This question was asked by a student in a class on Quantum Physics I am teaching in: Imagine the typical double-slit experiment with electrons. If there is no information obtained through which of the two slits the electron went, we observe an interference pattern; if we on the other hand scatter photons of the electrons right before the slit, we can find out through which slit they go and the interference pattern disappears. - Now, one can think of the electron's wave function to "collapse" from a delocalized state to a highly localized one when the photon interacts, and then it continues on its trajectory through one of the slits. But what if the scattering event with photons is moved further and further away from the two slits? Then, in principle, there comes a point at which we can perhaps no longer decide through which slit it eventually went (no information obtained, interference pattern returns?) or, in terms of the wave function collapse, the localized wave function starts to "spread out" again and become more and more delocalized. - Two questions: (1) What are your thoughts on this ("thought experiment")? (2) Do you know of any reference where such an experiment has actually been carried out? -- Thanks in advance for your feedback! /Ralph
The statement is ambiguous, since, while it refers to electrons, at some point it starts to mention photons, also. The standard reference, of course, is Feynman and real experiments are now possible with cold atoms and molecules. Recent papers are these: https://arxiv.org/pdf/1606.09442.pdf and http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332005000200004
Dear Ralph, it is an interesting question indeed and I am happy that the students have been motivated to think about this! There is a caveat in the idea to use light (a laser, or photon) to determine the position of the particle before it goes through the slits. The photon that is used in the measurement is going to disturb the particle wave. If we consider a single particle the scattering event is going to change the momentum of the particle and its energy. This means that the coherence in the wave of particles will be lost. This will indeed disturb the interference pattern. I think it doesn't help to move the scattering event further away, as long as the coherence in the wave has been destroyed. But if we would start with a beam of particles in a laser and all undergo the scattering with a photon, then the interference pattern should appear again (from the new particle wavefunction after the interaction with the photons). It is important that we have for this identical, undistinguishable particles. Putting a mark on one of them will mean that they are not identical and undistinguishable anymore.
Please correct me if I am wrong....I shall be thankful...
Interference pattern will reappear once it hold the condition "distance of measurement from double slit (a) >> diameter of source * separation between two slits (d) / wavelength(\lambda) of the particle(electron etc)".
Dear Anil, in itself, yes, if we have one kind of particles and they all interact with identical photons in the same way (this is what I meant above). Then we should have again a beam of particles with wave coherence. But if there isn't such coherence, think for example that a number of the particles interact with the photons and others don't, then even after having travelled a distance they will be different. Think of doing the experiment with electrons and neutrons. I think that then the electron wave and neutron wave are different and wouldn't lead to interference. But there could be interference related to having one wave of neutrons, and similarly, there could be interference for the particles in the electron wave.
Dear Peter sir, absolutely correct. For different particles, path length will be different which depends on scattering and accordingly coherence time.
But we can modify previous formula for two sources if we know the separation between electron source and neutron source i.e. lets say its "b" such that a>> b*d / ( \del \lambda), where a is distance of the measuring device form double slit, b is the separation between two sources, d is separation between two slits and \del \lambda is the spectral width of two sources. This condition holds to get interference fringes of good contrast. I will highly appreciate comments on this. Thanks sir...
Dear Anil, if we for simplicity consider a wave of identical particles (having a single wavelength), then your earlier equation looks OK to me. What happens if we have two kinds of particles? There will be two wavelengths say lambda_1 and lambda_2 and the question is when these will be sufficiently close to lead to interference of both ensembles of particles. If there is a spread in lambda_1 and in lambda_2 such that these overlap, there can again be interference. In this case I think that the distance behind the double slits must be sufficiently large that it is much larger than the difference in the two wavelengths. Is this what you had in mind?
Dear Peter Sir, Thanks. Two wavelengths have been taken care in
\del \lambda = lambda_1 * lambda_2 / path difference between two ~ lambda^2/ path difference . But the statement "distance behind the double slit" makes me confuse. If you mean the distance between measuring device and double slit then its yes. if its distance between double slit and screen, so that part we can take care according to fringe width concept. I think vacuum fluctuation is culprit for interference after large distance of measurement. I am not sure about this statement but its just my perception. Thanks...
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