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phonon44145
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Recently I came across the following two-photon state
sqrt(2) |2v,0h> + |1v,1h>
(as a side note, it results when a single, vertically polarized photon |1v> interacts with an excited atom and interaction is modeled by the Jaynes-Cummings hamiltonian - the first term is stimulated, the second - spontaneous emission). Of course, there should be normalization constant 1/sqrt 3 which I dropped to keep things simple.
So the number of photons is fixed (2 photons), but they can be both polarized vertically or that can be in orthogonal polarization modes. If one photon now passes through a horizontal polarizing filter and lands on the screen behind it, we know that photon was polarized horizontally. So the other one must certainly be polarized vertically and we can predict it is going to be absorbed in the filter. On the other hand, if we register an absorption event first, then we still can't tell if the other photon will be absorbed or transmitted.
My question:
1. What is the correlation among the two photons in the above state - are they mutually independent, are they (weakly) entangled, or neither?
2. Is it possible to factor out the vertical photon in the above expression to write the state as the product
|1v> (a|1v> + b|1h>)
and if not, why?
3. We now want to measure the polarization of each photon, and pass the given 2-photon state through a vertical polarizer. What are the probabilities of each outcome: a) |1v>|1v>, b) |1h>|1h>, c) |1v>|1h> ?
sqrt(2) |2v,0h> + |1v,1h>
(as a side note, it results when a single, vertically polarized photon |1v> interacts with an excited atom and interaction is modeled by the Jaynes-Cummings hamiltonian - the first term is stimulated, the second - spontaneous emission). Of course, there should be normalization constant 1/sqrt 3 which I dropped to keep things simple.
So the number of photons is fixed (2 photons), but they can be both polarized vertically or that can be in orthogonal polarization modes. If one photon now passes through a horizontal polarizing filter and lands on the screen behind it, we know that photon was polarized horizontally. So the other one must certainly be polarized vertically and we can predict it is going to be absorbed in the filter. On the other hand, if we register an absorption event first, then we still can't tell if the other photon will be absorbed or transmitted.
My question:
1. What is the correlation among the two photons in the above state - are they mutually independent, are they (weakly) entangled, or neither?
2. Is it possible to factor out the vertical photon in the above expression to write the state as the product
|1v> (a|1v> + b|1h>)
and if not, why?
3. We now want to measure the polarization of each photon, and pass the given 2-photon state through a vertical polarizer. What are the probabilities of each outcome: a) |1v>|1v>, b) |1h>|1h>, c) |1v>|1h> ?
