A few questions on Entanglement.

[kannank]

#1) Following the complementarity principle, a photon (plus everything) can behave *either* as a wave *or* as a particle at any instant. So if I setup a quantum erasure mechanism which switches the wave/particle behavior or path A, path B behaves similarly. If I arbitrarily consider 'wave behavior' as 0 and 'particle behavior' as 1, can I transmit binary information FTL?

#2) If all the electrons in path A is sent to a photoelectric cell with 100% efficiency, will the interference pattern disappear in path B? When a photon is used to eject and electron, instantaneously it proved that it is a particle, right?

Please help.

KANNAN K

 

[xts]

I think you should revise your understanding of 'complimentarity principle'. It very often leads to confusion, like yours.
That is not like Heisenberg's principle momentum-position complimentarity (you may measure one or second, but not both). Complimentarity principle says just that in some contextes photons (electrons, etc...) bahave as particles and in other contextes behave like waves.


When you make a double slit experiment, the photon behaves as a wave on its path (it interferes), but behaves as a particle, when hits photocell detecting it. It's behaviour is not of your choice. You can't order photon to wave-like behaviour nor to particle-one behaviour.

 

[DrChinese]

#1) Following the complementarity principle, a photon (plus everything) can behave *either* as a wave *or* as a particle at any instant. So if I setup a quantum erasure mechanism which switches the wave/particle behavior or path A, path B behaves similarly. If I arbitrarily consider 'wave behavior' as 0 and 'particle behavior' as 1, can I transmit binary information FTL?

#2) If all the electrons in path A is sent to a photoelectric cell with 100% efficiency, will the interference pattern disappear in path B? When a photon is used to eject and electron, instantaneously it proved that it is a particle, right?

Please help.

KANNAN K

Good questions. As it turns out, entangled particles do not produce the expected interference patterns. So you cannot use the technique you describe to send information FTL. See Fig. 2, page S290:

http://www.hep.yorku.ca/menary/courses/phys2040/misc/foundations.pdf

I would definitely recommend this article as it has a ton of great material relevant to your questions. Zeilinger is one of the greats.

 

[kannank]

Good questions. As it turns out, entangled particles do not produce the expected interference patterns. So you cannot use the technique you describe to send information FTL. See Fig. 2, page S290:

http://www.hep.yorku.ca/menary/courses/phys2040/misc/foundations.pdf

I would definitely recommend this article as it has a ton of great material relevant to your questions. Zeilinger is one of the greats.

Thanks for the link. Fig-2 was alright. But fig-3 caught my attention. Possibly by moving the lens between f and 2f, binary information could be encoded. One of the easiest setup for quantum erasure.

by the way, what's a Heisenberg lens & detector? can someone please explain me?

Also when path A is 'compromised', interference pattern in path B disappears. Does other wave properties like diffraction disappears too? Does path B refuse to get focused by a lens?!

 

[DrChinese]

Thanks for the link. Fig-2 was alright. But fig-3 caught my attention. Possibly by moving the lens between f and 2f, binary information could be encoded. One of the easiest setup for quantum erasure.

by the way, what's a Heisenberg lens & detector? can someone please explain me?

Also when path A is 'compromised', interference pattern in path B disappears. Does other wave properties like diffraction disappears too? Does path B refuse to get focused by a lens?!

Figure 3 does not allow information to be encoded. If you look carefully at the graph in Fig. 4, you will see the label for the Y axis is "conditional counts for D1". I.e. coincidences of D1 and D2. Nothing observable changes for Bob (D2) according to what Alice (D1) does, and vice versa.

 

[xts]

Advocatus diaboli voice:

With all respect to Anton Zeilinger, I don't like his explanation of the Dopfer's double slit experiment with momentum entangled photons, presented in "Experiment and the foundations...", which, as I see was confusing for Kannank as for many other its readers.

1. Zeilinger uses misleading language, implying causality. "Measurement destroys...", etc. It is easy to misunderstand him, and take that mere fact of registering photon in some eigenstate in one branch causes visible changes in other branch. It is not stressed enough that no pattern ever appear on the screen - the only patterns we may find are in correlations. Looking at Fig.4 and reading its caption you are getting the impression, that fringes could be seen on the screen if just beam intensity would be strong enough to use eye rather than photon counters. The importance of 'conditioning' is not stressed and may be easily overlooked (oh, yeah, that must be some technical trick to filter out the experimental noise...)
From my experience - majority of students reading this text misunderstand it this way.

2. The discussion neglects one issue: the crystal must be large, which is crucial to understand why the fringes are not seen.
I met the student, who thought that mere fact of being generated in an entangled pair makes the photon of different kind than ordinary ones - the special 'noninterferable' photon.
DrChinese uses the same misleading language: entangled particles do not produce the expected interference patterns, which is defendable, but definitely misleading!
The reason why we have no visible pattern is not an entanglement, but mere fact that direction of incoming photons is not well defined (if in place of our crystal we put a milky glass ball the same size, illuminated with a laser, we wouldn't see any fringes as well).
It is not that obvious at once that entanglement implies necessity of wide range of directions.

3. The experiment, although often used in discussions about EPR, Bell, etc., does not violate Bell's inequality and may fully be explained using hidden variables (even not so hidden - natural base is sufficient - pairs of photons in identical momentum eigenstates fully explain it), without involving any 'entanglement mysteries'. Zeilinger says:

One might still be tempted to assume a picture that the source emits a statistical mixture of pairwise correlated waves where measurement of one photon just selects a certain, already existing, wavelet for the other photon. It is easy to see that any such picture cannot lead to the perfect interference modulation observed.​

I don't understand his argument. Flat waves (of correlated directions randomly chosen in angle range much bigger than lambda/d where d is a span of double-slit) lead to exactly the same results, as reported in the article: perfect fringes if trigger is set at focal plane, no fringes at all if trigger is set at 2f - far from focus. More - fringes at D1 while triggering by D2 are also equally well explainable this way.
Dopfer's analysis of the experiment shows some 'entanglement mysteries', but A-Z had not shown them in his article, while Dopfer's work is not easily available, and only in German.

Nevertheless - the article is definitely worth reading!

 

[kannank]

Though we have disagreements on the nature of Entangled behavior, we have a consensus that entanglement does occur and a seemingly instantaneous decision making is taken by both the entangled paths.

I have a different question to this. Let's set the entanglement aside and go back to the original double slit experiment.

A perfectly 'compromised' double-slit will give no interference pattern at all and the 2 blobs of photons are created at the detector. What if we direct one of these blobs to another double-slit. Will it show interference or not?

I think it will.

My reasoning:

A photon under the complementarity principle can behave as a particle or wave, but never both.

Let's imagine a hypothetical 'perfectly un-observing' system (a system which doesn't ask photon to make a choice). Here photon has equal probability to be a wave or a particle

f(p)=f(w)=1/2

Now imagine the photon is subjected to a rigged double-slit. The photon here makes a choice to be a particle and it's particle properties are manifested.
f(w)=0
f(p)=1

Now the photon is further subjected to an normal double-slit. Here photon makes a choice to be a wave and its wave properties are manifested.
f(w)=1
f(p)=0

This is analogous to a tossing a fair-coin. When it is in transit, the probability of a head and a tail is the same

f(h)=f(p)=1/2

When it is subjected to an event of observation it has to make a choice of head or tail. Now if you pick it and toss it again, the original probabilities are reinstated.

This is valid for both entangled and unentangled systems.

Is my reasoning fair?

KANNAN

 

[xts]

I fully agree with results and idea behind your reasoning. I just don't like narration in terms of wave-particle complimentarity and sentences like "The photon here makes a choice to be a particle". Pure wave mechanical approach seems for me to be more straightforward, simpler, and allows to avoid many pitfalls.

After passing the slit (left or right) on the rigged blind, photons continues as spherical wave, originating on this slit. Then it interferes, producing fringe pattern at the screen.
The same applies to photons passing other slit. Those two patterns must be just added, as original sources (slits in 'rigged' blind) were not coherent. They produce the patterns shifted by $dL_1/L_2$ where $d$ is a span between slits, $L_1$ is a distance between 'normal' slits and the screen, and $L_2$ is a distance between 'rigged' slit and 'normal' one. If $L_1$ and $L_2$ are of similar magnitude, the shift will be unnoticeable, and the final pattern will exhibit nice fringes.

Actually, what you propose is very much like original Young's experiment: he used a setup of incoherent source (sun+mirrors+lenses), single slit to form a spherical wave, then double slit.

 

[kannank]

I just don't like narration in terms of wave-particle complimentarity and sentences like "The photon here makes a choice to be a particle". Pure wave mechanical approach seems for me to be more straightforward, simpler, and allows to avoid many pitfalls.

I didn't mean it to be photon 'deciding' anything literally. It's quite possible that photon is not the one who decides. This is what we see in an asymmetric quantum wave eraser.

And this is probably the quantum secret.

The idea behind doing a serial DS experiment was to say photons after being 'manipulated' in a 'rigged' event could recover its original indeterminate complementary state when subjected to another 'normal' event. I'm now working on the mathematics to see whether the interference fringe created by the second DS changes if the first DS is 'rigged' or not.

I'm super weak in the maths of physics. Do you think the final interference pattern will change depending on whether the intermediate DS experiment was rigged or not.

KANNAN

 

[xts]

Well, I just don't like the concept of 'complimentarity' and speaking about photons 'being waves' , or 'being particles'. I definitely prefer the view of propagating waves which just cause discrete 'clicks' in detectors rather than creating very-very-weak continuous images. But it is a matter of taste - if you feel comfortably (and smart enough to avoid pitfalls) with photons switching their nature like dr.Jekyll - its OK.

I'm now working on the mathematics to see whether the interference fringe created by the second DS changes if the first DS is 'rigged' or not.

Good luck. A hint for a special case to be easily analysed: make your second double slit sparser than first, and install it in such place, that constructive interference (of the first DS) occurs at the left slit of the 2nd blend, but negative occurs at the right one.

Do you think the final interference pattern will change depending on whether the intermediate DS experiment was rigged or not.

Once again - good luck with calculations! (Some practice will help to improve your 'super weak')
But you may try to picture that without any mathematics... What does it mean for photons (in your favourite terms of being particle or wave) that 2nd DS is rigged? Or in terms of coherence/decoherence?

 

[DrChinese]

A photon under the complementarity principle can behave as a particle or wave, but never both.

I believe this is, in a sense, a flaw which has been circulated over the years. Any particle can behave as a wave, particle, or a (partial) combination of both. That combination, of course, respects the Uncertainty Principle.

 

[DrChinese]

2. The discussion neglects one issue: the crystal must be large, which is crucial to understand why the fringes are not seen.
I met the student, who thought that mere fact of being generated in an entangled pair makes the photon of different kind than ordinary ones - the special 'noninterferable' photon.
DrChinese uses the same misleading language: entangled particles do not produce the expected interference patterns, which is defendable, but definitely misleading!
The reason why we have no visible pattern is not an entanglement, but mere fact that direction of incoming photons is not well defined (if in place of our crystal we put a milky glass ball the same size, illuminated with a laser, we wouldn't see any fringes as well).
It is not that obvious at once that entanglement implies necessity of wide range of directions.

I am not disputing what you are saying, as this point is one I do not understand completely.

As far as I know, a normal coherent photon stream from a well defined point source produces the usual interference pattern. So I don't see the source spread as being the difference here, as entangled photons can be collected into fiber and moved anywhere you like as well.

I have understood that entangled photons are incoherent, and that is the reason that they do not produce interference. However, I haven't seen any material that really explains this nuance. Does anyone have a useful reference?

 

[xts]

So I don't see the source spread as being the difference here

Source spread is what constitutes spatial incoherency. Point-like source may emit only spherical waves originating at it - in an eigenstate of precisely known position, unknown momentum.

entangled photons can be collected into fiber and moved anywhere you like as well.

Entangled only regarding their spin/polarisation. Not their traversal momentum (direction). As you collect them into singlemode fiber, you actually measure their position with accuracy of one micrometer (fibre core diameter), setting them in their spatial eigenstate.

I have understood that entangled photons are incoherent, and that is the reason that they do not produce interference.

Try thought experiment: we produce a pair of entangled photons. Then we send one of them (with mirrors and lenses) towards the most obscure part of the sky. Or we just destroy it absorbing on a black body.
What may be the difference between the remaining photon and 'ordinary' photon created e.g. in the light bulb?

The incoherency of entangled photons comes from their superposition of states. They are neither in eigenstate of position nor of momentum (otherwise entanglement would be trivial - just pair of identical eigenstate photons). But if you analyse just one photon of the pair, this incoherence does not differ from incoherence of randomly created photons.

You remember original Young's experiment. In order to make the wave illuminating double slit coherent, Young used a single slit, making effectively the source of light point-like. Very small crystal could still produce spin-entangled photons, but their spatial/momentum entanglement would be trivialised to position eigenstate.

However, I haven't seen any material that really explains this nuance. Does anyone have a useful reference?

I'll try to dig something - after dinner ;)
I remember some paper also by A-Z I think, I'll try to find it.

ADDED>>>
I can't find that A.Z.'s article (maybe I remember it wrong), but jumping over references I found good-looking review of such topics:
Spatial correlations in parametric down-conversion, S. P. Walborn et.al, http://arxiv.org/abs/1010.1236v1