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

[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

 

[SpectraCat]

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

The point of the experiment is not to detect all of the photons, but rather to establish correlations between the two members of the entangled pair based on whether or not the quantum eraser is in place. These coincidence measurements are required to reveal the interference pattern at the D0 detector. A large number of counts are acquired at each detector position.

 

[sanpkl]

we don't know where the photon would strike, so how would moving the detector help?

there is something abotu the experiment that i am missing

 

[Cthugha]

This is a genuine TWO-PHOTON interference phenomenon. The position where a photon strikes depends on its wavevector, which is random, so the position where it strikes D0 is random too. However, the position where it is detected will give you some information about the wavevector and as you have entangled photons also about the wavevector of the other photon. Therefore although the total photon distribution on the other detector is random the pattern of a subset of photons with well defined wavevector (as determined by the position of D0) is not random, but gives an interference pattern.

 

[sanpkl]

thanks cthugha and others

when the signal photon is detected at Do ...does not the wave function (entanglement) collapse?

if so, then whatever we do (to idler) after detection (of signal) at Do is immaterial?

 

[SpectraCat]

thanks cthugha and others

when the signal photon is detected at Do ...does not the wave function (entanglement) collapse?

if so, then whatever we do (to idler) after detection (of signal) at Do is immaterial?

Yes, it is true that the entanglement is destroyed by the measurement of the signal photon at D0, however, that leaves the idler photon in a *well-defined* state, which is correlated to the photon detected at D0. It is this correlation which, through coincidence counting, reveals the interference pattern when the quantum eraser is in place.

 

[sanpkl]

thanks spectracat.

now let's see if i got the next part right...

by delayed choice we also mean that...

even after the signal has been detected at Do, we can still "play" with the idler and get or not get interference pattern...(of course we would have to do photon by photon..)

i.e.

1 we can erase which way info and cause intereference pattern to disappear (after of course validating via coincidence counter..that only...the "matches/pairs" do-d1 etc..)
2. we can bring back which way info and get interference.


so in a sense ...does this mean/say...we can change the position of signal of Do...that happened in THE PAST...so to speak...

Yes, it is true that the entanglement is destroyed by the measurement of the signal photon at D0, however, that leaves the idler photon in a *well-defined* state, which is correlated to the photon detected at D0. It is this correlation which, through coincidence counting, reveals the interference pattern when the quantum eraser is in place.

 

[SpectraCat]

thanks spectracat.

now let's see if i got the next part right...

by delayed choice we also mean that...

even after the signal has been detected at Do, we can still "play" with the idler and get or not get interference pattern...(of course we would have to do photon by photon..)

i.e.

1 we can erase which way info and cause intereference pattern to disappear (after of course validating via coincidence counter..that only...the "matches/pairs" do-d1 etc..)
2. we can bring back which way info and get interference.


so in a sense ...does this mean/say...we can change the position of signal of Do...that happened in THE PAST...so to speak...

Well, that is the way that DCQE experiments are often sold .. you can decide if you like that interpretation or not. I have a different view, which is that the coincidence measurements reveal different components of the overall signal at D0, which does not show any interference. Since these coincidence measurements are by definition not complete until the second detector has registered, it is unclear to me why that shows anything relevant to temporal ordering. Basically, it shows that the predictions of QM are correct for this system.

As far as I am aware, no one has ever observed that recorded data has changed its values based on some delayed choice mechanism. What they see is that for two *different* data sets, recorded using *different* experimental configurations, the results are different: interference is observed when the QE is in place, which-path data is observed when it is not.

So, you have to be quite careful when saying that QM shows that past events can be changed, because this has never been shown directly to be true. No observed event has ever been shown to change its value. What people mean is that they infer a temporal ordering from perfectly reasonable deductions, such as the travel distance to detector D0 is shorter than for the other detectors, so the photon at D0 *must* have been recorded first. This seems reasonable to me. The next step is where they get weird, because they start saying things like, "the detector at D0 cannot know at the time the signal photon is measured whether we will have the QE inserted or not", to justify their interpretations of the rest of the measurements (i.e. that a past event has been changed.) However it has been shown time and time again that such statements simply do not pertain to QM measurements of this kind.

Anyway I hope this helps ... basically it can all be summed up as, "we can never observe a quantum system in the act of being quantum". I don't know who said it first (certainly not me), but it is worth remembering.

 

[Cthugha]

You cannot change the detections at D0 afterwards. But you have a choice whether you will be able to pick a subset of the detections at D0 by means of coincidence counting, which gives an interference pattern. If you get which-way information on the other side, there is no such subset available. So the delayed choice is more or less just a choice of a subset. You do not change the detections or their position at D0 afterwards at all.

 

[sanpkl]

nice answer SpectraCat. well presented.

i am with ya.


i am not a fan of the "past can be changed" hypothesis nor of the "many worlds" hypothesis...

however...i am holding/liking the below hypothesis in my mind...for the near future...

the signal photon at Do gets detected/recorded *only when* idler is...

till then signal photon "sort of hovers"...in a narrow range above Do...thus entanglement is broken only till the last...

this would explain most of the things in this experiment...i guess...

Well, that is the way that DCQE experiments are often sold .. you can decide if you like that interpretation or not. I have a different view, which is that the coincidence measurements reveal different components of the overall signal at D0, which does not show any interference. Since these coincidence measurements are by definition not complete until the second detector has registered, it is unclear to me why that shows anything relevant to temporal ordering. Basically, it shows that the predictions of QM are correct for this system.

As far as I am aware, no one has ever observed that recorded data has changed its values based on some delayed choice mechanism. What they see is that for two *different* data sets, recorded using *different* experimental configurations, the results are different: interference is observed when the QE is in place, which-path data is observed when it is not.

So, you have to be quite careful when saying that QM shows that past events can be changed, because this has never been shown directly to be true. No observed event has ever been shown to change its value. What people mean is that they infer a temporal ordering from perfectly reasonable deductions, such as the travel distance to detector D0 is shorter than for the other detectors, so the photon at D0 *must* have been recorded first. This seems reasonable to me. The next step is where they get weird, because they start saying things like, "the detector at D0 cannot know at the time the signal photon is measured whether we will have the QE inserted or not", to justify their interpretations of the rest of the measurements (i.e. that a past event has been changed.) However it has been shown time and time again that such statements simply do not pertain to QM measurements of this kind.

Anyway I hope this helps ... basically it can all be summed up as, "we can never observe a quantum system in the act of being quantum". I don't know who said it first (certainly not me), but it is worth remembering.

 

[sanpkl]

nice insight Cthugha. ...still trying to fully understand what you said...

just so i understand (the below) better..

why is there no subset available? (for which way info)

You cannot change the detections at D0 afterwards. But you have a choice whether you will be able to pick a subset of the detections at D0 by means of coincidence counting, which gives an interference pattern. If you get which-way information on the other side, there is no such subset available. So the delayed choice is more or less just a choice of a subset. You do not change the detections or their position at D0 afterwards at all.

 

[Cthugha]

I am not sure I get your problem exactly. Some time before I gave a rough and a bit simplified explanation of DCQE experiments in a different topic.
See this link:
https://www.physicsforums.com/showpost.php?p=2241460&postcount=8

Maybe that explanation is a bit easier to digest.

 

[sanpkl]

Cthugha,

I read your posting at https://www.physicsforums.com/showpost.php?p=2241460&postcount=8

I understand it somewhat...would you like to take a stab at the below cases and provide a short "layman" explanation?

the only explanation i can think off is that..somehow a subset won't be created...

case 1 we change from "which way" to "no which way info" after signal photon has been detected

(and of course before idler photon is detected)

case 2 we change from "no which way info" to "which way info" after signal photon has been detected

(and of course before idler photon is detected)

I am not sure I get your problem exactly. Some time before I gave a rough and a bit simplified explanation of DCQE experiments in a different topic.
See this link:
https://www.physicsforums.com/showpost.php?p=2241460&postcount=8

Maybe that explanation is a bit easier to digest.

 

[Cthugha]

Ok, let us assume that you have the DCQE setup as used by Kim, Kulik, Shih and Scully which we used earlier in this discussion and assume that we have some kind of mechanism which allows us to choose whether we have which path information (photon goes to D3 or D4) or we do not have which-way information (photon goes to D1 or D2).

Now let's have a look at the detections with which-way information. All detections going one way will end up at the same detector. There is no phase dependence of the detections at this detector so you get no subsets.

If you erase which-way information, you send the photon to the mirror leading to detectors D1 or D2. This part of the setup is pretty similar to a Mach-Zehnder interferometer. Whether a photon will end up at D1 or D2 will depend on the relative phase difference corresponding to the events "photon comes from slit A and reaches the mirror" and "photon comes from slit B and reaches the mirror". In a common Mach-Zehnder interferometer this phase shift is introduced by putting some sample in one arm of the interferometer. Here it is (randomly) produced by the downconversion process. Therefore this gives you the possibility to define two subsets: photons going to D1 and photons going to D2, which are characterized by different dependencies on the relative phase shift - just like in the Mach-Zehnder interferometer one will behave like sin^2(\frac{\Delta\Phi}{2}) and one will behave like cos^2(\frac{\Delta\Phi}{2}).

These subsets are also visible on the other side. One certain position of D0 corresponds to some well defined value of this phase difference as the paths from slit A and slit B to this position are different. Therefore you can correlate the detections at D0 with those at D1 or D2 and get the interference pattern.

If you now send photons to D1/D2 and put in some other which-way marker (for example by using polarization) all you do is to destroy the interference at the last mirror. This is like trying to use a Mach-Zehnder interferometer where you have different polarizations in both arms, which will also not show any interference.

 

[Frame Dragger]

"This is like trying to use a Mach-Zehnder interferometer where you have different polarizations in both arms, which will also not show any interference. "

Well said, thanks for the excellent example. I didn't think I was going to fully appreciate this one, but I THINK I do now.

 

[sanpkl]

Yes, well said Cthugha. Give me a day or two to digest it.

Simple questions

1. is a subset basically the patterns caused by EITHER whichway or "nowhichway"?
the total set being the positions of all the entangled photons that could be captured and this total set would show no pattern.
2. when both are there...no interference is noted?
3. is it possible, in the experiment, to get the location of the signal photon on Do prior to idler getting to the incidence counter?

a) the idler is delay by about 8 ns (of course we can increase/decrease this time difference). However during this 8ns are we able to tell where on the Do x-axis did the signal photon register? or do we have to wait for idler to be matched with signal in the co-incidence detector?

"This is like trying to use a Mach-Zehnder interferometer where you have different polarizations in both arms, which will also not show any interference. "

Well said, thanks for the excellent example. I didn't think I was going to fully appreciate this one, but I THINK I do now.

 

[Cthugha]

1. is a subset basically the patterns caused by EITHER whichway or "nowhichway"?
the total set being the positions of all the entangled photons that could be captured and this total set would show no pattern.
2. when both are there...no interference is noted?

Well, just compare this to the Mach-Zehnder interferometer where you also have two detectors.
If you send light along both paths, you can also get clicks at both detectors, but whether a photon goes to one detctor or the other will depend on the phase difference at the beam splitter. Therefore you get one subset "First detector" telling you that this subset will also have some well defined possible values of the relative phase and you get one subset "second detector" telling you this subset will have some different well defined possible values of the relative phase.
If you send the light only along one arm or the other you will have clicks at both detectors, but whether the light will go one way or the other at the beam splitter, is completely random. So the two subsets "first detector" and "second detector" do not carry any additional information, while these subsets are also subsets in terms of the relative phase in the case of no which-way information present. This later subset is the useful one, which allows for creation of an interference pattern (as it depends on phase).

3. is it possible, in the experiment, to get the location of the signal photon on Do prior to idler getting to the incidence counter?

a) the idler is delay by about 8 ns (of course we can increase/decrease this time difference). However during this 8ns are we able to tell where on the Do x-axis did the signal photon register? or do we have to wait for idler to be matched with signal in the co-incidence detector?

No, you can get the signal detection positions and times well before the idler is detected. No problem with that.

 

[sanpkl]

Cthugha,

first...let me ask about (slightly off tangent) the below:

cthugha wrote ---No, you can get the signal detection positions and times well before the idler is detected. No problem with that.[/QUOTE]

1. since we know what we did with the idler photon (before, as well as after, the signal was detected at Do...) ...
do we really need to match/compare/check with the idler photon in the coincidence counter?

Well, just compare this to the Mach-Zehnder interferometer where you also have two detectors.
If you send light along both paths, you can also get clicks at both detectors, but whether a photon goes to one detctor or the other will depend on the phase difference at the beam splitter. Therefore you get one subset "First detector" telling you that this subset will also have some well defined possible values of the relative phase and you get one subset "second detector" telling you this subset will have some different well defined possible values of the relative phase.
If you send the light only along one arm or the other you will have clicks at both detectors, but whether the light will go one way or the other at the beam splitter, is completely random. So the two subsets "first detector" and "second detector" do not carry any additional information, while these subsets are also subsets in terms of the relative phase in the case of no which-way information present. This later subset is the useful one, which allows for creation of an interference pattern (as it depends on phase).



No, you can get the signal detection positions and times well before the idler is detected. No problem with that.

 

[Cthugha]

1. since we know what we did with the idler photon (before, as well as after, the signal was detected at Do...) ...
do we really need to match/compare/check with the idler photon in the coincidence counter?

Of course we have to. You just know that the photon will go to the beam splitter, but without coincidence counting you do not know, which exit port the photon will take. This is the necessary bit of information you still need.

 

[sanpkl]

Of course we have to. You just know that the photon will go to the beam splitter, but without coincidence counting you do not know, which exit port the photon will take. This is the necessary bit of information you still need.

you are talking about the idler, i assume.

do you mean ...

we don't know if the photon will go to d1/d2 or d3/d4 ?

 

[Cthugha]

You do not know whether a photon for which there is no which-way information available will end up at D1 or D2. What the other photons do, does not really matter.

 

[sanpkl]

You do not know whether a photon for which there is no which-way information available will end up at D1 or D2. What the other photons do, does not really matter.

and this is because do-d1 and do-d2 have a phase difference and if combined no interference would show?...thus we need to separate d1 and d2...and get the patterns are shown in the paper

anything more you want to add to this?

 

[Cthugha]

No, sounds good to me.

 

[sanpkl]

a typographical error in the below link?
http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

a quote from the above link...

However, what makes this experiment possibly astonishing is that, unlike in the classic double-slit experiment, the choice of whether to preserve or erase the which-path information of the idler need not be made until after the position of the signal photon has already been measured by D0.

the word "after" should be replaced with "before"
or better still
the above sentence needs be rephrased/corrected with something like below

The which-path
or both-path information of a quantum can be erased or
marked by its entangled twin even after the registration
of the quantum. - kim paper

 

[sanpkl]

thanks cthugha and spectracat for enhancing my understanding of quantum mechanics

i think i have figured the fallacy about the past being changed...

when the signal photon is detected (at Do)...all the below happens

- the wave function collapses

- the state of both the entangled photons is frozen (which way or both way and in case of which way...also the slit A or slit B)

- its just that we don't what that state is till the idler photon arrives and is checked with signal via the conincidence counter

- thus both the photon become "determinate" once the signal is detected, even the idler path becomes determinate...however we can only tell once we compare via coincidence counter

- thus the past cannot be changed

 

[sanpkl]

can the (screen of) Do detector be made more bigger so that we don't have to constantly keep moving it by a step motor?