Instant communication with a modified ZWM apparatus?

[al onestone]

I have given a brief explanation of the ZWM study and a modified apparatus below, but for those wishing to become more familiar with the ZWM study the actual references are (experimental paper first and theoretical second)

X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991).
L. J. Wang, X. Y. Zou, and L. Mandel, Phys. Rev. A 44, 4614 (1991).

Possibly Mandel's finest work.

Two figures are attached, one is the ZWM apparatus and its explanation is as follows:

The pump beam goes to the 50/50 beamsplitter (BS) and then pumps one of two downconversion crystals (DC1 and DC2) which transform the photon into two photons (signal and idler) with each having roughly half the frequency/energy. The idler from DC1 is forced to transmit through the DC2 crystal so that it retains coherence between the output of the two crystals. The two signal outputs from DC1 and DC2 are combined at a detector Ds.
There are two types of interference here, first is the interference in the coincidence counter (CC). When one of the optical paths is varied there is interference as a function of the combined phases (φs + φi). The coincidence interference results from indistinguishability between the combined pathways from DC1 to Ds and Di -or- from DC2 to Ds and Di. We cannot tell which way the pump photon went after the beam splitter.
The second interference occurs at detector Ds and is a simple function of the phase. The interference that occurs at this detector is a lower order. It is simply the indistinguishability between the optical paths from the pump photon to detector Ds. If the detector has a count you cannot tell if it came from DC1 or DC2 depending on which path it took after the beam splitter.
The coincidence interference(4th order) requires that all four optical paths to the two detectors be identical (or at least differing by no more than a coherence length). The interference at Ds (2nd order) requires the two optical paths from BS to DC1 to Ds and from BS to DC2 to Ds be identical.
By placing the neutral density filter (NDF) between DC1 and DC2 in the idler path i1, the interference at detector Ds vanishes. Why? Because the paths to Ds from the pump are now distinguishable. How? If the pump photon goes to DC1 and downconverts then the signal will go to Ds but the idler will be attenuated by the filter and you will not get a coincidence count at Di. If the pump photon goes to DC2 and downconverts then the signal will go to Ds and the idler will go to Di and there will be a coincidence count. So the presence or non-presence of a coincidence count at Di is the measurement which will determine whether the pump photon went to DC1 or DC2 to downconvert. So by inserting the NDF into the idler path, Mandel has eliminated the interference at detector Ds. And it is worth noting that the interference effect at Ds can only be negated by a distinguishability measurement which occurs at a second detector Di which is spatially separated from Ds, and that these measurements don’t actually need to be made to negate the interference. Mandel notes that these measurements at Di need only be in principle possible to negate the interference pattern. He got the same results without even making the distinguishing measurements. Absolutely Brilliant! Now look at how we modify this to create instant communication.

The second figure is for my modified ZWM apparatus and its explanation is as follows:

In the Modified ZWM we make the simple change in the positioning of the filter, and instead of analysing the interference at Ds we look at the interference at detector Di by modulating the optical path length between DC1 and DC2 with a modulator (PM). This modulates the pathlength from BS to DC1 to Di relative to the pathlength of BS to DC2 to Di. The question is, is there interference at detector Di like there was at Ds? Interestingly enough, Mandel referred to this detector as “superfluous” to the detection at Ds. This implies that there is interference at Di but this is not a thorough analysis. In the ZWM paper, Mandel does the combined field amplitude for the three fields (pump signal and idler) at the crystal in order to arrive at a counting rate for the coincidence effect and a counting rate for the detector Ds. No analysis is given for the counting rate at Di.
If I am correct, and there is an additional interference effect (2nd order) at Di then this interference can be negated with the filter being placed in the s1 path near Ds. By minimising the distance between the filter (NDF) and Ds, and maximising the distance between Ds and Di, such that the latter is much greater than the former, we would be negating the interference effect at Di instantaneously byattenuating the s1 path with the NDF.
If all my reasoning is sound up to here then we are a small step away from modulation between the extreme cases (insertion of the NDF and non-insertion) to produce a modulation of the interference at Di. Instant communication.
Where have I gone wrong this time?

 

[mfb]

Mandel referred to this detector as “superfluous” to the detection at Ds.

In his setup, not in yours, I think.

This implies that there is interference at Di

In his setup with NDF, there is no interference at Di, assuming his NDF blocks all photons (otherwise there might be some interference left).
Di will detect a photon in 50% of the cases, Ds will always detect one photon, and if you replace the NDF by a detector it will detect one in the other 50%.

As long as the signal photons are flying around, you won't detect interference at Di, regardless of the phase shift in the PM.
After the experiment, you can compare Di and Ds and may note some correlation effects from your setup.

This is similar to the delayed choice quantum eraser and other experiments. An individual measurement is usually not very interesting, but you can see some correlation between the measurements if you compare the signals of multiple detectors afterwards.

 

[al onestone]

mfb, your comment "As long as the signal photons are flying around, you won't detect interference at Di, regardless of the phase shift in the PM." tells me you're missing something about my setup and his.
In Mandel's setup the signal detector has the complete visibility of 2nd order interference, but only when there is no NDF. When the NDF is placed into the apparatus, there is distinguishability, and so the visibility of interference is attenuated (with a dependence on the transmissivity of the NDF).
In my setup the idler detector should have complete visibility of interference, but only when there is no NDF. When the NDF is placed into the apparatus (except now in one of the signal paths) then the interference at the idler detector is attenuated.
And remember, the four optical paths are identical, so no signal photons are "flying around" anymore at the time of detection.

 

[zonde]

In my setup the idler detector should have complete visibility of interference, but only when there is no NDF. When the NDF is placed into the apparatus (except now in one of the signal paths) then the interference at the idler detector is attenuated.
And remember, the four optical paths are identical, so no signal photons are "flying around" anymore at the time of detection.

You are not creating interference in idler detector. What happens in Mandel's setup is coherent downconversion in DC2 with downconversion in DC1.
How insertion of NDF in s1 path can affect that coherent downconversion when s1 does not go through DC2?

 

[StevieTNZ]

As Vanadium 50 has said before (before you rudely had a go at him) "QM says you cannot do what you are trying to do". I do not know why you continue to go down the faster-than-light thought experiment line.

 

[al onestone]

Remember, Vanadium 50 had the first go at me, not the other way around. In reply to the statement "QM says you cannot do what you are trying to do", this is not a strictly quantum mechanical experiment. This is a pseudo quantum-classical experiment. The preparation is quantum mechanical, in both cases, with and without the NDF filter. Obviously, to insert and remove the NDF is not a quantum mechanical procedure. It is a classical one. So try to get Vanadium 50 and the rest of the QM theoretician community to model "the insertion and removal of NDF" as a quantum mechanical procedure or operation.
This experiment models a classical modulation between two DISTINCT quantum mechanical preparations.

What this experiment comes down to is can the second detector, the idler detector Di, produce interference with o.p.d.? If it can then this experiment works. What is needed is someone whom can explain why or why not Di can produce interference.

Zonde : your comment "You are not creating interference in idler detector"
I'm not trying to create interference in Di, I'm assuming that interference in Di was always possible (with my setup and with Mandel's). Mandel never treated what was happening at detector Di because he considered it "superfluous". But was he right about this? He naturally neglected the detector Di in his treatment because it naturally has a lower counting rate, but this is due to experimental limitation. It was easier for him to produce the 2nd order interference effect at Ds. And I think he missed out on something.

Does anybody know ABSOLUTELY what is happening at Di?

 

[StevieTNZ]

Remember, Vanadium 50 had the first go at me, not the other way around. In reply to the statement "QM says you cannot do what you are trying to do", this is not a strictly quantum mechanical experiment. This is a pseudo quantum-classical experiment. The preparation is quantum mechanical, in both cases, with and without the NDF filter. Obviously, to insert and remove the NDF is not a quantum mechanical procedure. It is a classical one. So try to get Vanadium 50 and the rest of the QM theoretician community to model "the insertion and removal of NDF" as a quantum mechanical procedure or operation.
This experiment models a classical modulation between two DISTINCT quantum mechanical preparations.

What this experiment comes down to is can the second detector, the idler detector Di, produce interference with o.p.d.? If it can then this experiment works. What is needed is someone whom can explain why or why not Di can produce interference.

Zonde : your comment "You are not creating interference in idler detector"
I'm not trying to create interference in Di, I'm assuming that interference in Di was always possible (with my setup and with Mandel's). Mandel never treated what was happening at detector Di because he considered it "superfluous". But was he right about this? He naturally neglected the detector Di in his treatment because it naturally has a lower counting rate, but this is due to experimental limitation. It was easier for him to produce the 2nd order interference effect at Ds. And I think he missed out on something.

Does anybody know ABSOLUTELY what is happening at Di?

Everything is in principle quantum mechanical. So I don't know where classicality fits in.

And as far as I'm concerned, Vanadium didn't have a go at you. He suggested you learn QM first. There is nothing wrong with saying that.

 

[zonde]

Zonde : your comment "You are not creating interference in idler detector"
I'm not trying to create interference in Di, I'm assuming that interference in Di was always possible (with my setup and with Mandel's). Mandel never treated what was happening at detector Di because he considered it "superfluous". But was he right about this? He naturally neglected the detector Di in his treatment because it naturally has a lower counting rate, but this is due to experimental limitation. It was easier for him to produce the 2nd order interference effect at Ds. And I think he missed out on something.

As I understand it Mandel's reasoning was that 2nd order interference is visible exactly because there is no interference at Di.

Does anybody know ABSOLUTELY what is happening at Di?

I do not understand the point of your question. This information is absent in the paper about experiment. So do you mean that someone from this forum might have repeated that experiment? Or what?

 

[mfb]

I'm not trying to create interference in Di, I'm assuming that interference in Di was always possible (with my setup and with Mandel's).

You don't get interference with the NDF in one idler path.

Mandel never treated what was happening at detector Di because he considered it "superfluous".

Probably because he ruined the interference with the NDF, and therefore the Di detector is not interesting any more.

 

[zonde]

Does anybody know ABSOLUTELY what is happening at Di?

Ok, here is the way how to get closer to that question.
We can compare Mandel's setup with DCQE experiment. Here if we swap idler with signal photon and throw out BSa and BSb we get quite similar setups.

Now in DCQE there is no 2nd order interference in signal (Mandel's idler) arm. And actually there shouldn't be 2nd order interference in idler (Mandel's signal) arm too but this is not explicitly tested.

 

[al onestone]

To mfb: Your comments "You don't get interference with the NDF in one idler path" and "he ruined the interference with the NDF, and therefore the Di detector is not interesting any more."

Here's how it works. When Mandel sets up his apparatus, he has the NDF ABSENT from the experiment. With this setup he gets interference (2nd order) at the signal detector. When he inserts the NDF into the idler1 path, it gives "which path" information about the idler (and consequently about the signal also). The interference is attenuated by the NDF, so the visibility becomes a function of the transmissivity of the NDF.

In my setup, I assume that there is also 2nd order interference at the idler detector ( which Mandel considers insignificant in his study because it is the same as at the signal detector). But in my setup, I insert the NDF in the signal pathway, s1, to attenuate the interference at the idler detector.
The question is, am I correct about there being interference at the idler detector also?

 

[al onestone]

To Zonde: Your link to the DCQE is relevant. The DCQE is a similar experiment but it has a definite preparation. It uses the postselection of idler detection to filter out what signal photons are interfering. This, I'll remind you, is all with one single continuous preparation, which does not change with time.
In both the ZWM setup and my modification of it, there is always a choice between insertion of the NDF and non-insertion of the NDF. (In a later paper Mandel actually uses a time dependent NDF mounted on a shutter). This means we're modulating (slowly) between two different preparations, one with the "which path" information(insertion of the NDF) and one without the "which path" information(non-insertion of the NDF).

Another point, in the DCQE, you DO NOT under any circumstances get interference at the signal detector D_o , UNLESS you use postselection of the idlers. You have to "sift out" the interference afterwards. In the ZWM we automatically get interference because the induced coherence from the idler1 passing through DC2.

I have a feeling my thought experiment is still valid (Modified ZWM) but we still have to get to the bottom of things.

 

[al onestone]

To zonde: Your earlier questions "So do you mean that someone from this forum might have repeated that experiment? Or what?"

No, I'm hoping that someone can confirm weather or not there is interference at the idler detector (when there is no NDF at all). Mandel does the math for the signal detector then he calls the idler detector "superfluous". This implies that the exact same mathematical treatment applies to the idler detector as he does for the signal detector. This would imply that there is interference at D_i. But am I correct with this reasoning?

 

[al onestone]

After futher examination of the original papers, I have found that Mandel reports the counting rate at the idler detector D_i, and it is a non varying function which would result from spontaneous emission from the two crystals. There is only interference at the idler detector and in the coincidence detection.

Therfore this thought experiment does not work. On to the next one.