# Variation of double slits experiment

Setup goes something like this: the laser gun fires only 1 photon each time and the only way for the photon to appear on the hidden screen is for them to be reflected from the 2 narrow mirrors.(see image below)

I was watching a ping pong match and suddenly this pops into my mind.

Will there be any interference pattern based on my setup?

I argue that 1 photon now does not have the chance to interfere with itself like the double slits so there will not be any zebra pattern showing up but I might be wrong. Also if I coat both mirrors with Polaroid so that one mirror is left circularly polarized while the other is right circularly polarized, what will appears on the hidden screen if any?

• All you have to do is the experiment. Commented Aug 20, 2016 at 4:40
• user6760 Please always keep in mind that a single edge is enough to bear an intensity distribution and this holds also for single shoted photons. So any discussion about slits, double slits and polarisers has to be discussed under attention of this fundamental phenomenon. Commented Aug 20, 2016 at 13:22
• physics.stackexchange.com/questions/158105/… Commented Aug 20, 2016 at 19:50

As an experimental physicist I would advice you to do the experiment.

What the theory predicts for single photons is what the boundary conditions the wavefunction of the photon has obeyed for the particular experiment. This wavefunction is complex and carries the phase information for building up the classical electromagnetic wave. It should not be surprising because both the classical wave and the photons it is composed of are solutions of the same maxwell equations, in the case of the photon treated as operators on the wavefunction.

Thus, if interference is seen in a classical light experiment,the single photon distributions will build up to the interference pattern. The classical em distribution is the probability density of finding a photon at a screen, and thus it is the square of the wavefunction of the individual photon. For links look at this answer of mine.

• This is a good explanation, but it falls short of actually answering the question. We do expect the photon so interfer with itself here right? Commented Aug 20, 2016 at 5:02
• The phrase "the photon to interfere with itself" is wrong physics. The photon as a quantum mechanical entity propagates with a probability function. This probability function when squared will show interferences for the photon , because of the boundary conditions, if interferences are observed in the macroscopic classical em wave. If the classical wave shows no interferences, the the single photon accumulated distribution will also not show interferences. A poton by itself is just a footprint of a point on the screen, displaced according to its wavefunction. Commented Aug 20, 2016 at 6:21
• Yes I agree. But it is interesting that this notion that a photon interferes with itself was expressed as such by Dirac in his book. I think this has mislead many people for a long time. I do however think one can say a bit more. Commented Aug 20, 2016 at 6:27
• @flippiefanus photons cannot interfere with themselves. Commented Aug 20, 2016 at 7:06
• @BillAlsept: read my comment carefully, I didn't say they can. Commented Aug 20, 2016 at 8:26

There is perhaps a bit more that we can add to the answer of anna v in the context of an experiment done with single photons. How would one do such an experiment? First one would need to do the alignment. One would set up the light source(s) so that no light falls on the screen directly. It would be important that the light is coherent so that one should in principle be able to see interference if there is an overlap. Then one would place the mirrors for the light to be reflected onto the screen so that the two reflected beams overlap on the screen. To do this alignment, one would first use a bright source that one can see - classical light. If the light is coherence one should see interference on the screen.

Now the setup is done and one can turn to the single photon case. So in some way one modifies the light source (not important how) so that it emits one photon at a time. (Just to be more specific what we mean by this: the light intensity is low enough so that the photons are registered individually by the detector.) The screen needs to be replace by a detector array that can detect single photons (they do exist). We then wait for a while to accumulate enough detections of single photons to see if the resulting pattern shows an interference pattern.

What will we see? Well, as anna v explained, if we saw interference with the classical light we will also see interference in the case of single photons. Why? Because, the theory that describes the classical case and the theory that describes the quantum case for single photons in a linear system are identical. These theories have been tested quite thoroughly so we trust them.