Is a slit automatically also a detector?

[friend]

Suppose you're shooting electrons one at a time through a double-slit experiment. If we don't detect which slit an electron enters, you get a fringe pattern on the screen beyond the slits. If you detect which slit the electrons go through, then the fringe pattern is lost.

However, wouldn't the electric charge of an electron going through a slit disturb the atoms that make up the surface of a slit, ever so slightly, no matter which slit it goes through? And if those atoms remain displaced or their state changed due to the force of the electric charge passing nearby, then wouldn't that constitute a record of which slit the electron traveled through? Yes, it would be very difficult to read that slight displacement of atoms, but in theory it would still be which slit information, right? So would the fringe pattern remain or disappear if a record of which slit it entered remains recorded by the displacement of atoms on the surface of the slits?

 

[gomyhr]

Let me answer your last question first: if a record of which slit it entered remains recorded any any way, the fringe pattern will disappear. Actually, on of the effects observed in the large-molecule double-slits experiments pioneered by the Zeilinger group in Vienna, was that for hot molecules, the fringe pattern would disappear. This is because hotter molecules will emit photons (more often and with smaller wavelength then colder molecules) and the photon will in principle give away the position of the molecule.

Your argument about the electron disturbing the atoms at the surface of the slits, ever so slightly, would be correct if the electrons and atoms were classical objects. But then again there would be no fringe pattern ;-)

Since the atoms on the surface are also quantum objects, any disturbance, or excitation as they are usually called, will have to have a minimum magnitude. It will typically be in the form of a phonon in the material around the slit. Instead of every electron giving away its positon by disturbing the surface slightly a small fraction gives away their position my distrubing the surface in a less subtle way, and these few electrons will not contribute to the fringe pattern.

And just to refine the previous pargraph a bit: phonons do not necessary have a minimum energy. But phonons are collective excitation of many particles (quantized sound waves) and phonons with low energy are less localized (have longer wavelength) than those with higher energy. So some electrons will create low-energy phonons in the material around the slits, but the phonons will carry almost no information about which slit the electron that excited it went through. So in this case, the minimum magnitude in the previous paragraph is really the minimum energy for the disturbance to carry information about the path of the electron.

 

[friend]

Let me answer your last question first: if a record of which slit it entered remains recorded any any way, the fringe pattern will disappear. Actually, on of the effects observed in the large-molecule double-slits experiments pioneered by the Zeilinger group in Vienna, was that for hot molecules, the fringe pattern would disappear. This is because hotter molecules will emit photons (more often and with smaller wavelength then colder molecules) and the photon will in principle give away the position of the molecule.

Very interesting. Thank you! I'll have to look this up. So then, does this mean that higher energy electrons would not have a fringe pattern because they would have more of a tendency to radiate photons to the surface of the slits and cause vibrations? I wonder if that experiment has been done.

And just to refine the previous pargraph a bit: phonons do not necessary have a minimum energy. But phonons are collective excitation of many particles (quantized sound waves) and phonons with low energy are less localized (have longer wavelength) than those with higher energy. So some electrons will create low-energy phonons in the material around the slits, but the phonons will carry almost no information about which slit the electron that excited it went through. So in this case, the minimum magnitude in the previous paragraph is really the minimum energy for the disturbance to carry information about the path of the electron.

This seems to suggest that indeed particles do cause disturbances in the slits. But those disturbances dissapate so as to become undetectable. Do the disturbances have to dissipate before the particle reach the fringe detector screen? Is that even possible for very fast electrons?

 

[Cthugha]

Very interesting. Thank you! I'll have to look this up. So then, does this mean that higher energy electrons would not have a fringe pattern because they would have more of a tendency to radiate photons to the surface of the slits and cause vibrations? I wonder if that experiment has been done.

Higher energy electrons typically only have higher kinetic energy which typically does not introduce or strengthen any interaction with the slits. As said above, the situation is different for molecules which indeed radiate photons if they are hot. It should be noted that the molecule double slit has also been performed with varying quality of vacuum. If the vacuum becomes worse, the interference pattern washes out as the molecules interact more often with the particles which are around. That effect would also work for electrons.

This seems to suggest that indeed particles do cause disturbances in the slits. But those disturbances dissapate so as to become undetectable. Do the disturbances have to dissipate before the particle reach the fringe detector screen? Is that even possible for very fast electrons?

The question is whether some disturbance is enough to change the state of the slit. For example the typical possible effect an electron passing by could have on a slit (say its momentum or position) will often be small compared to the uncertainty of these quantities which is already present due to the uncertainty principle and is therefore unable to change the state of the slit.

 

[friend]

Higher energy electrons typically only have higher kinetic energy which typically does not introduce or strengthen any interaction with the slits. As said above, the situation is different for molecules which indeed radiate photons if they are hot. It should be noted that the molecule double slit has also been performed with varying quality of vacuum. If the vacuum becomes worse, the interference pattern washes out as the molecules interact more often with the particles which are around. That effect would also work for electrons.

What if the slits were charged - metal slits with a voltage applied. Then it would seem that the electrons would almost certainly interact with the slits, right? Does the application of a voltage on slits make the fringe pattern dissapear. It sounds like this would be the type of experiment which could easily be turned on and off to eliminate any ambiguity about this. Has this ever been done?

 

[friend]

Let me answer your last question first: if a record of which slit it entered remains recorded any any way, the fringe pattern will disappear.

Here is a link to a report that unequivocally states that you most certainly can have which slit information and a fringe pattern at the same time. They use entangled photon in a Delayed Choice Experiment:

http://arstechnica.com/science/2012...rticle-duality-in-the-double-slit-experiment/

Actually, on of the effects observed in the large-molecule double-slits experiments pioneered by the Zeilinger group in Vienna, was that for hot molecules, the fringe pattern would disappear. This is because hotter molecules will emit photons (more often and with smaller wavelength then colder molecules) and the photon will in principle give away the position of the molecule.

I found where they were able to get a fringe pattern with large molecules. But I couldn't find any mention about "hot" molecules verse "cold" molecules. Do you have a reference to this study you're mentioning? Thank you.

 

[Cthugha]

What if the slits were charged - metal slits with a voltage applied. Then it would seem that the electrons would almost certainly interact with the slits, right?

Well, it still depends on how strongly they interact. For example one could also say that in a common Mach-Zehnder-interferometer-like which-way experiment one could have a look at the two mirrors which are positioned in every possible path and check their recoil upon reflection of a photon to determine which way the photon took. However, the mass of the mirrors is so huge that the momentum transfer by the photon is far too tiny to change the state of the massive mirror and drowns in uncertainty. I also would not expect the single electron to have any detectable influence on the slits. On the other hand the charged slits may have an influence on the electron which could change its momentum and therefore destroy the interference pattern. But I do not know whether someone tested this. There are so many tests of the double slit that people rarely repeat what is basically the same experiment using just different mechanisms as which-way markers.

Here is a link to a report that unequivocally states that you most certainly can have which slit information and a fringe pattern at the same time. They use entangled photon in a Delayed Choice Experiment:

http://arstechnica.com/science/2012/...it-experiment/

That link is a bit misleading. Basically, having an interference pattern means that you have two indistinguishable physical processes that lead to the same final result. In the paper you mention Schleich and others managed to start with the pump the light field in a state (TEM01 mode) which has two maxima. Now the two different paths originating from these two maxima both take one slit, but are nevertheless different paths which correspond to different wavevectors which again show interference. It is a very nice paper, though.

 

[gomyhr]

I found where they were able to get a fringe pattern with large molecules. But I couldn't find any mention about "hot" molecules verse "cold" molecules. Do you have a reference to this study you're mentioning? Thank you.

I think I read it in New Scientist quite few years back. This seems to be the original article:
Hackermueller et al: "Decoherence of matter waves by thermal emission of radiation" http://arxiv.org/abs/quant-ph/0402146 (it appeared in Nature as per the DOI, but that version is paywalled).

 

[gomyhr]

This seems to suggest that indeed particles do cause disturbances in the slits. But those disturbances dissapate so as to become undetectable. Do the disturbances have to dissipate before the particle reach the fringe detector screen? Is that even possible for very fast electrons?

Dissipation does not play a role here. If which-way information is created and then dissipates, it still exists, it is just much harder to get to (i.e. impossible in practice, but possible in theory, which is what matters).

You can think about it as four orthogonal states of the slit system: |no_disturbance>, |left_disturbed>, |right_disturbed>, |delocalized_excitation>. The slit will end up in a superposition of those states, with most weight on undisturbed. When you check, you get |no_disturbance> with hight probability - which means you collapsed your wavefunction from slight disturbance (the superposition) into no disturbance. Only when you measure |right_disturbed> or |left_disturbed> would you get which-way information and those electrons will not contribute to the fringe pattern. Even if we do not measure the slits state, we get the same fringe pattern, since the measurements could be done in theory.