Hypothesizing on photon mode of travel in double slit or similar experimental setups

[sanpkl]

Delayed choice in half silvered mirror or double slit

For now, I am focussing only on the half silvered mirror:

there are two paths/arms that are created.

My question is:

1. If a detector/obstruction is placed on either of the two paths after the photon has passed but before its hit the final detector

- does the interference disappear? ...i would think ofcourse it does

2. If a detector/obstruction is placed after it has hit the final detector but not been measured yet

- does the interference disappear?

Please let me know if there are any clarifications required or if you want to make some corrections to the above experiment

 

[Cthugha]

I suppose you assume a delayed choice quantum eraser setup like the one used by Kim, Kulik, Shih and Scully (http://arxiv.org/abs/quant-ph/9903047) and when you say "the photon" you only talk about the idler and leave the signal unaltered on its way to detector D0.

Regarding 1):
If you create a situation where you block one arm and can be sure that the photon has already passed the position where you put the block, the interference pattern will still be there if you repeatedly remove and insert the block after the photon has passed - unless of course there is a large difference between the length of both paths.

Regarding 2):
As soon as the photon hits the detector, this is a measurement. It does not really matter, whether you write a number on a hard disk or whether you look at the results. So this case is basically the same as 1).

 

[SpectraCat]

For now, I am focussing only on the half silvered mirror:

there are two paths/arms that are created.

My question is:

1. If a detector/obstruction is placed on either of the two paths after the photon has passed but before its hit the final detector

- does the interference disappear? ...i would think ofcourse it does

2. If a detector/obstruction is placed after it has hit the final detector but not been measured yet

- does the interference disappear?

Please let me know if there are any clarifications required or if you want to make some corrections to the above experiment

Yeah ... some clarification is needed ... how do you make an interferometer with just a single half-silvered mirror? You need at least some other regular mirrors in there. Have you looked at Wheeler's original delayed-choice thought experiment? Is that what you are asking about? You need to show us a picture or your setup, or a least give a more detailed description.

That said, I think I can answer your question #2: There is no distinction between a photon "hitting the detector" and "being measured" in QM. They are the same event.

 

[sanpkl]

Spectra, Cthugha, and others who are interested:

Sorry, I need to describe the setup.
I am talking about 2 experimental setups.
1. Half silvered mirror = Mach–Zehnder interferometer = the link below
http://en.wikipedia.org/wiki/Mach-Zehnder_interferometer
2. Delayed choice quantum eraser = the link below
http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser
3. Double slit delayed choice, we can simply make one setup up where a detector is placed at different point in time during the movement of the photon from the slits to the screen.

First question: Are the three setups essentially the same as far as the conceptual questions we discuss in this thread are concerned?

Second Question: My understanding is that even if one of the paths is blocked or detector is placed after the photon has passed. The interference pattern WILL disappear. This is contrary to what Cthugha is saying.

Next questions: can follow after we come to understanding of the second question.

Also I have posting a new thread on a different topic. Here is an attempt to hypothesize as to what is happening (travel mode of the photon) during the experiment. Look forward to your responses. However let try to stick to the different topics in different threads to reduce confusion.

 

[sanpkl]

This is in reference to the two experiments:
1. Half silvered mirror = Mach–Zehnder interferometer = the link below
http://en.wikipedia.org/wiki/Mach-Zehnder_interferometer
2. Delayed choice quantum eraser = the link below
http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

The attempt of this post is to hypothesize on how the photon travels after it
- Exits the double slit or after it hits the FIRST half silvered mirror

Hypothesis 1:
The photon becomes a wave and half wave goes through one slit/path and half through the other

Hypothesis 2:
The photon has both particle and wave at SAME time.
The photon takes one of the two paths and the wave splits into half. Half wave goes through one slit/path and half through the other.

Now to test Hypothesis 1 (or actually even 2) :

Lets say we put a detector on either path :
1. Are we ever able to measure any property of the wave that would suggest its half a wave?
For example intensity is half or some other property is half?
I think the answer is: we either measure single particle or no particle, zero or one but no half.
Is that correct?

Now to test hypothesis 2:

I read somewhere that now they are able to (vaguely?) figure out which slit the photon went through *without* disturbing the interference pattern which is equal to without collapsing the wave function (?).

a) Can someone shed light on that experiment?

b) Also is it true that interference phenomena also works with Bucky balls (a bunch of carbon atoms)?

 

[sanpkl]

if i were to summarize the above in a few lines then it would be somthing like:

1. Are we ever able to measure/notice the split in the wave (function) after it has gone through the double slit or the half silvered mirror?

2. Are we vaguely able to tell which path the photon took without collapsing the wave (function)?

 

[SpectraCat]

This is in reference to the two experiments:
1. Half silvered mirror = Mach–Zehnder interferometer = the link below
http://en.wikipedia.org/wiki/Mach-Zehnder_interferometer
2. Delayed choice quantum eraser = the link below
http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

The attempt of this post is to hypothesize on how the photon travels after it
- Exits the double slit or after it hits the FIRST half silvered mirror

Hypothesis 1:
The photon becomes a wave and half wave goes through one slit/path and half through the other

Hypothesis 2:
The photon has both particle and wave at SAME time.
The photon takes one of the two paths and the wave splits into half. Half wave goes through one slit/path and half through the other.

Now to test Hypothesis 1 (or actually even 2) :

Lets say we put a detector on either path :

The results of this experiment are known ... you can even find them on wikipedia. They don't shed any light on the questions you are trying to ask. I would also say that your first hypothesis is stated in a non-standard way. Your second hypothesis sounds like a re-phrasing of the deBroglie-Bohm interpretation, except for that stuff about "half-waves" .. I don't know what those are.

1. Are we ever able to measure any property of the wave that would suggest its half a wave?
For example intensity is half or some other property is half?
I think the answer is: we either measure single particle or no particle, zero or one but no half.
Is that correct?

I am still unclear on what you are talking about with the half wave stuff. Your description of the possible results of a particle detection are correct; only discrete, whole particles are observed.

Now to test hypothesis 2:

I read somewhere that now they are able to (vaguely?) figure out which slit the photon went through *without* disturbing the interference pattern which is equal to without collapsing the wave function (?).

I am pretty sure what you describe is impossible based on the laws of QM. You are going to need more than a "vague" recollection of such an experiment to proceed here. Please describe it more completely, and/or provide a reference.

b) Also is it true that interference phenomena also works with Bucky balls (a bunch of carbon atoms)?

Yes, the double-slit experiment has been performed for Bucky-balls, and interference is observed.

 

[ZapperZ]

This is in reference to the two experiments:
1. Half silvered mirror = Mach–Zehnder interferometer = the link below
http://en.wikipedia.org/wiki/Mach-Zehnder_interferometer
2. Delayed choice quantum eraser = the link below
http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

The attempt of this post is to hypothesize on how the photon travels after it
- Exits the double slit or after it hits the FIRST half silvered mirror

Hypothesis 1:
The photon becomes a wave and half wave goes through one slit/path and half through the other

Hypothesis 2:
The photon has both particle and wave at SAME time.
The photon takes one of the two paths and the wave splits into half. Half wave goes through one slit/path and half through the other.

Now to test Hypothesis 1 (or actually even 2) :

Lets say we put a detector on either path :
1. Are we ever able to measure any property of the wave that would suggest its half a wave?
For example intensity is half or some other property is half?
I think the answer is: we either measure single particle or no particle, zero or one but no half.
Is that correct?

Now to test hypothesis 2:

I read somewhere that now they are able to (vaguely?) figure out which slit the photon went through *without* disturbing the interference pattern which is equal to without collapsing the wave function (?).

a) Can someone shed light on that experiment?

b) Also is it true that interference phenomena also works with Bucky balls (a bunch of carbon atoms)?

Before you do your "hypothesizing", maybe you should first read this set of experimental results:

1. J.J. Thorn's et al. at http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf
2. T.L. Dimitrova and A. Weis, Am. J. Phys. v.76, p.137 (2008) at http://doc.rero.ch/lm.php?url=1000,43,2,20080918095145-UZ/weis_wpd.pdf
3. https://www.physicsforums.com/showpost.php?p=1246862&postcount=37

Zz.

 

[Cthugha]

First question: Are the three setups essentially the same as far as the conceptual questions we discuss in this thread are concerned?

No, they are pretty different. A Mach-Zehnder interferometer measures single photon interferences. A delayed choice quantum eraser measures two-photon interferences. This means you create two photons with a fixed phase relationship and create interferences in the joint detection probability. Accordingly you will only see interference patterns in the COINCIDENCE DETECTIONS of two detectors in a DCQE setup, but never on one detector alone.

Second Question: My understanding is that even if one of the paths is blocked or detector is placed after the photon has passed. The interference pattern WILL disappear. This is contrary to what Cthugha is saying.

Well, this question is not exactly trivial. You will need not just one photon, but a lot of photons to build up the interference pattern, so there are several possibilities.

a) You have a stream of photons present. In this case blocking one arm will of course prevent further build-up of the interference pattern.

b) You repeatedly fire single photons and place the block in one arm after you are sure the photon has passed and remove it again before the next photon arrives. As a result there will be some interference pattern. However, the path differences between both arms must be very small as the duration of a single photon pulse in the time domain is usually very short - somewhere in the femtosecond range. If the difference in travel time between both arms is longer than that, you will never see interference - no matter whether one arm is blocked or not.

 

[Cthugha]

I read somewhere that now they are able to (vaguely?) figure out which slit the photon went through *without* disturbing the interference pattern which is equal to without collapsing the wave function (?).

Well you cannot do that without disturbing the interference pattern, but you can do it without destroying it. In fact distinguishability $$D=|P_A -P_B|$$ of the two possible paths the photon can take (where $$P_A$$ is the probability that the photon took one path and $$P_B$$ is the probability that it took the other path) and the visibility V of the interference pattern are related by the Englert–Greenberger duality relation:
$$D^2+V^2\le1$$

So you can have some knowledge of the photon path (for example a 75% chance to go one way and a 25% chance to go the other way) at the cost of reduced visibility of the interference pattern. However, you cannot get both at the same time with arbitrary precision.

 

[sanpkl]

Spectra cat below is one of the article which is claiming both which way and interference pattern at same time, however its not the article i saw earlier ..still searching for it..

http://www.dipankarhome.com/Non%20Classical%20interence%20and%20which%20path%20information%20in%20a%20gamma%20angular%20correlation%20experiment%20using%20a%20heavy%20ion%20orbiting%20reaction.pdf

 

[sanpkl]

Cthugha, thanks for clarifing that...the 75%, 25% thing. I got it. that's what that article meant. I understand it now from you. thanks.

I am still thinking about your comment that interference pattern will stay...will get back a bit later...

Well you cannot do that without disturbing the interference pattern, but you can do it without destroying it. In fact distinguishability $$D=|P_A -P_B|$$ of the two possible paths the photon can take (where $$P_A$$ is the probability that the photon took one path and $$P_B$$ is the probability that it took the other path) and the visibility V of the interference pattern are related by the Englert–Greenberger duality relation:
$$D^2+V^2\le1$$

So you can have some knowledge of the photon path (for example a 75% chance to go one way and a 25% chance to go the other way) at the cost of reduced visibility of the interference pattern. However, you cannot get both at the same time with arbitrary precision.

 

[sanpkl]

Cthuga,

i did not understand what you meant by path difference should be very small in the below quote. I thought the paths are same length in the Mach-Zehnder_interferometer.

let me start with the Mach-Zehnder_interferometer setup.

http://en.wikipedia.org/wiki/Mach-Zehnder_interferometer

lets assume each path is 8 light minutes long (i.e. about the distance between sun and earth).

after say about 1 light minute distance we place a block on one of the paths however we place it after 1 light minute...i.e. after the photon has supposed crossed that point...

and we keep doing it (after every individual photon has passed) as you suggested in the quote below...

my understanding is that we won't see a interference pattern.

2. Now a modifications to the experiment...we remove a detector (erase which way information) after a photon has crossed a certain point...say...placed at 1 light minute distance...

in this case, my understanding is that...interference pattern willl happen. of course we have to do it photon at a time to build the pattern.

thus if we erase which way information , even after a photon has crossed the point (where we setup our appratus to determine which way information) the interference pattern will happen.

in short: if we can surely erase ( or vice versa...i.e. bring back )which way infromation even after the photon has passed...we will

1. get interfernce pattern if which way info is erased
2. no get interfernce pattern if which way info is recreated

this is true even after the photon has crossed the "observation point".




______

b) You repeatedly fire single photons and place the block in one arm after you are sure the photon has passed and remove it again before the next photon arrives. As a result there will be some interference pattern. However, the path differences between both arms must be very small as the duration of a single photon pulse in the time domain is usually very short - somewhere in the femtosecond range. If the difference in travel time between both arms is longer than that, you will never see interference - no matter whether one arm is blocked or not.[/QUOTE]

 

[SpectraCat]

Spectra cat below is one of the article which is claiming both which way and interference pattern at same time, however its not the article i saw earlier ..still searching for it..

http://www.dipankarhome.com/Non%20Classical%20interence%20and%20which%20path%20information%20in%20a%20gamma%20angular%20correlation%20experiment%20using%20a%20heavy%20ion%20orbiting%20reaction.pdf

I haven't had time to read that paper in detail, but I have three observations after skimming it.

1) The authors of the paper are interpreting someone else's data and experiment ... that is fine in principle, but it means that their logic should be carefully checked before accepting their conclusions, because they aren't bringing anything new to the table except an interpretation. In this case, their interpretation is based on a whole slew of extrapolations and justifications as described on page 35, none of which I am prepared to concede are correct without careful thought.

2) I am not sure if this really qualifies as an example of what you are talking about ... I did not see any clear explanations in there of why the gamma ray bursts emitted by the carbon nuclei should provide "which path" information in any context analogous to a double-slit experiment.

3) The following quotation from their conclusions on p. 36 is puzzling, and makes me wonder how well they understand what they are talking about: (italics are the authors' emphasis).

"We emphasize that here this particular feature is consistent with the formalism of quantum mechanics. Note that the interference here cannot be explained by using any classical picture. This experiment therefore highlights that it is classical wave-like interference and “which path” information which are mutually exclusive and not any interference in general."

 

[Cthugha]

i did not understand what you meant by path difference should be very small in the below quote. I thought the paths are same length in the Mach-Zehnder_interferometer.

You can build it this way, but it is not necessarily so. You can create small differences. These are usually not important, but they can be when it comes to short pulses.

lets assume each path is 8 light minutes long (i.e. about the distance between sun and earth).

after say about 1 light minute distance we place a block on one of the paths however we place it after 1 light minute...i.e. after the photon has supposed crossed that point...

and we keep doing it (after every individual photon has passed) as you suggested in the quote below...

my understanding is that we won't see a interference pattern.

Why should we not? As the photon has already passed you will get no which-way information by putting the block there.

2. Now a modifications to the experiment...we remove a detector (erase which way information) after a photon has crossed a certain point...say...placed at 1 light minute distance...

in this case, my understanding is that...interference pattern willl happen. of course we have to do it photon at a time to build the pattern.

No, putting and removing a position detector there will not work. As soon as a photon interacts in an irreversible way with a detector giving which-way information you will not be able to restore the interference pattern. In order to do so you need a reversible which-way marker. Usually you have photons of known polarization and use a plate causing a rotation of the polarization as a which way marker. Now by measuring the polarization at the detector you will know, which way the photon went and there will be no interference pattern. However, you can recover indistinguishability of both paths again by inserting a filter in the recombined beam, which transmits both polarizations with 50% probability and absorbs them with the same probability. In this case the which-way information has been erases again and the pattern will appear.

 

[sanpkl]

SpectraCat,

We can ignore/skip/discard the below article. Cthuga has clarified the issue...namely you can change the probablities between the slits and this will disturb the interference pattern.


However we cannot get both (namely which way and interference pattern) with high precision.


So we can close this particular point.

Thanks,

San

I haven't had time to read that paper in detail, but I have three observations after skimming it.

1) The authors of the paper are interpreting someone else's data and experiment ... that is fine in principle, but it means that their logic should be carefully checked before accepting their conclusions, because they aren't bringing anything new to the table except an interpretation. In this case, their interpretation is based on a whole slew of extrapolations and justifications as described on page 35, none of which I am prepared to concede are correct without careful thought.

2) I am not sure if this really qualifies as an example of what you are talking about ... I did not see any clear explanations in there of why the gamma ray bursts emitted by the carbon nuclei should provide "which path" information in any context analogous to a double-slit experiment.

3) The following quotation from their conclusions on p. 36 is puzzling, and makes me wonder how well they understand what they are talking about: (italics are the authors' emphasis).

"We emphasize that here this particular feature is consistent with the formalism of quantum mechanics. Note that the interference here cannot be explained by using any classical picture. This experiment therefore highlights that it is classical wave-like interference and “which path” information which are mutually exclusive and not any interference in general."

 

[sanpkl]

cthugha, i agree with all of what you wrote below.

i have a few questions regarding the reversible which way marker.

let abbreviate...i.e. RWWM = reversible which way marker

pls make modifications/corrections/caveats where required


1. the RWWM keeps the **ability/information** to find (or erase) which way information

2. however which way information can only be obtained after the photon has hit the screen/detector?

3. if at any point which way information is actually obtained the wave function would collapase and is **irreversible**

4. thus essentially the RWWM just keeps the ability but not the actual information on which path the photon took...till the photon actually hits the detector/screen

5. the actual path the photon took can be determined after it has hit the screen (and of course if the RWWM has not been used to erase the info)

6. i did not understand the part where something (entangled photons?) have to be compared in the coincidence counter to arrive at results/which way info.

You can build it this way, but it is not necessarily so. You can create small differences. These are usually not important, but they can be when it comes to short pulses.



Why should we not? As the photon has already passed you will get no which-way information by putting the block there.



No, putting and removing a position detector there will not work. As soon as a photon interacts in an irreversible way with a detector giving which-way information you will not be able to restore the interference pattern. In order to do so you need a reversible which-way marker. Usually you have photons of known polarization and use a plate causing a rotation of the polarization as a which way marker. Now by measuring the polarization at the detector you will know, which way the photon went and there will be no interference pattern. However, you can recover indistinguishability of both paths again by inserting a filter in the recombined beam, which transmits both polarizations with 50% probability and absorbs them with the same probability. In this case the which-way information has been erases again and the pattern will appear.

 

[sanpkl]

I am revising/modifying 4 since i think its not correct

4. thus essentially the RWWM just keeps the ability however if we make use of that ability then the wavefunction would collapse irreversibly...

4 a) can we find which way info before the photon hits the detector via the RWWM?

 

[Cthugha]

1):
Yes, I think so.

2):
Yes, however, one should note that any irreversible interaction can be considered as a detector, whether it is the screen or some random dust particle in the air, which absorbs the photon.

3):
In principle yes. But let me emphasize that it does not matter, whether you (as a person) really obtain the information or not. It is enough that some irreversible interaction happened, which could enable you to obtain the information.

4):
Basically yes. There are interpretations of QM, which do not describe this act as a wave function collapse, but the observable physics stay the same. SO I agree.

4)a):
If you consider each irreversible interaction as a detector then you cannot get COMPLETE which way information before the photon hit the detector. However, you can of course get some which-way information for example by weak measurements or simply by setting up the experiment in such a way that the photon is more likely to go one way.

5):
Ok.

6):
The quantum eraser experiments are a bit more difficult than common double slit interference experiments. Here you entangle two photons and have one interact with a detector. Now you can choose, whether you can get an interference pattern or not by making a choice on what you do with the other photon after the first one has been detected. However, what is often not told is that the interference cannot be seen as a pattern on the screen where the first photon is detected, but in the joint count rates of both photons. Basically this is a kind of subsampling giving results like:

If I detected the other photon at this special position at the detector, the corresponding simultaneous detections of the first photon at the first detector will show an interference pattern. If I detected the other photon at a different position at the detector, the corresponding simultaneous detections of the first photon at the first detector will show a different interference pattern. If I superpose all of these patterns the result will be washed out and show no pattern at all. So in DCQE experiments you will see interferences only in measurements of the joint detection rates of two entangled photons.

 

[DrChinese]

Well you cannot do that without disturbing the interference pattern, but you can do it without destroying it. In fact distinguishability $$D=|P_A -P_B|$$ of the two possible paths the photon can take (where $$P_A$$ is the probability that the photon took one path and $$P_B$$ is the probability that it took the other path) and the visibility V of the interference pattern are related by the Englert–Greenberger duality relation:
$$D^2+V^2\le1$$

So you can have some knowledge of the photon path (for example a 75% chance to go one way and a 25% chance to go the other way) at the cost of reduced visibility of the interference pattern. However, you cannot get both at the same time with arbitrary precision.

For anyone interested, here is a reference on the above:

http://arxiv.org/abs/0807.5079"

"A recent experiment performed by S. S. Afshar et al. has been interpreted as a violation of Bohr's complementarity principle between interference visibility and which-path information in a two-path interferometer. We have reproduced this experiment, using true single-photon pulses propagating in a two-path wavefront- splitting interferometer realized with a Fresnel's biprism, and followed by a grating with adjustable transmitting slits. The measured values of interference visibility V and which-path information, characterized by the distinguishability parameter D, are found to obey the complementarity relation V^2+D^2=<1. This result demonstrates that the experiment can be perfectly explained by the Copenhagen interpretation of quantum mechanics. "

 

[sanpkl]

This is in reference to the last paragraph. i did not understand it. i am trying to understand it by reading more on it...

in the meantime...can you help with the below?

1. I still do not understand yet as to why both photons need to be compared.

2. to make it a little easier let's call the photon that hits the detector as d and its entangled twin as t.

3. in the experiment, what is being done with t after d has hit the detector?

4. once d has hit the detector the wave function has collapsed, so now whatever we do with t won't matter...is this correct? any additions/modifications?

5. the interference pattern is formed by d. is there some need to compare with t?

6. do we also note t's position on a separate detector?...as part of the experiment...and it that critical in understanding the intereference pattern caused by d? how?

7. what does a coincidence counter mean?

8. i have more questions but first i need to understand the part of the experiment...after d has been detected , what we do?

9. what do you mean by "other photon at the special position"? other photon = t?

is the other photon detected at a different dector or same detector?

10 rest later...after i finish reading the experiement

1):
Yes, I think so.

2):
Yes, however, one should note that any irreversible interaction can be considered as a detector, whether it is the screen or some random dust particle in the air, which absorbs the photon.

3):
In principle yes. But let me emphasize that it does not matter, whether you (as a person) really obtain the information or not. It is enough that some irreversible interaction happened, which could enable you to obtain the information.

4):
Basically yes. There are interpretations of QM, which do not describe this act as a wave function collapse, but the observable physics stay the same. SO I agree.

4)a):
If you consider each irreversible interaction as a detector then you cannot get COMPLETE which way information before the photon hit the detector. However, you can of course get some which-way information for example by weak measurements or simply by setting up the experiment in such a way that the photon is more likely to go one way.

5):
Ok.

6):
The quantum eraser experiments are a bit more difficult than common double slit interference experiments. Here you entangle two photons and have one interact with a detector. Now you can choose, whether you can get an interference pattern or not by making a choice on what you do with the other photon after the first one has been detected. However, what is often not told is that the interference cannot be seen as a pattern on the screen where the first photon is detected, but in the joint count rates of both photons. Basically this is a kind of subsampling giving results like:

If I detected the other photon at this special position at the detector, the corresponding simultaneous detections of the first photon at the first detector will show an interference pattern. If I detected the other photon at a different position at the detector, the corresponding simultaneous detections of the first photon at the first detector will show a different interference pattern. If I superpose all of these patterns the result will be washed out and show no pattern at all. So in DCQE experiments you will see interferences only in measurements of the joint detection rates of two entangled photons.

 

[sanpkl]

Please see the below link

http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

Two Questions

1. instead of seeing the intereference pattern of signal photon on Do, can we (in addition, double check) see it by superimposing D1 & D2 patterns?

2. Please see below paragraph. the frequency of each of the photons is half the original photon. does it wavelenght also change?

However, after the slits a beta barium borate crystal (labeled as BBO) causes spontaneous parametric down conversion (SPDC), converting the photon (from either slit) into two identical entangled photons with 1/2 the frequency of the original photon.

 

[sanpkl]

Cthugha,

thanks for posting your reply. i understood your last paragraph as well.

1):
Yes, I think so.

2):
Yes, however, one should note that any irreversible interaction can be considered as a detector, whether it is the screen or some random dust particle in the air, which absorbs the photon.

3):
In principle yes. But let me emphasize that it does not matter, whether you (as a person) really obtain the information or not. It is enough that some irreversible interaction happened, which could enable you to obtain the information.

4):
Basically yes. There are interpretations of QM, which do not describe this act as a wave function collapse, but the observable physics stay the same. SO I agree.

4)a):
If you consider each irreversible interaction as a detector then you cannot get COMPLETE which way information before the photon hit the detector. However, you can of course get some which-way information for example by weak measurements or simply by setting up the experiment in such a way that the photon is more likely to go one way.

5):
Ok.

6):
The quantum eraser experiments are a bit more difficult than common double slit interference experiments. Here you entangle two photons and have one interact with a detector. Now you can choose, whether you can get an interference pattern or not by making a choice on what you do with the other photon after the first one has been detected. However, what is often not told is that the interference cannot be seen as a pattern on the screen where the first photon is detected, but in the joint count rates of both photons. Basically this is a kind of subsampling giving results like:

If I detected the other photon at this special position at the detector, the corresponding simultaneous detections of the first photon at the first detector will show an interference pattern. If I detected the other photon at a different position at the detector, the corresponding simultaneous detections of the first photon at the first detector will show a different interference pattern. If I superpose all of these patterns the result will be washed out and show no pattern at all. So in DCQE experiments you will see interferences only in measurements of the joint detection rates of two entangled photons.

 

[sanpkl]

thanks for the link Dr Chinese.

Would you like to answer my two question (above) about delayed choice quantum eraser?

San

For anyone interested, here is a reference on the above:

http://arxiv.org/abs/0807.5079"

"A recent experiment performed by S. S. Afshar et al. has been interpreted as a violation of Bohr's complementarity principle between interference visibility and which-path information in a two-path interferometer. We have reproduced this experiment, using true single-photon pulses propagating in a two-path wavefront- splitting interferometer realized with a Fresnel's biprism, and followed by a grating with adjustable transmitting slits. The measured values of interference visibility V and which-path information, characterized by the distinguishability parameter D, are found to obey the complementarity relation V^2+D^2=<1. This result demonstrates that the experiment can be perfectly explained by the Copenhagen interpretation of quantum mechanics. "

 

[DrChinese]

2. Please see below paragraph. the frequency of each of the photons is half the original photon. does it wavelenght also change?

However, after the slits a beta barium borate crystal (labeled as BBO) causes spontaneous parametric down conversion (SPDC), converting the photon (from either slit) into two identical entangled photons with 1/2 the frequency of the original photon.

Yes, it doubles the wavelength when the frequency is cut in half.

There are some interesting element of the conversion process. You get 2 photons from 1 in DOWN conversion. There is a mirror process called UP conversion in which you get 1 photon from 2! Also, you don't only get exact splitting. There are a range of outputs around a mean which is 1/2 frequency.

 

[Cthugha]

1. instead of seeing the intereference pattern of signal photon on Do, can we (in addition, double check) see it by superimposing D1 & D2 patterns?

I am not sure I know what you mean.

Well, there is no interference pattern of the signal photon at D0. Never. So I suppose you mean the interference pattern in the coincidence count pattern.
For the same reason there are no interference patterns on D1 or D2 and of course also no simultaneous coincidence counts at D1 and D2 simultaneously.

If you are, however, talking about superposing the coincidence count patterns of D0-D1 and D0-D2 you will notice that the two interference patterns are exactly out of phase and superposing them will lead to no interference pattern at all. This is also the reason why you see no interference pattern at D0 without doing coincidence counting.

 

[sanpkl]

Cthugha,

thanks for your reply

let me see if i got this right...

1. There is a pattern caused by signal photon (s) and idler photon (i).
Are they not two separate patterns on separate screens?

the fact that they might not have intereference pattern ...will discuss later

2. In this conversation let's assumed that the noise has been eliminated by considering only the pattern of the entangled photons.

3. now we have two patterns...one caused by s and one caused by i.

4. are they exactly similar?

5. now from these patterns if we only remove the s photons (as well as their corresponding twin i photons) that were detected at d3 and d4...

we get interference pattern

is that correct.

6. for 5...if we remove D1 and D2 photons but keep D3 and d4...we get no interfernce patterns.

7. thus we have a double check...either check the s photon pattern (after noise elimination and using only d1 d2 detected photons or d3 and d4) or check the i photon pattern.

San

I am not sure I know what you mean.

Well, there is no interference pattern of the signal photon at D0. Never. So I suppose you mean the interference pattern in the coincidence count pattern.
For the same reason there are no interference patterns on D1 or D2 and of course also no simultaneous coincidence counts at D1 and D2 simultaneously.

If you are, however, talking about superposing the coincidence count patterns of D0-D1 and D0-D2 you will notice that the two interference patterns are exactly out of phase and superposing them will lead to no interference pattern at all. This is also the reason why you see no interference pattern at D0 without doing coincidence counting.

 

[sanpkl]

When one photon hits a BBO crystal and its energy is transferred to two photons.


1. when a photon hits the BBO its energy is transferred to the two emitted photons.
does the energy of the two photons (emitted from the BBO) equal to half of the "original" photon?

2. a quanta is the smallest form of energy (particle). it cannot be split/broken further.

Yes, it doubles the wavelength when the frequency is cut in half.

There are some interesting element of the conversion process. You get 2 photons from 1 in DOWN conversion. There is a mirror process called UP conversion in which you get 1 photon from 2! Also, you don't only get exact splitting. There are a range of outputs around a mean which is 1/2 frequency.

 

[Cthugha]

1. There is a pattern caused by signal photon (s) and idler photon (i).
Are they not two separate patterns on separate screens?

No, they are not two pattern on two screens.

For the further discussion please have a look at Figures 3,4 and 5 in http://xxx.lanl.gov/pdf/quant-ph/9903047. It is easier to discuss it when you see the actual patterns.

2. In this conversation let's assumed that the noise has been eliminated by considering only the pattern of the entangled photons.

Ok.

3. now we have two patterns...one caused by s and one caused by i.

4. are they exactly similar?

No. At first it is important to say that D0 is a small detector. So you have to move it along the axis to get some pattern. If you do that without coincidence counting you will get a pattern, which looks like the one in figure 5 (although that is taken for a different situation, it will loke like that). D1 to D4 are large detectors. Here you can never get a pattern because they are usually not position sensitive. They just tell you, whether a photon has been detected or not. If they were position sensitive, they would still show no interference. The light used is too incoherent to show a single photon interference pattern under the experimental conditions used here.

6. for 5...if we remove D1 and D2 photons but keep D3 and d4...we get no interfernce patterns.

Yes, this is shown in figure 5.

5. now from these patterns if we only remove the s photons (as well as their corresponding twin i photons) that were detected at d3 and d4...

we get interference pattern

Not exactly.If you remove those detected at D3 and D4, you will get the coincidence counts of D0 with D1 and D2. Have a look at figure 3 and 4, which give the corresponding patterns. If you just remove D3 and D4 coincidence counts, you will get a superposition of the two patterns shown in figures 3 and 4. As you see the peaks of figure 3 are at the position of the dips of figure 4 and vice versa. If you superpose them, you will therefore get no pattern at all as the dips and peaks cancel out. You will, however, get one interference pattern for just keeping coincidence counts with D1 and you will get one different pattern for just keeping coincidence counts with D2 as shown in figures 3 and 4.

7. thus we have a double check...either check the s photon pattern (after noise elimination and using only d1 d2 detected photons or d3 and d4) or check the i photon pattern.

I hope it is now clearer that there are no distinct i and s patterns.

 

[Mentz114]

When one photon hits a BBO crystal and its energy is transferred to two photons.1. when a photon hits the BBO its energy is transferred to the two emitted photons.
does the energy of the two photons (emitted from the BBO) equal to half of the "original" photon?

2. a quantum is the smallest form of energy (particle). it cannot be split/broken further.

My understanding is that the incident photon is absorbed and its energy becomes phonon or magneton excitations which are then transferred to two other atoms which then emit.

 

[DrChinese]

My understanding is that the incident photon is absorbed and its energy becomes phonon or magneton excitations which are then transferred to two other atoms which then emit.

I can't believe that atoms would emit the 2 photons... I would think it is more the crystal lattice as a whole. I looked but could not find anything much which explains the actual structure of a PDC crystal. And I think the theory of it is quite complicated (like 80 pages). Does anyone have something which explains this? Most papers simply talk about the conservation rules, which is useful for performing an experiment but presupposes the pump photon has already split.

 

[sanpkl]

thanks for your replies cthugha, mentz and dr chinese...please see the experiment below...look forward to your comments...

In this experiment http://xxx.lanl.gov/PS_cache/quant-ph/pdf/9903/9903047v1.pdf
We use the same experimental setup however there are some modifications as below.

We can call it predetermined (or predecided) delayed choice quantum eraser.

Lets assume signal photon hits after 5ns. (ns = nano seconds)
The idler photon hits after 5+8 ns = 13 ns

ns = nano seconds
s1 = first signal photon
i1 = first idler photon = entangled twin of s1
s2 = second signal photon
i2 = second idler photon = entangled twin of s2

Experiment 1
Steps
1. We pump photon 1…s1 and i1 emerge from the BBO crystal.
2. s1 hits at 5ns at that point we have kept which path information for i1
3. we note s1 position on detector Do …………AT TIME 5ns
4. at 12ns we erase which path information
5. at 13ns idler photon is detected
6. we repeat the same for photon 2…. s2 and i2 emerge from the BBO crystal
7. we keep repeating this…..for say ….1000 photons
What pattern would we observe on Do? Our understanding of DCQE would say…we would observe an interference pattern?

Experiment 2
Same as 1….except….at step 2…we do not keep which path information
And at step 4 we bring back which path information
What pattern would we observe on Do? Our understanding of DCQE would say…we would NOT observe an interference pattern?

Experiment 3:
Is same at experiment 1 except s1 position is measured at 13 ns and not 5 ns

Experiment 4:
Is same at experiment 2 except s1 position is measured at 13 ns and not 5 ns

 

[Cthugha]

If you needed absorption and phonons to get down conversion or up conversion you would burn the crystal before you get a sensible signal, I fear. Sum and difference frequency generation in up and down conversion are a special case of three wave mixing. Therefore you need a material with $$\chi^{(2)}$$ nonlinearity. This means you need a material where the polarization response on the incoming electric field can not be described by a harmonic oscillator model, but you need to include higher orders resulting in the optical version of an anharmonic oscillator. And just like in a classical anharmonic oscillator you get oscillation components at sum and difference frequencies.

If you want a more microscopic picture this is pretty much the same as for normal light propagation in materials. The eigenstates of the em-field in material are almost always coupled to some collective excitations of the material like plasmons and this interaction can change the light field as described above.

 

[Mentz114]

Cthugha,
thanks for that. Eighty pages ? Sum and difference of frequencies is good enough for me.

( this is a bit off topic now ).

 

[sanpkl]

in the below and other quantum eraser experiments...

the detector is moved by a trackor...however since the position of photon is randomly determined...how would the experimenter know where (which position) to keep the detector?

are a lot of photons missed because the detector is not at the correct position in time?


pls see...http://en.wikipedia.org/wiki/Quantum_eraser_experiment