Meaning of Single Photon Interference Minima

[LikesIntuition]

In the double slit experiment, when we send out one photon at a time, what does the appearance of minima in our interference pattern mean? When a single photon is fired, I understand (using "understand" very loosely) that the photon will interfere with itself. When this happens, does it still have to land on the wall in front of the slit and it is limited to the bright bands defined by interference, or are there times where we will fire the photon and it will destructively interfere with itself and we won't see it land on the wall? Because if that's the case, energy would just be disappearing.

I can try to clarify if need be.

Thanks!

 

[DrClaude]

In the double slit experiment, when we send out one photon at a time, what does the appearance of minima in our interference pattern mean?

It means that there are regions where the probability of detecting the photon is very low.

When this happens, does it still have to land on the wall in front of the slit and it is limited to the bright bands defined by interference, or are there times where we will fire the photon and it will destructively interfere with itself and we won't see it land on the wall?

In an idealized experiment, the probability of detecting the photon must be one. It is the probability amplitude (i.e., the wave function) that will show areas of constructive or destructive inteference. It is not the photon interfering with itself.

 

[jtbell]

The interference pattern redistributes the photons (and the energy that they carry) so that there are more of them in the maxima and fewer of them in the minima, than we would expect if there were no interference. No photons or energy "disappear".

 

[LikesIntuition]

Alright, so every time we send a photon through the double slit, we will detect one after the slit? And it's two wave functions describing the photon as it moves through each slit that interfere with each other?

If that's the case, what's the difference between talking about the photon and it's wave function?

 

[bhobba]

Well actually, without going into the details, you don't have a wave-function for photons.

But the double slit can be done with electrons so let's consider that instead.

The wave-function encodes all the quantum properties of the electron.

Also you may like to see an actual quantum explanation of the double slit:
http://cds.cern.ch/record/1024152/files/0703126.pdf

Interestingly it hasn't really got anything to do with waves.

Thanks
Bill

 

[Nugatory]

If that's the case, what's the difference between talking about the photon and it's wave function?

In the double-slit experiment, when you fire one photon you get one spot on the photographic film behind the slits. You'll say that one spot is where the particle hit, and we're talking about the particle not the wave function.

As you fire more photons more spots on the film will appear; these spots will gradually build up a pattern of dark and light regions corresponding to the areas of constructive and destructive interference. Now we're talking about the wave function.