why you are here talking about a phase shift that results from entanglement.In my example, I would have thought that the phase relation between the two components of the photon wave function, which is responsible for interference, is well-defined only at the level of the larger system composed of the photon and the entangled particle in the box, such that one can produce interference effects only in a suitable experiment including the larger system? For in this case, probabilities for results of measurements performed only on the photon are calculated as if the wave function had collapsed to one or the other of its two components/paths, but in fact the phase relations have merely been distributed over a larger system. Or is that what you mean by a phase shift?

 

[Michel Therrien]

I have two questions about the following type of scenario:

We have a laser sending photons through the usual double slit apparatus giving us the usual interference pattern, except that now we introduce some physical matter (that are not photons) that the photons will interact with before going through the double slit apparatus. The only assumption I want to make about this introduced physical matter and the nature of the interactions is that the photons will become entangled with that physical matter before those photons make it to the double slit apparatus.

Question (1): will the fact that the photons entangled with that matter destroy the interference pattern? I suspect it might, since I think (think) the reason why large molecules (larger than buckyballs) don't exhibit interference effects in the double slit experiment, is because they entangle with air molecules. However, I'm not sure: is this a matter of degree? Does just "a little bit of entanglement" (for each photon that makes it to the apparatus) only make a little bit of difference to the pattern? If so, is there a rigorous definition of "a little bit of entanglement"? Is there a measure of "how much" entanglement with the environment destroys the interference completely?

Question (2): if the answer to (1) is that we still get (some amount of) the interference pattern, then is it the case that affecting the introduced physical matter can affect the shape of the interference pattern? Here, by "affecting the introduced matter", I mean changing their states in some way without collapsing them.

Any insights here would be greatly appreciated!

What if you did the experiment in the dark?