How does one detect which slit a photon has passed through in a double slit experiment?
Would the double slit experiment change if the photons were to pass through vacuum tubes instead of slits?
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Polarizing each slit with polarizations that are at 90 degrees out from each other is one way. Then viewing the screen with a polarization that is congruent with one of the slits will reveal through which slit the light passed. When viewing the screen with polarization that is 45 degrees to each slit an interference pattern will be seen. I did this with a interferometer but it works with the double slit too. see time frame 1:47
Now you are specifically asking about detection, which is not well defined in QM. You mean measuring, and QM measurements are always measurements of specific observables.
It is very important to differentiate measurement, and interaction.
There is no holistic act of "observing all properties of a system at once" like there is in classical mechanics - a measurement is always specific to the one observable it measures, and the measurement irrevocably alters the state of the system being measured. People often use "detect a particle" as shorthand for "perform a position measurement of a particle".
I actually asked a question about this:
Now there are different types of interactions, and yes it is possible to interact with a photon at a slit without destroying the interference pattern.
The three main types of interaction are:
elastic scattering, in this case the photon keeps its energy, phase and the interference pattern is still there
inelastic scattering, in this case the photon gives part of its energy to the atom, changes phase and the interference pattern disappears
absorption, in this case the photon gives all its energy to the absorbing atom/electron, and the photon ceases to exist. This is what happens at the actual screen, when you see a dot.
Most detectors usually do 1. or 2., and in case of elastic scattering, the pattern is still visible.
Although the electrons (which were shot one by one) could still pass through the filtered slit, the filter caused more of the electrons to undergo inelastic scattering rather than elastic scattering. As the physicists explained, an electron undergoing inelastic scattering is localized at the covered slit, and acts like a spherical wave after passing through the slit. In contrast, an electron passing through the unfiltered slit is more likely to undergo elastic scattering, and act like a cylindrical wave after passing through that slit. The spherical wave and cylindrical wave do not have any phase correlation, and so even if an electron has a probability to pass through both slits, the two different waves that come out cannot create an interference pattern on the wall behind them.