San K said:
Sorry if the question is too basic.
What happens when a pair of entangled particles are sent through a double slit? (Same time) ...in case they are
1. Only momentum entangled
2. Only position entangled
3. Only spin entangled
If the particles are entangled in position, then they are also entangled in momentum, since entanglement is a property of the state which doesn't change with coordinate transformation (including Fourier transforms)
So if they are entangled in position, they must also be entangled in momentum, or...
...going to spherical coordinates, they must be entangled in angular momentum if they are entangled in angular position.
Polarization is different, since it is a completely independent degree of freedom (i.e. you cannot deduce the polarization knowing the position/momentum, etc). So you could say the photons were polarization entangled and not position/momentum entangled
If the photons are polarization entangled, that won't affect how they propagate through the two slit experiment, since that is determined by their momentum; you would see an ordinary fringe pattern.
If the photons are position-momentum entangled, then pair by pair, they could act as single photons, and the fringe pattern would again be ordinary, but this depends on the particular kind of entangled state, and whether the light is coherent or not.
One way you can really see something weird going on with entanglement is when you look at the correlations between particles.
As a particular example, you could ask the question, "given that a photon has hit the screen here, where is the likely location of the partner photon?" Depending on the entangled state, we might expect the photons to be on top of each other (within uncertainty), or to be anticorrelated, landing on completely opposite sides of the screen.
What you would be able to say is that if the pair of photons is entangled, given that you know where one photon hit, the other photons likely impact location is well-determined.
Just by looking at the fringe pattern as a whole, it may well look like an ordinary fringe pattern, but if you had timing information, of when each photon hit the screen and where, you would definitely be able to work out that you have entangled light.
I do research on entangled light, and you can show that if your photons are strongly correlated in both position and momentum, or say in different components of the polarization, you can prove that there's entanglement there.
