Stimulated emission and polarization - a thought experiment

[Erik Ayer]

Imagine that one has a single photon of 632nm. It enters the back end of an open-ended HeNe laser tube - one with no mirrors - and along its path, causes the emission of another photon. According to the wikipedia entry on stimulated emission (https://en.wikipedia.org/wiki/Stimulated_emission), the new photon will have the same phase, frequency, polarization, and direction as the original. My question concerns the polarization.

Say the original photon was in a superposition state as far as its polarization was concerned. What, then, does it mean to say that the new photon has the same polarization? Will both photons be in a superposition state, or will the original collapse into an eigenstate which will be matched by the new photon? If this is not the case and both photons are in superposition, what happens when they hit a polarizing beam splitter? If both photons are in superposition, then they should both transmit and reflect and go down both paths, but at some point, they will hit something that causes them to collapse (unless this is part of a Mach-Zehnder interferometer, but never mind that), and I'm wondering whether they will both have gone the same way.

If so, this almost seems like a form of entanglement. Taken further, if the original photon causes emission of several photons, each of which causes emission of more, what is the (polarization) state of them all? They could either all be in a superposition state and later all go the same way at the PBS, or the original could collapse into an eigenstate and the rest follow.

I assume that I'm stupid and don't understand at least one critical aspect of what's going on. How am I stupid?

 

[DrChinese]

Imagine that one has a single photon of 632nm. It enters the back end of an open-ended HeNe laser tube - one with no mirrors - and along its path, causes the emission of another photon. According to the wikipedia entry on stimulated emission (https://en.wikipedia.org/wiki/Stimulated_emission), the new photon will have the same phase, frequency, polarization, and direction as the original. My question concerns the polarization.

Say the original photon was in a superposition state as far as its polarization was concerned. What, then, does it mean to say that the new photon has the same polarization? Will both photons be in a superposition state, or will the original collapse into an eigenstate which will be matched by the new photon? If this is not the case and both photons are in superposition, what happens when they hit a polarizing beam splitter? If both photons are in superposition, then they should both transmit and reflect and go down both paths, but at some point, they will hit something that causes them to collapse (unless this is part of a Mach-Zehnder interferometer, but never mind that), and I'm wondering whether they will both have gone the same way.

If so, this almost seems like a form of entanglement. Taken further, if the original photon causes emission of several photons, each of which causes emission of more, what is the (polarization) state of them all? They could either all be in a superposition state and later all go the same way at the PBS, or the original could collapse into an eigenstate and the rest follow.

I assume that I'm stupid and don't understand at least one critical aspect of what's going on. How am I stupid?

Welcome to PhysicsForums, Erik!

I may not be able to answer all of your questions, but I may be able to help. Generally, the 2 (or more) photons you mention will not be polarization entangled even if the polarization is the same. Therefore, their path through a subsequent PBS will not necessarily be the same. You may get some additional information from this thread and its references:

https://www.physicsforums.com/threads/is-laser-light-polarized-or-unpolarized.282195/

 

[Erik Ayer]

Welcome to PhysicsForums, Erik!

I may not be able to answer all of your questions, but I may be able to help. Generally, the 2 (or more) photons you mention will not be polarization entangled even if the polarization is the same. Therefore, their path through a subsequent PBS will not necessarily be the same. You may get some additional information from this thread and its references:

https://www.physicsforums.com/threads/is-laser-light-polarized-or-unpolarized.282195/

It seems like the stimulated photon(s) shouldn't be entangled with the original - that would be way too easy. However, I don't know how to reconcile the properties of "having the same polarization" while the polarization is in a state of superposition. Somewhere that's got to break.

At the link you give is a discussion on whether laser light in generally polarized. In this case, however, I'm kind of thinking of what would happen if a single photon was sent into a laser tube, causing more photons to be stimulated. I would think that all the photons created like this would have the same polarization as the original, and again, that runs smack into the problem of polarization being in superposition.

In the experiment devised by Nick Herbert called FLASH, he proposed a system that included using a laser tube to copy photons so that the polarizations at different angles could be measured. It lead to the no-cloning theorem. It seems like my idea is slightly different but also very similar.

 

[DrChinese]

It seems like the stimulated photon(s) shouldn't be entangled with the original - that would be way too easy. However, I don't know how to reconcile the properties of "having the same polarization" while the polarization is in a state of superposition. Somewhere that's got to break.

At the link you give is a discussion on whether laser light in generally polarized. In this case, however, I'm kind of thinking of what would happen if a single photon was sent into a laser tube, causing more photons to be stimulated. I would think that all the photons created like this would have the same polarization as the original, and again, that runs smack into the problem of polarization being in superposition.

In the experiment devised by Nick Herbert called FLASH, he proposed a system that included using a laser tube to copy photons so that the polarizations at different angles could be measured. It lead to the no-cloning theorem. It seems like my idea is slightly different but also very similar.

Most normal lasers will have all output light at a fixed identical polarization. So no polarization entanglement there.

I realize you are trying to start with a single seed photon that is itself in a superposition. This "might" be possible in principle. But then it cannot take on a polarization if there is to be entanglment. That I am not sure can be prevented when emission is stimulated. I have never heard of entangled photons emerging from a laser, but I would be far from the authority on that point.

 

[Erik Ayer]

I agree, in order to have entanglement, the "seed" would have to stay in superposition and all the stimulated photons would have to stay in superposition. It seems like they *should*, but I also haven't seen any experiments that test it. It all comes down to a stimulated photon being a copy of the original.

Meredith instruments gets laser tubes with no mirrors - they said they sent a bunch on to a guy who uses them just recently. It would be interesting to try this experiment: use one laser and a bunch of neutral density filters to get about one photon per send and send it into the open-ended tube to get a clot of them out. Then send that to a PBS with detectors on both paths and see if they both fire at the same time (so they each get photons from each clot). Setting this up, however, would be non-trivial :)

Thank you for your replies!

 

[DrChinese]

I agree, in order to have entanglement, the "seed" would have to stay in superposition and all the stimulated photons would have to stay in superposition. It seems like they *should*, but I also haven't seen any experiments that test it. It all comes down to a stimulated photon being a copy of the original.

Meredith instruments gets laser tubes with no mirrors - they said they sent a bunch on to a guy who uses them just recently. It would be interesting to try this experiment: use one laser and a bunch of neutral density filters to get about one photon per send and send it into the open-ended tube to get a clot of them out. Then send that to a PBS with detectors on both paths and see if they both fire at the same time (so they each get photons from each clot). Setting this up, however, would be non-trivial :)

Thank you for your replies!

The way I would deliver a single photon in a superposition would be to start with an entangled pair; use one to "herald" (idler) and the other as the seed (signal). The idler would need to be registered in such a way as to erase any polarization information, I believe this is feasible. You would then have 1 photon to start with which is in a superposition of polarizations.

Honestly I have no idea where you would go from there. There are a lot of different issues involved when there are Fock states and I am insufficiently versed to help on this. I think lasers do not operate in states that would yield entanglement in part precisely because photon number is not fixed.

 

[Erik Ayer]

The way I would deliver a single photon in a superposition would be to start with an entangled pair; use one to "herald" (idler) and the other as the seed (signal). The idler would need to be registered in such a way as to erase any polarization information, I believe this is feasible. You would then have 1 photon to start with which is in a superposition of polarizations.

Honestly I have no idea where you would go from there. There are a lot of different issues involved when there are Fock states and I am insufficiently versed to help on this. I think lasers do not operate in states that would yield entanglement in part precisely because photon number is not fixed.

It would be difficult to get a downconverted photon pair that would be the right wavelength for a gas laser. For 632nm, that would be a pump at 316 - definitely not laser-diode friendly :) Interesting idea though. So if a HeNe outputs primarily polarized light, that would create primarily polarized "clots" of photons coming out of the amplifier tube. Orienting the PBS at 45 degrees would then give a 50-50 change if transmission vs. reflection.

Then, if two detectors are place at the tow possible paths, if only one went off at a time (per clot), that would indicate that all the photons in the clot were collapsing to the same polarization and were, thus, entangled. I strongly suspect both detectors would go off, meaning the photons of the clot randomly collapsed to horizontal and vertical. However, that would mean that they didn't have the same polarization as the seed photon.

Incidentally, you mention that this isn't really your field. I have a bachelors in physics, and it was the third major that got tacked on because it was cool. that makes me even less of an expert.

 

[Nugatory]

Then, if two detectors are place at the two possible paths, if only one went off at a time (per clot), that would indicate that all the photons in the clot were collapsing to the same polarization and were, thus, entangled. I strongly suspect both detectors would go off, meaning the photons of the clot randomly collapsed to horizontal and vertical.

Yes, that is what happens. But...

However, that would mean that they didn't have the same polarization as the seed photon.

That does not follow, because "has the same polarization" doesn't mean that they will produce the same result in response to every polarization measurement. It means that they will produce the same result when subjected to one particular polarization measurement and different results with the same probability distribution when subjected to other measurements. For example, if I prepare a bunch of photons in the vertically polarized state and then send them through a diagonally-oriented polarizer I expect each one to pass or not pass with 50% probability - they all are in the same state, but they don't all produce the same result for that measurement (or any other measurement except of vertical and horizontal polarization).

You started this thread by saying "Say the original photon was in a superposition state as far as its polarization was concerned", and you're anticipating different behavior than if the original photon was not in a superposition state. That premise is flawed because there is no such thing as a photon not in a superposition state - you just have to choose a different basis. For example, the vertically polarized state is also a superposition of +45 and -45.

 

[Erik Ayer]

Yes, that is what happens. But...
That does not follow, because "has the same polarization" doesn't mean that they will produce the same result in response to every polarization measurement. It means that they will produce the same result when subjected to one particular polarization measurement and different results with the same probability distribution when subjected to other measurements. For example, if I prepare a bunch of photons in the vertically polarized state and then send them through a diagonally-oriented polarizer I expect each one to pass or not pass with 50% probability - they all are in the same state, but they don't all produce the same result for that measurement (or any other measurement except of vertical and horizontal polarization).

You started this thread by saying "Say the original photon was in a superposition state as far as its polarization was concerned", and you're anticipating different behavior than if the original photon was not in a superposition state. That premise is flawed because there is no such thing as a photon not in a superposition state - you just have to choose a different basis. For example, the vertically polarized state is also a superposition of +45 and -45.

Excellent points, thank you for straightening out my logic, or lack thereof :) So if the seed photon is in superposition relative to the table (assuming everything is sitting on a table), the stimulated photons will also be in superposition relative to the table - they will have the same polarization relative to the table as the seed. However, what they do after that can be different for each photon.

I need to rethink my entire idea and back-propagate the fix to the logical error.