What's up with the absorptive quantum eraser?

[ab_gladsaxe]

What's up with the "absorptive" quantum eraser?

In the famed "quantum eraser" of physics, there is two distinct types, one type which uses an absorptive apparatus for the method of "unmarking the path" and one which does not. For the absorptive type of quantum eraser we have a clear fallacy in its explanation.

The absorptive quantum eraser is designed as follows:

Step1) Set up an interference effect.

Step2) Introduce a path marker in one of the interfering paths (if the interfering system is photons and they are polarized in one direction, then a suitable path marker would be a half wave plate). Now you won't measure interference because the paths are marked (by distinct polarizations of horizontal and vertical).

Step3) Now introduce an absorptive apparatus in the experiment just prior to the detector which will project the system's state onto a "subensemble". In the example of photons with distinct polarizations, this amounts to the insertion of a polarizer which is oriented half way between horizontal and vertical, 45degrees. Now you will attenuate the beam by half, but the portion that gets to the detector will display interference. These photons are in a +45degree polarized state so it is not known as to weather they traversed the horizontal or vertical path.

This explanation has a fallacy. The absorptive apparatus that "unmarks the path" is actually selecting out (absorbing) the -45degree polarized photons and allowing the +45degree polarized photons to pass. These photons that pass are the one's that apparently display interference, but in fact it is the absorbed photons that are displaying the interference. The photons that pass are also "displaying" interference but only in a sense that we are actually conducting an "absorption spectroscopy" experiment. The photons that are absorbed by the polarizer are being absorbed by atoms whose final states are one-to-one with the -45degree polarized state of the photons (so it is not possible to measure the atom's state in order to determine the path of the absorbed photon). If you were actually using the -45degree polarizing material as a detector (in principle the absorption is a measurement), then it would be noticed that the measurement (the absorption) is actually displaying interference. This interference is an interference between distinguishable states of polarization. This is why people are so easily misled in this fallacy, because they accept, by convention, that interference is not possible between distinguishable states. Rubbish I say!

Here is a publication by Kwiat-Englert on the quantum eraser, where they present results of a non-absorptive eraser but they give an explanation using the absorptive one which presents the fallacy I've mentioned. Look on page 3.

http://research.physics.illinois.edu/QI/photonics/papers/WheelerChapterFinal.pdf

 

[Cthugha]

This explanation has a fallacy. The absorptive apparatus that "unmarks the path" is actually selecting out (absorbing) the -45degree polarized photons and allowing the +45degree polarized photons to pass. These photons that pass are the one's that apparently display interference, but in fact it is the absorbed photons that are displaying the interference. The photons that pass are also "displaying" interference but only in a sense that we are actually conducting an "absorption spectroscopy" experiment. The photons that are absorbed by the polarizer are being absorbed by atoms whose final states are one-to-one with the -45degree polarized state of the photons (so it is not possible to measure the atom's state in order to determine the path of the absorbed photon). If you were actually using the -45degree polarizing material as a detector (in principle the absorption is a measurement), then it would be noticed that the measurement (the absorption) is actually displaying interference. This interference is an interference between distinguishable states of polarization. This is why people are so easily misled in this fallacy, because they accept, by convention, that interference is not possible between distinguishable states. Rubbish I say!

Pretty much none of that is correct. You can decompose a vertical polarization into components of + 45 degrees and - 45 degrees. In the same manner you can decompose the horizontal polarization into components of +45 and +135 degrees. The polarizer at 45 degrees allows a part of the light field equivalent to the +45 degrees component to pass. Usually it reflects the -45 degrees and +135 degrees component (but you could make an absorbing version, too). -45 degrees and +135 degrees is also the same axis of polarization (just a pi phase shift) and thus these two components are also not distinguishable. If you disagree, feel free to come up with an experiment showing how to distinguish them.

 

[ab_gladsaxe]

...You can decompose a vertical polarization into components of + 45 degrees and - 45 degrees. In the same manner you can decompose the horizontal polarization into components of +45 and +135 degrees. The polarizer at 45 degrees allows a part of the light field equivalent to the +45 degrees component to pass. Usually it reflects the -45 degrees and +135 degrees component (but you could make an absorbing version, too)...

In principle, the polarizer at 45 degrees will allow all of the +45degree polarized light to pass and all of the -45/+135degree polarized light is absorbed. (I've already stated this above.) So now we all understand how a polarizer works. The point is, the absorption is a measurement. This measurement is displaying interference. The interference is between distinguishable states of H and V polarized light (H + V = +45degrees).

 

[Cthugha]

So now we all understand how a polarizer works. The point is, the absorption is a measurement. This measurement is displaying interference. The interference is between distinguishable states of H and V polarized light (H + V = +45degrees).

Maybe now we know how polarizers work, but not really what distinguishability means. If you have probability amplitudes for two distinguishable paths, that means you in principle have a possibility to tell which path the photon took after the measurement. So how do you do that?

Your fallacy lies in attributing the indistinguishability to the states of the light field. This is not what matters. It is the indistinguishability of the paths between emission and detection process (including of course also the detection process) which matters. Kwiat and Englert also consider the paths, for example on page 4 of the pdf you linked. If you placed the polarizer at H or V, you would get distinguishability. At 45 degrees you do not.

 

[ab_gladsaxe]

If you have probability amplitudes for two distinguishable paths, that means you in principle have a possibility to tell which path the photon took after the measurement. So how do you do that?

The point is that you do not have the ability to distinguish the paths. Before the photon is absorbed it might be H or V polarization, but the atom in the polarizer that absorbs the photon only absorbs 45degree polarization. Therefore each photon absorbed must project from the mixed H and V state to a definite 45degree state (which are essentially the same thing because the mixed H and V states are coherent). You cannot measure the state of the atom after absorption to determine the polarization of the absorbed photon, unlike with the case of a normal detector where the absorbing atoms could in principle be measured to determine the state of polarization of the absorbed photons. So, with a normal detector there is no interference because there is "post-measurement" distinguishability of the polarization/path of the photon. But when you use a 45degree polarizing material as a detector (like in the quantum eraser where it is used as a "path unmarker") there is no such "post-measurement" distinguishability so there is interference in the measurement. And that interference is between distinguishable states of H and V polarization. And that interference is being measured in all such quantum eraser protocols with an absorptive "path unmarker" that recreates interference.

Here's how to understand this by an example in the link.

In the absorptive quantum eraser there is always a fringe/anti-fringe pattern. Experimentalists always say that the absorbing medium allows some of the system to pass and this is detected in an interference pattern. The truth is that the only interference being displayed is in the absorbing medium, in a fringe pattern. The detector after the absorbing medium only displays the anti-fringe pattern because that is what is left over after the absorption. In the link to Kwiat-Englert you can see this in the figures (b) and (c) on page 3. In figure (b) we have the "marked paths" so we get a Gaussian with no interference. In figure (c) we have the solid line fringe pattern (with an absorptive +45degree polarizer inserted) and the dashed line anti-fringe pattern (with an absorptive -45degree polarizer inserted). Note, the fringe pattern and the anti-fringe pattern add to total the Gaussian of figure (b).

We must conclude, that when the +45degree polarizer is inserted to produce the fringe pattern, it is absorbing a data set that is the difference between (b) and the fringe pattern. That data set perfectly replicates the anti-fringe pattern. Therefore the absorbing +45degree polarizer is displaying interference in the anti-fringe pattern.

A similar analysis applies to the insertion of the -45degree polarizer which produces the anti-fringe pattern at the detector and the fringe pattern at the polarizer.

 

[Cthugha]

The point is that you do not have the ability to distinguish the paths.

Yes, exactly!

But when you use a 45degree polarizing material as a detector (like in the quantum eraser where it is used as a "path unmarker") there is no such "post-measurement" distinguishability so there is interference in the measurement. And that interference is between distinguishable states of H and V polarization. And that interference is being measured in all such quantum eraser protocols with an absorptive "path unmarker" that recreates interference.

Sorry, but that is simply not a sensible usage of terminology in physics. It makes absolutely no sense to talk about distinguishable states of light fields without explicitly having a certain experimental setup in mind. Sure, one could call states of the light field for which some measurement exist, which could distinguish them "distinguishable", but that is a pretty meaningless quality and NOT the normal meaning of distinguishable vs. indistinguishable.

The distinguishabilty in quantum optics is ALWAYS about different pathways from the same initial to the same final states and never about some states the light field might have in between. Attributing distinguishability to the states of the light fields in between is just misleading and even hiding the important physics.

We must conclude, that when the +45degree polarizer is inserted to produce the fringe pattern, it is absorbing a data set that is the difference between (b) and the fringe pattern. That data set perfectly replicates the anti-fringe pattern. Therefore the absorbing +45degree polarizer is displaying interference in the anti-fringe pattern.

Ehm...isn't that trivial? Of course both of the beams resulting in the fringe and the anti-fringe pattern display interference. You can easily see that using a polarizing beam splitter (at the correct angle) instead.