Can A Single Photon Be Split Into 45 and 135 Degree Polarization?

[StevieTNZ]

Really two questions:

1. In the Do-It-Yourself Quantum Eraser article written by Rachel Hillmer and Paul Kwiat (published in Scientific American, May 2007), on page 93 there are instructions to cut in half horizontally a D-orientated (45 degrees clockwise from V), and an A-orientated (45 degrees counterclockwise from V), polariser and join them together. Are there such polarisers that are orientated as the final product of doing the above, but are applicable to a single photon passing through it (so either the photon will be 45 degrees polarised, or 135 degrees polarised)?

2. If a V polarised photon is tested in the polariser described above, because it has 1/2 probability of passing or failing the 45 degree, and 135 degree, tests, if it fails the 45 degree polariser, is it a candidate of now having probability 1 of passing the 135 degree polariser, or still 1/2 probability of passing the 135 degree polariser?

 

[StevieTNZ]

Would a circularly polarised photon be in a superposition of 45 degree and 135 degree polarisation? Is there a polariser that let's through all the photons in that superposition? What would the probabilites of V and H polarised photons passing/failing that polariser be?

 

[Ken G]

I guess I should read that article, because it seems to me that "putting together" 45 and 135 degree polarizers results in something that transmits no light at all. That is certainly true if the light first encounters one polarizer and then the other, but maybe there's some way to encounter both "at the same time"-- but that sounds like it would have to be like having no polarizer at all. I can't see any way to get something that transmits either 45 or 135 degree polarization, and nothing else. It would violate the superposition principle-- V polarization is an equal superposition of 45 and 135, so if 45 passes, and 135 passes, then V would have to pass also. One might imagine inducing a relative phase shift between 45 and 135, but that would only shift V into elliptical polarization, it wouldn't give only 45 or 135 and nothing else.

On that last question, circular polarization can be a superposition of 45 and 135-- if there is a pi/2 phase difference between the two polarizations. The superposition yields V if there is a 0 phase difference between them. But as far as I know, when I think of a polarizer I think of something that still invokes the principle of superposition, not some nonlinear optics device that does not support that principle. They must be talking about something more complicated than what I'm imagining.

 

[StevieTNZ]

I can't see any way to get something that transmits either 45 or 135 degree polarization, and nothing else. It would violate the superposition principle-- V polarization is an equal superposition of 45 and 135, so if 45 passes, and 135 passes, then V would have to pass also.

If a photon is in V polarisation, it has 1/2 probability for passing a 45 degree test. But in saying that, it also has 1/2 probability for failing the test, and if it fails (and we could somehow deflect the photon onto another path), is it guaranteed that it'll pass a 135 degree polariser? Or will it maintain its V polarisation and have 1/2 probability of going through a 135 degree polariser?

 

[Edgardo]

1. In the Do-It-Yourself Quantum Eraser article written by Rachel Hillmer and Paul Kwiat (published in Scientific American, May 2007), on page 93 there are instructions to cut in half horizontally a D-orientated (45 degrees clockwise from V), and an A-orientated (45 degrees counterclockwise from V), polariser and join them together. Are there such polarisers that are orientated as the final product of doing the above, but are applicable to a single photon passing through it (so either the photon will be 45 degrees polarised, or 135 degrees polarised)?

2. If a V polarised photon is tested in the polariser described above, because it has 1/2 probability of passing or failing the 45 degree, and 135 degree, tests, if it fails the 45 degree polariser, is it a candidate of now having probability 1 of passing the 135 degree polariser, or still 1/2 probability of passing the 135 degree polariser?

I suppose you mean this article: Do-It-Yourself Quantum Eraser

1. In order to have a 45° polarizer just take your polarizer sheet and rotate it provided you know its axis. Do the same for -45°=135°. Bring them close together and attach the wire between them. On a side note that angle is not important. It is only important that the left and right polarizer are oriented orthogonal to each other (see here). When you shine your laser on the wire a single photon will pass both sides and is in a superposition of -45° and +45° polarization.

2. The V polarized photon will be in a superposition of both 45° and 135° polarization (see above).

 

[Ken G]

If a photon is in V polarisation, it has 1/2 probability for passing a 45 degree test. But in saying that, it also has 1/2 probability for failing the test, and if it fails (and we could somehow deflect the photon onto another path), is it guaranteed that it'll pass a 135 degree polariser?

Yes, such a "test" will normally establish the polarization to be 135. It might depend on how you do it, but that would be the standard expectation AFAIK.

Or will it maintain its V polarisation and have 1/2 probability of going through a 135 degree polariser?

If the photon polarization is determined to be linear along 135, then it is no longer V. Note also that V is always a superposition of 45 and 135, you don't need to do anything to it to get that.

 

[Edgardo]

I suppose you mean this article: Do-It-Yourself Quantum Eraser

1. In order to have a 45° polarizer just take your polarizer sheet and rotate it provided you know its axis. Do the same for -45°=135°. Bring them close together and attach the wire between them. On a side note that angle is not important. It is only important that the left and right polarizer are oriented orthogonal to each other (see here). When you shine your laser on the wire a single photon will pass both sides and is in a superposition of -45° and +45° polarization.

2. The V polarized photon will be in a superposition of both 45° and 135° polarization (see above).

After thinking about it again I think my answer is wrong: Behind the double slit with polarization sheets the photon is not in a superposition of -45° and +45°. Rather it has collapsed to -45° or +45°.
(Though I am not sure, sorry! )