Controlled delayed quantum erasure?

[jarekd]

In standard delayed choice quantum erasure experiment ( http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser ), the which-way information is randomly erased in one path, what chooses between classical and quantum behavior for the second path (if there is interference pattern). The "delayed" means that changing lengths of optical ways, we can make that the erasure (reason) is made after the result.
As the erasure is made randomly, we couldn't use this time reversed reason-result relation. But what if there would be a configuration where we can control if the erasure is made?
And it turns out that there is such configuration - proposed and tested by group of Walborn. Here is a decade old http://grad.physics.sunysb.edu/~amarch/Walborn.pdf , http://grad.physics.sunysb.edu/~amarch/ :
http://grad.physics.sunysb.edu/~amarch/PHY5656.gif
BBO produces two entangled photons - first polarization x, second y or oppositely.
Photon s comes through double slit before which there are installed two different quarter wave plates(QWP): changing linear polarization to circular in two different ways.
Finally there are two possibilities:
x y R L
y x L R
where succeeding columns are: linear polarization of p, initial linear polarization of s, circular polarization of s after going through slit 1, circular polarization of s after going through slit 2.
So if we know only the final circular polarization of s, we still don't know which slit was chosen, so we should get interference on the second path. But if we would additionally know if p is x or y, we would know which slit was chosen for s and so interference pattern would disappear.
So let us add linear polarizer on p path - depending on its rotation, we can or cannot get required information - it can erase the which-path information, choosing between quantum and classical behavior for s.
If s detector is in the first minimum of interference, we control statistics it observes by rotating polarizer on path p.

Changing lengths of optical paths, we would get delayed version, which seems to allow to control statistics in the past, by rotating polarizer in the future.
It suggests that something is wrong with such setup, but I don't see what - does anybody see where is the problem?

 

[San K]

Changing lengths of optical paths, we would get delayed version, which seems to allow to control statistics in the past, by rotating polarizer in the future.
It suggests that something is wrong with such setup, but I don't see what - does anybody see where is the problem?

Welcome to the forum jarekd.

The statistics in the past are not being controlled.

We need the co-incidence counter to filter out the set of photons. When we vary the optical length the pattern changes because a different set of photons are being filtered (from the overall blob/pile of photons)

There is no future changing the past -- happening here.

Perhaps Venn diagrams could be used to explain this visually.

 

[jarekd]

Hi San K,
Indeed the natural answer is the coincidence counter (to filter entangled photons). But what if there would be none?
Entangled photons - which got through SPDC in BBO, have twice larger wavelength - can be easily filtered e.g. by a prism.

Even without filtering, let us fix the s detector in the first (largest) minimum of the interference - it would have largest statistical difference between classical and quantum (erased) behavior.
Rotating the p polarizer, we would change s statistics of entangled photons only (statistics of not entangled should not be affected) - shouldn't polarizer rotation still cause a difference of the total number of photons in s detector?

 

[Cthugha]

Hi San K,
Indeed the natural answer is the coincidence counter (to filter entangled photons). But what if there would be none?

The main reason for using coincidence counting is not filtering entangled photons as opposed to noise.

If you have a look at the PRA paper, you will find that the upper detector is a very narrow one which will only detect photons from a narrow range of angles. The coincidence counting is needed for filtering the entangled photons within this narrow range of angles. As a comparison, try to do the double slit experiment with a point source at home and move the source away from the center between the two slits. The interference pattern will change (because the path difference from the source to the two slits will change). Without coincidence counting you see a superposition of many interference patterns summing up to no pattern at all. Only coincidence counting allows one to single out one of these patterns. If you moved the upper detector around, you would find a different pattern in the coincidence count signal.

Or as Walborn himself puts it: the main point in DCQE is clever bookkeeping.

 

[jarekd]

Thank you Cthugha, but I have to admit that I don't understand your explanation.
"Without coincidence counting you see a superposition of many interference patterns summing up to no pattern at all."
I think you have meant that the fringe (Fig. 4) and antifringe (Fig. 5) patterns sum to the classical pattern? But each of them is for a different angle of the polarizer...

Let us analyze the situation for a fixed polarizer angle. I think you agree that filtering is not a problem, can be done e.g. by a prism - using that entangled photons have twice longer wavelength.
So observing a photon by s detector means that it is already entangled.

The question remains (usually answered by the coincidence counter) if the second entangled photon will be observed by p detector - so there is some probability depending on its effectiveness.
If it will be also observed, the s detector statistics depends on the angle of polarizer.
If it will be not observed, the s detector statistics should not depend on the angle (?).

The coincidence counter would allow to restrict to the first case.
Without it, we would have sum of both cases, which should also depend on the angle of the polarizer?

 

[Cthugha]

Thank you Cthugha, but I have to admit that I don't understand your explanation.
"Without coincidence counting you see a superposition of many interference patterns summing up to no pattern at all."
I think you have meant that the fringe (Fig. 4) and antifringe (Fig. 5) patterns sum to the classical pattern? But each of them is for a different angle of the polarizer...

No, I do not mean that. You will get fringe and antifringe patterns at different positions if you move the upper detector (the one left in place in the experiment which you do not scan for position) around.

The double slit pattern you see in a normal double slit experiment depends strongly on the position of your light source. You can have a maximum or a minimum at the center and every other position depending on the position of your light source relative to the slits. This happens because light arriving at an angle imposes a phase difference at the slits due to different travel paths to the two slits. This changes the interference pattern. The resulting pattern will be offset by this phase difference. Entangled light consists of a wide range of emission angles. So you will get many of these patterns at once (which means no pattern at all) unless you filter for just one of these. This is what having a narrow detector in the upper arm of the experiment does.

 

[jarekd]

Ok, I think I have finally understood - thank you Cthugha.
The problem is that lack of detection of some p photons is not caused by ineffectiveness of p detector as I thought, but they were stopped by the polarizer.
It means that without the coincidence counter, we would indeed observe the sum of fringe (Fig. 4) and antifringe (Fig. 5) patterns.

Maybe you could also help me understanding problem with another situation which seems to allow for sending information back in time - CPT analogue of free electron laser (FEL)?
In standard FEL we enforce electrons to move in sinus-like pattern, what stimulates photon emission. These photons are later absorbed by a target, exciting it.
As physics is most probably CPT symmetric, imagine CPT analogue of this situation: excited target deexcitates - producing photons finally absorbed by positron moving in opposite direction ... but the situation is stimulated by the sinus-like trajectory - we get stimulated absorption setting instead of standard stimulated emission.

So imagine we constantly excite the target (e.g. sodium lamp), surround it with detectors - we should see energy conservation.
Now imagine that there is a small hole in detectors to the FEL in stimulated absorption setting (oppositely directed) - shouldn't turning it on change the lamp-detectors energy balance?