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

[SpectraCat]

Spectra cat , i do remember what i learned earlier. i do understand it conceptually.

all i am saying is we already have two *well defined*, *well demarcated* intereference patterns after a million photons have struck. now i am talking about just one photon. the millionth and one photon, say...

Ques: can we not tell if its on the first interference pattern or the second?

Attempted self answer: we cannot tell its on the first or second because its too early too tell? one photon not a interfrence maketh? we need more photons and then also use the conincidence counter (and correlate wioth idler) to separate them?

You still don't seem to get the fundamental point here ... we do not "have two well-defined interference patterns" until we look at the *separate* coincidence channels. Your original question was asking about drawing conclusions from looking only at the signal photon measurements to make a *prediction* about the fate of the idler photon *passing through the interferometer*. That is clearly a physical impossibility based on common sense, let alone the laws of QM.

You cannot say anything regarding the idler photon until it has been measured. If it shows up on D1 or D2, then it passed through the interferometer, and which-path info was erased. If it shows up on D3 or D4, then we know which source (A or B) it came from. The interference pattern you are talking about only exist/make sense for *pairs* of photons corresponding to coincidence measurements at detectors D1 and D2 .. there is no "measurement" in this case until both photons have been detected. The number of coincidences preceding a particular measurement, whether it is the first or the million-and-first, is completely irrelevant.

 

[Cthugha]

where would be find the million plus one photon? on figure 3/4 or figure 5/6? (Figure 6 is nto given in the paper however we can assume is it same as figure 5.)

As you erase which-way information (assuming that you can do it willingly which is not possible in the Kim paper), the idler photon will end up at D1 or D2. This means when doing coincidence counting you will find it at figure 3 or 4.

we measure the position of signal photon and see if its on the interference of Figure 3 OR Figure 4.

we should be able to tell if signal is on which curve because the million photons before it have created two nice interference patterns. we stopped the experiment after million photons and drew the nice/clear interference patterns before sending the millionth plus one photon.

so now we can predict which detector idler will strike...if signal position is discovered on figure 3...then idler will strike detector D1. if signal position is discovered on figure 4 then...idler will strike D2.

Well, if you had no background noise, perfect detectors detecting every photon, perfect fringe visibility (this means a large number of counts at one position in figure 3 and no counts at all at the same position in figure 4 or vice versa) and have already recorded the interference patterns by coincidence counting you could predict at which detector (D1 or D2) the idler will end up if you recorded the corresponding idler at a position with zero counts for one of the two coincidence count interference patterns and send so few photon pairs around that you can be unambiguously sure which idler photon belongs to which signal photon. That this works is trivial. The measurement at D0 defines the relative phase between A and B and this relative phase is exactly what determines the idler photon behavior at the final beam splitter.
But of course it does not work the other way around. If you detect an idler photon at D1 or D2 you cannot say at which position the signal will hit D0.

Your original question was asking about drawing conclusions from looking only at the signal photon measurements to make a *prediction* about the fate of the idler photon *passing through the interferometer*. That is clearly a physical impossibility based on common sense, let alone the laws of QM.

Eh? The possibility to make a prediction on one side based on the measurement on the other side is pretty much what entanglement is about.

 

[SpectraCat]

Ok, maybe I see where your confusion arises. Are you are thinking of the D0 detector as representing some "screen" where we have a 2D-trace representing the interference patterns? That is certainly not correct. If we replaced D0 by a "screen", we would see a 1-D line (or band, since its thickness will not be zero). The integrated pattern of all the photons along that band will show a roughly Gaussian distribution peaked in the center. The question you are asking concerns a signal photon that hits such a "screen" at a particular location x'. Do you really think we can learn anything about its corresponding idler photon simply from observing that location? From the context of your question, it seems like you think that such a "screen" would somehow be divided into "bins", and all the photons landing in a given "bin" are correlated with idler photons going to a particular detector. This is not the case ... signal photons can hit any location on the "screen", irrespective of where their idler photon ends up.

The y-axis in figures 3 and 4 corresponds to coincidence counts, which are proportional to the detection rate (i.e. intensity) of photons hitting D0 at a particular location. So all we can say based on the observed interference patterns is that a signal photon that hits a particular "bin" has a X probability of corresponding to a coincident detection event of the idler at D1, and Y probability of corresponding to a coincident detection at D2.

So, perhaps that helps put my earlier answers into the proper context, and helps you to understand why the interference patterns are observable only through the coincidence measurements.

 

[sanpkl]

thanks Spectra,

sorry if this is getting too much for you. maybe you can make a last attempt...:-) or its ok...you can not respond...i do understand the whole thing...and i know you and cthugha are saying same thing and i agree with it...

yes my post was abotu predicting idler from signal...and i see your logic...and i realize that i my logic is way off...

(though i think you and cthugha are correct, i want to be sure i am 100% convinced, i am 99% now, i do understand you)

however before we get to that...

let's say we have looked at the *separate* coincidence channels for the first million photons.

now we get two well defined patterns...let's say we have done it exactly the way kim-scully et al would have done it.

now i send one photon...we measure its position... can we tell if it falls on the first or the second interference pattern?

if its close to the first pattern then its on first, if its close to the second then its on second.

however i think the reason we cannot tell is because ** both ** the interfernce patterns overlap...in a sense.

thus we cannot tell from a single photon on which interference pattern it lies...

reading cthugha's response.

You still don't seem to get the fundamental point here ... we do not "have two well-defined interference patterns" until we look at the *separate* coincidence channels. Your original question was asking about drawing conclusions from looking only at the signal photon measurements to make a *prediction* about the fate of the idler photon *passing through the interferometer*. That is clearly a physical impossibility based on common sense, let alone the laws of QM.

You cannot say anything regarding the idler photon until it has been measured. If it shows up on D1 or D2, then it passed through the interferometer, and which-path info was erased. If it shows up on D3 or D4, then we know which source (A or B) it came from. The interference pattern you are talking about only exist/make sense for *pairs* of photons corresponding to coincidence measurements at detectors D1 and D2 .. there is no "measurement" in this case until both photons have been detected. The number of coincidences preceding a particular measurement, whether it is the first or the million-and-first, is completely irrelevant.

 

[Cthugha]

So all we can say based on the observed interference patterns is that a signal photon that hits a particular "bin" has a X probability of corresponding to a coincident detection event of the idler at D1, and Y probability of corresponding to a coincident detection at D2.

Indeed, that might be the best wording.

 

[sanpkl]

yes spectra you see my confusion...i am imagining a 2d...or a 2d being constructed...after noting position of Do on x axis...let me read and digest your post ...before i respond.

i just realized that my understanding about the pattern/graphs generation is wrong ...after reading your post below...

ok...i got it...in summary/short:

1. one cannot tell by the position of single signal photon...if it lies on Do-D1 pattern or Do-D2 pattern because of 2

2. the graphs are probability distributions.

3. plus there is a bit more...

now i will post the next thought i had ( after i have read Cthugha's last post) ...thanks Spectra cat and Cthugha...

Ok, maybe I see where your confusion arises. Are you are thinking of the D0 detector as representing some "screen" where we have a 2D-trace representing the interference patterns? That is certainly not correct. If we replaced D0 by a "screen", we would see a 1-D line (or band, since its thickness will not be zero). The integrated pattern of all the photons along that band will show a roughly Gaussian distribution peaked in the center. The question you are asking concerns a signal photon that hits such a "screen" at a particular location x'. Do you really think we can learn anything about its corresponding idler photon simply from observing that location? From the context of your question, it seems like you think that such a "screen" would somehow be divided into "bins", and all the photons landing in a given "bin" are correlated with idler photons going to a particular detector. This is not the case ... signal photons can hit any location on the "screen", irrespective of where their idler photon ends up.

The y-axis in figures 3 and 4 corresponds to coincidence counts, which are proportional to the detection rate (i.e. intensity) of photons hitting D0 at a particular location. So all we can say based on the observed interference patterns is that a signal photon that hits a particular "bin" has a X probability of corresponding to a coincident detection event of the idler at D1, and Y probability of corresponding to a coincident detection at D2.

So, perhaps that helps put my earlier answers into the proper context, and helps you to understand why the interference patterns are observable only through the coincidence measurements.

 

[sanpkl]

Indeed, that might be the best wording.

yes that is what i was looking for.

Well worded! Spectra cat. now reading Cthugha's post

 

[SpectraCat]

As you erase which-way information (assuming that you can do it willingly which is not possible in the Kim paper), the idler photon will end up at D1 or D2. This means when doing coincidence counting you will find it at figure 3 or 4.

Ok, I guess I glossed over that aspect of his question .. I was assuming that all 4 idler detectors were still in play.

Well, if you had no background noise, perfect detectors detecting every photon, perfect fringe visibility (this means a large number of counts at one position in figure 3 and no counts at all at the same position in figure 4 or vice versa) and have already recorded the interference patterns by coincidence counting you could predict at which detector (D1 or D2) the idler will end up if you recorded the corresponding idler at a position with zero counts for one of the two coincidence count interference patterns and send so few photon pairs around that you can be unambiguously sure which idler photon belongs to which signal photon. That this works is trivial. The measurement at D0 defines the relative phase between A and B and this relative phase is exactly what determines the idler photon behavior at the final beam splitter.

Are you sure this is correct? First of all, it would only provide definitive answers for a very small subset of photons that hit D0 at locations corresponding to the minimum/maximum intensities of the fringes. Second of all, even for those subsets, it will only work if the minimum intensities in a given pattern correspond to a detection rate of zero, and it was my understanding that this is not possible. Is it really possible to tailor the phase characteristics of a single photon so that one can predict with certainty which path it will take upon encountering a beam-splitter or a half-silvered mirror? If so, then I will have to reconsider my comments.

But of course it does not work the other way around. If you detect an idler photon at D1 or D2 you cannot say at which position the signal will hit D0.

Why not? It seems to me that there is no difference between the two cases, assuming that we have position-sensitive detection at both locations. If predictive power is allowed from observing the signal photon path, it should also be from observing the idler-photon path.

Eh? The possibility to make a prediction on one side based on the measurement on the other side is pretty much what entanglement is about.

Of course, but the position of detection at D0 does not give us the information we need to predict unambiguously the path which the idler photon will take upon encountering the beam splitter, does it? (see my question above).

 

[sanpkl]

SpectraCat wrote:

<Of course, but the position of detection at D0 does not give us the information we need to predict unambiguously the path which the idler photon will take upon encountering the beam splitter, does it? (see my question above).>

I agree with Spectra Cat.

However, do we all also agree that, this is because:

we don't know (with *absolute certainty*) if the detected position of signal photon "falls/lies" on the interference pattern of figure 3 or 4 (or fig 5 or 6)?

Until we correlate with idler in the co-incidence counter

 

[Cthugha]

Are you sure this is correct? First of all, it would only provide definitive answers for a very small subset of photons that hit D0 at locations corresponding to the minimum/maximum intensities of the fringes. Second of all, even for those subsets, it will only work if the minimum intensities in a given pattern correspond to a detection rate of zero, and it was my understanding that this is not possible. Is it really possible to tailor the phase characteristics of a single photon so that one can predict with certainty which path it will take upon encountering a beam-splitter or a half-silvered mirror? If so, then I will have to reconsider my comments.

Well, this would of course just work under perfect experimental conditions, with no background noise and of course just for extremely few positions of D0. In principle this is possible. Whether this can indeed be realized under realistic lab conditions is a different question. I mean - this is pretty much the same as asking "is it possible to have completely destructive interference in one exit port of a Mach-Zehnder-interferometer". Under some well defined experimental conditions it is possible.

Why not? It seems to me that there is no difference between the two cases, assuming that we have position-sensitive detection at both locations. If predictive power is allowed from observing the signal photon path, it should also be from observing the idler-photon path.

This case would be more difficult. There are just two detectors D1 and D2, but lots of possible positions of D0. So while it is possible to say that D0 detections at some positions x1, x2 and x3 will lead to idler detections at D1, you will only be able to say that a detection at D1 will mean a signal detection at position x1 or x2 or x3 and maybe even some other position. However, you could get some probability distribution.

 

[sanpkl]

Cthugha,

are you saying that:

once we have determined the position of signal photon on D0,
the entanglement is broken
the path of idler is now fixed/sealed/predetermined

 

[Cthugha]

Broken? Well, you break the superposition.

Just compare this to the simplifying case of two spin-entangled particles. You can have particle 1 with spin up and particle two with spin down or the other way round. If you measure for example spin down on one particle, you now know what that you would measure spin up on the other.

In the DCQE experiments the measurement is different. You gain phase information. And once you do so on the side of D0 you get a well defined phase and can therefore predict what will happen on the other side - as phase is the property which determines what happens in a Mach-Zehnder interferometer. However in most cases this will be a probabilistic prediction like "with 70% probability that photon will go to D1".

 

[sanpkl]

Cthugha,

assuming you have not given up on my questions/posts...:-)

so proceeding further on our line of thought/understanding...

you wrote:

<As you erase which-way information (assuming that you can do it willingly which is not possible in the Kim paper), the idler photon will end up at D1 or D2. This means when doing coincidence counting you will find it at figure 3 or 4.>


in the experiment...(either the scully kim one or my minor modification of it)

at the time/moment when signal photon position was measured, we did *have* which way information.

the which-way information is erased (in idler) after the signal photon has been measured.

however quantum mechanics (or your quote above) would say that the position of signal photon would correspond to which way information being erased?

1. how do we explain this?

2. while in the kim scully setup we might not "willingly" be able to erase which way info, there are sereval other delayed choice quantum eraser experiments where we do have the ability to erase or not erase which way information at our will?

for example Wheeler's delayed choice ?

http://news.sciencemag.org/sciencenow/2007/02/16-04.html

As you erase which-way information (assuming that you can do it willingly which is not possible in the Kim paper), the idler photon will end up at D1 or D2. This means when doing coincidence counting you will find it at figure 3 or 4.



Well, if you had no background noise, perfect detectors detecting every photon, perfect fringe visibility (this means a large number of counts at one position in figure 3 and no counts at all at the same position in figure 4 or vice versa) and have already recorded the interference patterns by coincidence counting you could predict at which detector (D1 or D2) the idler will end up if you recorded the corresponding idler at a position with zero counts for one of the two coincidence count interference patterns and send so few photon pairs around that you can be unambiguously sure which idler photon belongs to which signal photon. That this works is trivial. The measurement at D0 defines the relative phase between A and B and this relative phase is exactly what determines the idler photon behavior at the final beam splitter.
But of course it does not work the other way around. If you detect an idler photon at D1 or D2 you cannot say at which position the signal will hit D0.



Eh? The possibility to make a prediction on one side based on the measurement on the other side is pretty much what entanglement is about.

 

[sanpkl]

well said!

Broken? Well, you break the superposition.

Just compare this to the simplifying case of two spin-entangled particles. You can have particle 1 with spin up and particle two with spin down or the other way round. If you measure for example spin down on one particle, you now know what that you would measure spin up on the other.

In the DCQE experiments the measurement is different. You gain phase information. And once you do so on the side of D0 you get a well defined phase and can therefore predict what will happen on the other side - as phase is the property which determines what happens in a Mach-Zehnder interferometer. However in most cases this will be a probabilistic prediction like "with 70% probability that photon will go to D1".

 

[Cthugha]

at the time/moment when signal photon position was measured, we did *have* which way information.

the which-way information is erased (in idler) after the signal photon has been measured.

however quantum mechanics (or your quote above) would say that the position of signal photon would correspond to which way information being erased?

1. how do we explain this?

The position of the signal photon itself does not depend on whether you erase which-way info or not (still assuming that we can somehow do it willingly). However, if you do, the idler will enter the Mach-Zehnder like part of the setup leading to detectors D1 and D2. If you do not erase which-way info the idler photon the idler will never enter that part of the setup and will go to D3 or D4. This part is not phase sensitive so any position detected at D0 can lead either to a detection at D3 or D4.

2. while in the kim scully setup we might not "willingly" be able to erase which way info, there are sereval other delayed choice quantum eraser experiments where we do have the ability to erase or not erase which way information at our will?

For example in the double slit quantum eraser experiment performed by Walborn (http://pra.aps.org/abstract/PRA/v65/i3/e033818]) you can willingly choose whether you keep or erase which way info in terms of the polarization of the light in the two paths.

 

[sanpkl]

how do we explain the fact that the same/fixed position (of signal)... say (x,y) = (5,7)

can lie on
figure 3/4 if we erase which way (for idler)
and
figure 5/6 if we keep which way (for idler)




if photon is driving on highway I-5 the photon is on I-5
if photon is driving on I-10, the photon is on I-10
if the photon is on intersection of I-5 and I-10 then its possibe for the photon to be aligned with either I-5 or I-10


also see below from http://www.bottomlayer.com/bottom/kim-scully/kim-scully-web.htm

<<The position of a photon at detector D0 has been registered and scanned. Yet the actual position of the photon arriving at D0 will be at one place if we later learn more information; and the actual position will be at another place if we do not.>>

 

[Cthugha]

how do we explain the fact that the same/fixed position (of signal)... say (x,y) = (5,7)

can lie on
figure 3/4 if we erase which way (for idler)
and
figure 5/6 if we keep which way (for idler)

Why should there be a problem? Figures 3/4 and figures 5/6 are the results of two completely different measurements on the idler.

As soon as the signal is detected the signal part of the experiment is done. You determined a position - or equivalently a relative phase. I think the whole experiment would be much easier to understand if you exchanged the position axis with an axis showing the relative phase. And now the choice is whether to send the idler to a detector setup, which is sensitive to this relative phase (detectors D1/D2 leading to figures 3/4) ot to a detector setup which is not sensitive to the relative phase (leading to figures 5/6).

also see below from http://www.bottomlayer.com/bottom/kim-scully/kim-scully-web.htm

<<The position of a photon at detector D0 has been registered and scanned. Yet the actual position of the photon arriving at D0 will be at one place if we later learn more information; and the actual position will be at another place if we do not.>>

Please be careful with that page. Most of the commentary there is nonsense - and I do not quite believe the endnote saying Dr. Kim reviewed the commentary.

 

[sanpkl]

Cthugha, thanks for clarifying about the experiment.
My understanding on the generation of figures 3,4,5,6, is very limited.
Can you please correct/modify the below?

0. Does "joint detection" mean anything beyond correlating in the co-incidence counter?

1. What is the y-axis (labeled coincidence) measuring in figures 3,4,5,6? Searching through the kim paper to see if I can find the answer.

for example on figure 3, one of the signal photon's position is (x,y) = (1.5, 120).

what does 120 mean?

2. Figures 3/4, 5/6 are constructed based on position of signal photon, the idler (other than simply confirming it’s the right twin signal photon) has nothing to do with it
3. You wrote: Figures 3/4 and figures 5/6 are the results of two completely different measurements on the idler.
I thought/assumed: Figures 3/4 and figures 5/6 are the result of measurements on the signal. What did you mean?
4. Phase difference between signal and idler can be measured, as well as determined theoritically, however the signal has already made the pattern/position, so

 

[Cthugha]

0. Does "joint detection" mean anything beyond correlating in the co-incidence counter?

Not really.

1. What is the y-axis (labeled coincidence) measuring in figures 3,4,5,6? Searching through the kim paper to see if I can find the answer.

for example on figure 3, one of the signal photon's position is (x,y) = (1.5, 120).

what does 120 mean?

It is just the number of simultaneous detections of the signal at a given position and the idler at a given detector in a fixed time interval. So all they do is to put the detector at position x and wait for say 60 seconds and count all the simultaneous detections of signal photons at D0 at this position and for example idler photons at D1. The absolute number of simultaneous detections is then shown on the y-axis. Then they move the detector to the next position and wait again for 60 seconds.

So for example for Fig. 3 there have been 120 simultaneous detections if the detector is positioned at position x=1.5.

2. Figures 3/4, 5/6 are constructed based on position of signal photon, the idler (other than simply confirming it’s the right twin signal photon) has nothing to do with it

Well the idler at least tells whether the detection of the signal needs to be added to figure 3, 4, 5 or 6. This is more than nothing.

3. You wrote: Figures 3/4 and figures 5/6 are the results of two completely different measurements on the idler.
I thought/assumed: Figures 3/4 and figures 5/6 are the result of measurements on the signal. What did you mean?

As I said before conincidence counting is always a measurement on signal AND idler. But the measurement on the signal side is always the same. But on the other side the measurement apparatus is either phase sensitive (idler going to D1/D2 in a Mach-Zehnder-like setup) or not (idler going to D3/D4).

4. Phase difference between signal and idler can be measured, as well as determined theoritically, however the signal has already made the pattern/position, so

The phase difference between signal and idler is completely irrelevant. The phase difference between the possibilities of having the signal and idler emitted from position A or from position B (or equivalently the phase difference between the photon going through one slit or the other slit of the double slit and ending up at one certain position at the detector) is the quantity that matters.

 

[sanpkl]

conincidence counting is always a measurement on signal AND idler. But the measurement on the signal side is always the same. But on the other side the measurement apparatus is either phase sensitive (idler going to D1/D2 in a Mach-Zehnder-like setup) or not (idler going to D3/D4).

1. since we know the emission time of the signal and idler photons, (and path length) we can figure out what time signal (and even idler) would strike Do.

thus can we not separate the signal photon, from the noise by simply considering the photon which struck Do at the expected/calculated arrival time?
or
is the "fine tuning" via formula (or clock) is not good enough and thus we need a coincidence counter?

2. still trying to understand how signal photons patterns can be "clump" or "interference" after the fact.

one idea that comes to mind is that:
once the position of signal is determined, the path of idler is fixed between D3/D4 (i.e.. figure 3/4) and D1/D2 (figure 5/6). though we cannot control the choice between 3 and 4.

however in some experiments we can "willingly" change the path of idler between fig 3/4 or fig 5/6...

 

[Cthugha]

1. since we know the emission time of the signal and idler photons, (and path length) we can figure out what time signal (and even idler) would strike Do.

thus can we not separate the signal photon, from the noise by simply considering the photon which struck Do at the expected/calculated arrival time?
or
is the "fine tuning" via formula (or clock) is not good enough and thus we need a coincidence counter?

Even if you could so it would still be pointless as you still do not know whether the idler photon will go to D1 or D2. Only if you know tha, too, you will seee the interference pattern. Without coincidence counting there is NEVER an interference pattern as (I repeat) the superposition of the coincidence patterns from D0D1 and D0D2 will sum up to no patter at all. If you do not know at which detector the corresponding idler to a signal ends up, you will NEVER get ANY interference pattern.

Or do you mean that you just want to run a clock to take only detections at the detectors into account which originate from the same time at the entangled source? This IS the essence of coincidence counting.

2. still trying to understand how signal photons patterns can be "clump" or "interference" after the fact.

one idea that comes to mind is that:
once the position of signal is determined, the path of idler is fixed between D3/D4 (i.e.. figure 3/4) and D1/D2 (figure 5/6). though we cannot control the choice between 3 and 4.

however in some experiments we can "willingly" change the path of idler between fig 3/4 or fig 5/6...

Make a sketch yourself and calculate it. Start with a basic double slit, assume an initial phase difference of 0, draw the lines from the slits to the different detector positions and calculate the phase differences from the two slits to the different detector positions from the path length difference and draw the pattern. Now model incoherent illumination of the double slit by calculating the pattern for several initial random phase difference between the two slits. Finally superpose all of them and you will see that you get no patternat all.

Now do the same for a Mach-Zehnder-interferometer. Assume there is no which-path information. Start with 0 initial phase difference between the slits and calculate the probability that the phozon goes to D1 and D2, respectively. Now calculate the probability distribution for several initial phase differences.

Now have a look at the coincidences. Start by picking some initial phase difference. where the photons in the Mach-Zehnder part will either go all to D1 or all to D2. Now have a look at the double slit side and compare the interference pattern you calculated for this exact initial phase difference. Do the same for several phase differences and look at the probability that the idler photons go either to D1 or D2.

As a final step model the whole coincidence count experiment. Just choose one of the two detectors D1 or D2 and look at some position at D0. Now sum over all possible initial phase differences and calculate the mean joint probability that the idler will end up at D1 if the signal was detected at this very position. You will get the interference patterns shown in the Kim paper.

You can also calculate the coincidence counts of D0 and D3 if you like, but these are trivial. The number of photons going to D3 does not dpend on the initial phase difference and is therefore constant.

However, this experiment is difficult to grasp unless you do the calculations yourself. Those are, however, pretty simple, so do it yourself if you want to fully understand what is going on.

 

[sanpkl]

Even if you could so it would still be pointless as you still do not know whether the idler photon will go to D1 or D2. Only if you know tha, too, you will seee the interference pattern. Without coincidence counting there is NEVER an interference pattern as (I repeat) the superposition of the coincidence patterns from D0D1 and D0D2 will sum up to no patter at all. If you do not know at which detector the corresponding idler to a signal ends up, you will NEVER get ANY interference pattern.

agreed on the above. i forgot, for a moment, that we need to separate out D1 and D2 photons.

let me go over the next paragraph and get back

 

[eaglelake]

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

Sorry for jumping in so late. With reference to the original questions----
We assume a one photon experiment using a Mach-Zehnder interferometer where the photons are emitted so slowly that there is only one photon at a time in the apparatus. The half silvered mirror mentioned is the initial beamsplitter. With no obstructions in place, we set up so that photons are always detected in D1(constructive interference) and no photons are ever detected in D2 (destructive interference). Conversely, if one of the paths is blocked, we get equal numbers of photons in each detector (no interference).

The first question describes a "delayed choice" experiment. . Such experiments were anticipated by Bohr who stated,
“-------it can make no difference, as regards observable effects obtainable by a definite experimental arrangement, whether our plans for constructing or handling the instruments are fixed beforehand or whether we prefer to postpone the completion of our planning until a later moment when the particle is already on its way from one instrument to another.”

We can wait until the very last moment to decide which experiment to do! The experiment is determined by the apparatus in place at the instant the photon is detected. If one of the paths is blocked prior to photon detection there is no interference; half the time photons end up in D1 and half the time they are found in D2. It does not matter when the obstruction occured. Even if we believe that the photon had already passed through the initial beamsplitter (so that we do not know which path was taken) there is still no interference.

The second question was also answered by Bohr. He recognized that the experiment is not complete without a measurement result; there is no experiment to discuss without an experimental result that is obtained at the instant the photon is detected. Detection is an irreversible event that gives closure to the experiment. As expressed by Wheeler, "No elementary phenomenon is a phenomenon until it is a registered phenomenon."

Once the photon has been detected, the experiment is over and done. Any changes made after detection do not affect the result, which is already known. The interference obtained at photon detection is still the recorded result.

Best wishes.

 

[sanpkl]

Once the photon has been detected, the experiment is over and done. Any changes made after detection do not affect the result, which is already known. The interference obtained at photon detection is still the recorded result.

cthugha, eagle,

all of the below might have been answered before but i just wanted to go over it again...with a different rephrasing...

with reference to the delayed choice quantum eraser...http://arxiv.org/abs/quant-ph/9903047

1 a) when a signal photon has been detected on Do, has not the pattern of signal photon (Though *unknown* to us, till we compare with idler in coincidence counter) already been fixed/sealed? does that mean same as "experiment is over"?

i understand that a single photon not a pattern make, i am referring to the direction/potential

1. b) once the signal photon is measured is the fate/path of the idler also "somewhat" sealed (with a high probability)?

this would resolve/invalidate the "past can be changed" hypothesis/misunderstanding, i guess

2. once the signal photon is measured, we till don't know which figure 3,4,5,6 would it fall, until we compare with idler?

this would resolve/invalidate the "faster than light information travel" hypothesis/misunderstanding, i guess

3. the position of the signal photon on Do has nothing to do with what is what we are doing to the idler at that point in time (i.e. at the exact time the signal strikes Do). if i remember correctly cthugha said similar.

this would help resolve/invalidate the "past can be changed" hypothesis/misunderstanding, i guess

cthugha wrote
<In the DCQE experiments the measurement is different. You gain phase information. And once you do so on the side of D0 you get a well defined phase and can therefore predict what will happen on the other side - as phase is the property which determines what happens in a Mach-Zehnder interferometer. However in most cases this will be a probabilistic prediction like "with 70% probability that photon will go to D1">

for me the "70% (or higher than 50%) probablity" explains a lot...

4. i guess that this would also help reduce the need for "many worlds" hypothesis

5. wave function collapses (for both twins-- idler and signal) when either the signal or idler photon is detected?

 

[sanpkl]

Even if you could so it would still be pointless as you still do not know whether the idler photon will go to D1 or D2. Only if you know tha, too, you will seee the interference pattern. Without coincidence counting there is NEVER an interference pattern as (I repeat) the superposition of the coincidence patterns from D0D1 and D0D2 will sum up to no patter at all. If you do not know at which detector the corresponding idler to a signal ends up, you will NEVER get ANY interference pattern.

is it possible to make the phase difference betwen D1 and D2 such that the patterns of signal photon (for D-D1 and Do-D2) would be separated by a "clear" distance?

 

[Cthugha]

We assume a one photon experiment using a Mach-Zehnder interferometer where the photons are emitted so slowly that there is only one photon at a time in the apparatus.[...]
We can wait until the very last moment to decide which experiment to do! The experiment is determined by the apparatus in place at the instant the photon is detected. If one of the paths is blocked prior to photon detection there is no interference; half the time photons end up in D1 and half the time they are found in D2. It does not matter when the obstruction occured. Even if we believe that the photon had already passed through the initial beamsplitter (so that we do not know which path was taken) there is still no interference.

This reasoning is wrong, but it is such a common fallacy that it has almost become a standard answer. In fact you are answering the wrong question. The common cheap way to do photon-by-photon interference experiments lies in reducing the intensity so much that the mean intensity predicts there will be only one photon inside the interferometer on average. However doing so will only change the amplitude of the light field, but not the relative noise properties. Accordingly there is photon number noise and you can never be sure there is only one photon present and you will have lots of probability amplitudes leading to the same result. Under these circumstances indeed the interference pattern will vanish as you can never be completely sure that the photon has already passed the slits.

However by performing this experiment using a nonclassical light source like a real heralded single photon source the situation is completely different. By using nonclassical light you can construct a situation where you can be completely sure that the photon has already passed the slits. If you now close one of the slits afterwards, the Mach-Zehnder-interference pattern will not vanish. Although the result you describe matches the situation you describe, that situation does not match the question asked. If the photon has passed the slits for sure, you can block a slit without changing the situation.

is it possible to make the phase difference betwen D1 and D2 such that the patterns of signal photon (for D-D1 and Do-D2) would be separated by a "clear" distance?

The phase difference between simultaneous detections D0-D1 and D0-D2 is given by the geometry and the simple fact that the photon is either transmitted or reflected at the beam splitter. Therefore the phase difference is always $$\pi$$. Or did I get your question wrong?

 

[sanpkl]

If the photon has passed the slits for sure, you can block a slit without changing the situation.

thank for clarifying Cthugha. Excellent posts by you.

Would time (i.e. distance/vel of light) be a good enough calc to make sure that the photon has passed the slits?

i.e. by X nano seconds the photon would have passed the point where we are to keep the block...is that good enough?

Can you also respond to my post number 94? thanks

The phase difference between simultaneous detections D0-D1 and D0-D2 is given by the geometry and the simple fact that the photon is either transmitted or reflected at the beam splitter. Therefore the phase difference is always . Or did I get your question wrong? .

can the phase difference be increased beyond pie (say 2 pie or more) by having more transmittors/reflectors in the path?

the phase changes only when reflected thus...the word transmittor can be removed from the above sentence

Originally Posted by Cthugha

Broken? Well, you break the superposition..

superposition = wavefunction?
breaking superposition = collapsing wavefunction?

You determined a position - or equivalently a relative phase..

you have been mentioning relative phase..which i do not undertand yet... what is it? relative to what/idler?

the signal photon would have a position , how can we get relative phase info (since we do not know yet which pattern/figure would it lie on)

 

[Cthugha]

Would time (i.e. distance/vel of light) be a good enough calc to make sure that the photon has passed the slits?

i.e. by X nano seconds the photon would have passed the point where we are to keep the block...is that good enough?

If you exactly knew the emission time, you could do so. However exactly knowing the emission time (without changing the experimental situation completely) is not as trivial as it seems.

Can you also respond to my post number 94? thanks

It is time to go home for me. I hope you can wait until tomorrow. ;)

can the phase difference be increased beyond pie (say 2 pie or more) by having more transmittors/reflectors in the path?

No, this is a matter of geometry. Both partial beams must meet at the final beam splitter. So you could only change the phase difference by those multiples of pi which leave the situation unaltered in principle or lead to a mirrored situation.

superposition = wavefunction?
breaking superposition = collapsing wavefunction?

Well, yes. The two-photon wavefunction (which can have any phase difference concerning slits A and B) is projected onto a state of well-known phase difference for the remaining photon.

 

[sanpkl]

Originally Posted by SpectraCat

So all we can say based on the observed interference patterns is that a signal photon that hits a particular "bin" has a X probability of corresponding to a coincident detection event of the idler at D1, and Y probability of corresponding to a coincident detection at D2.

just to reconfirm/rehearse:

however, in actuality, we cannot tell which "bin" the signal photon has hit, till we compare with the idler?

we can only say *if* the signal photon has hit the (Do-D1) bin (i.e lies on figure 3) then the likely hood of idler photon being detected at D1 is say...80%

 

[sanpkl]

It is time to go home for me. I hope you can wait until tomorrow. ;)

yes, can wait...no rush...:-)

 

[Cthugha]

however, in actuality, we cannot tell which "bin" the signal photon has hit, till we compare with the idler?

we can only say *if* the signal photon has hit the (Do-D1) bin (i.e lies on figure 3) then the likely hood of idler photon being detected at D1 is say...80%

No, that is not the problem. If you already recorded the interference patterns for a while, you could tell the probability distribution of the idler hitting D1 or D2 by knowing the detection position on D0.

However, you can never tell before whether the signal "hit the D0-D1 bin" or the "D0-D2 bin" (or equivalently whether it lies on Fig. 3 or 4). You can just tell where it hit on D0. To get the D1 or D2-info beyond a probabilistic description you need information from the idler.

However, the remaining answers will really have to wait until tomorrow morning.

 

[sanpkl]

one of the major fallacy with "past is/canbe changed, many worlds" is the misunderstanding that:

the "decision" is happening when idler i detected. this is incorrect.

the truth is that:

the experiment is over when signal photon is detected (earlier detection) and not when idler photon i detected (later).

the "probalilistic firming/decision/choice" happens when the signal photon (or which ever is detected first) is detected.

the wave function (of various superimposition states) collapses when signal photon (or to be more precise when whichever photon is detected earlier) is detected and not when idler is detected.


QED. thanks to Cthugha, EagleLake and Spectra Cat

 

[DrChinese]

one of the major fallacy with "past is/canbe changed, many worlds" is the misunderstanding that:

the "decision" is happening when idler i detected. this is incorrect.

the truth is that:

the experiment is over when signal photon is detected (earlier detection) and not when idler photon i detected (later).

I think the context of the entire experiment is relevant. Not just the "first" detection. How you interpret the results is dependent on that context, and that will not be known until later - when all of the results can be brought together into a single place. And then it will in fact appear "as if" the past was dependent on the future.

You can interpret this in different ways. And there are other delayed choice experiments which evidence the same thing. Consider Zeilinger et al:

http://arxiv.org/abs/quant-ph/0201134

From middle of page 5:

"Such a delayed-choice experiment was performed by including two 10 m optical fiber
delays for both outputs of the BSA. In this case photons 1 and 2 hit the detectors delayed
by about 50 ns. As shown in Fig. 3, the observed fidelity of the entanglement of photon 0 and
photon 3 matches the fidelity in the non-delayed case within experimental errors. Therefore,
this result indicate that the time ordering of the detection events has no influence on the
results..."

 

[Cthugha]

the experiment is over when signal photon is detected (earlier detection) and not when idler photon i detected (later).

the "probalilistic firming/decision/choice" happens when the signal photon (or which ever is detected first) is detected.

the wave function (of various superimposition states) collapses when signal photon (or to be more precise when whichever photon is detected earlier) is detected and not when idler is detected.

Well, this is a rather hard wording. The experiment is not really over when you detect the signal - however, the setting is fixed. You can still choose whether to make a which-way experiment or an interference experiment on the idler. Either of those is a measurement, too.

You could say the signal side of the experiment is over. You will not change the position the signal was detected after the detection. However, you can still change the kind and amount of information you can gain from knowing the position where the signal was detected.

 

[sanpkl]

Well, this is a rather hard wording. The experiment is not really over when you detect the signal - however, the setting is fixed.

cthugha, thanks for correcting and providing insight into the experiment.

You can still choose whether to make a which-way experiment or an interference experiment on the idler. Either of those is a measurement, too.

ok. now let's say we detected the signal photon position and its at (x, y) = (1.5, 120) and it lies on figure 3.

actually y does not matter..its just a count (that can be converted to probability).

so, let's assume, we are reasonably sure (after pattern formed by gazillion photons prior) that signal photon position lies on figure 3.

now

1. if we choose which way info...are we likely to detect idler at D1?
2. if we do not chose which way info...are we likely to detect idler at?
2b) the signal is on fig 3, suggesting interference and no which way..however if we make which way experiment on idler...then won't signal be saying interference and idler which way?

my guess/answer to 2b) is that ...when we force idler (to say which way) the entanglement with signal is broken..so we can no longer expect them (idler and its twin signal)to say the same thing..

or in other words what behavior of idler (i.e. which detector it will land up at) can we expect (probabilistically) if

Case 1. we choose to make a which-way experiment on idler
Case 2. we choose to make an interference experiment on the idler.

**given that** signal seems to be (with high probability) on the pattern of figure 3...

sorry if this makes you feel i am going back to square one...don't worry...just answer the best you can...if you will...

You could say the signal side of the experiment is over. You will not change the position the signal was detected after the detection. However, you can still change the kind and amount of information you can gain from knowing the position where the signal was detected.

i have a feeling this is really well said...well summarized...till i fully digest and assimilate this.

Please give example of kind and amount of information one can gain (about idler?) from knowing the position of where signal was detected. this will help me understand better.