Delayed choice quantum eraser setup with no beam splitter

[Athraxin]

TL;DR Summary

Delayed choice with no beam splitter

Hello Dear Physicists,

I know this question probably discussed many times before. But I need a clear answer about this setup in case there is no beam splitter.

What is gonna happen in this situation? My classical intuitions say I will see a correlated interference pattern on both screens(or detectors) but in reality I have no idea.

My Regards.

 

[Nugatory]

What do you mean by “correlated” interference pattern?

 

[vanhees71]

It's very unclear, which experiment you describe. Where is the picture taken from?

 

[Athraxin]

What do you mean by “correlated” interference pattern?

which means they are the same interference pattern. In other setups, we can see difference interference patterns like destructive or constructive etc.

 

[Athraxin]

It's very unclear, which experiment you describe. Where is the picture taken from?

It is very clear actually but I've just changed some parameters, I've removed all detectors except D0 and beam splitters. I've put in a lens for idler photons to interfere with each other but I clearly have no idea what will happen.

 

[vanhees71]

It is very clear actually but I've just changed some parameters, I've removed all detectors except D0 and beam splitters. I've put in a lens for idler photons to interfere with each other but I clearly have no idea what will happen.

Please give the description of the original setup and then describe what you changed. It's impossible to answer your question without knowing the details. I could guess, but that's dangerous, because the things can get pretty subtle.

 

[Athraxin]

Please give the description of the original setup and then describe what you changed. It's impossible to answer your question without knowing the details. I could guess, but that's dangerous, because the things can get pretty subtle.

This is the original setup published by Yoon-Ho Kim.

[1] Kim, Y.-H., Yu, R., Kulik, S. P. and Shih, Y. Delayed “choice” quantum eraser. Phys. Rev. Lett. 84, 1-5 (2000).
[2] Fankhauser, Johannes (2019). "Taming the Delayed Choice Quantum Eraser". Quanta. 8: 44–56.

These are the results on dedectors.

[3] https://en.wikipedia.org/wiki/Delay...le:KimDelayedChoiceQuantumEraserGraphsSVG.svg

In my new setup,
I've removed D2,D3,D4,BeamSplitters,Mirros. I've put in a lens instead prism for idler photons to interfere with each other like signal photons, set D1 as a screen for the idlers.

 

[vanhees71]

I see. Then, if you simplify the setup as you do, of course no interference patterns occur (neither on Screen 0 nor on Screen 1). That's, because the photons that interfere on Screen 0 and Screen 1 are from uncorrelated sources since the preparation of entangled photon pairs through parametric down conversion is an entirely spontaneous, i.e., completely random process. So the two entangled pairs used in the experiment are completely uncorrelated with each other, i.e., you superimpose two completely incoherent light sources at Screen 0.

That's also confirmed, BTW, by the original setup: If you take all 4 subsensembles together, i.e., add the 4 plots for $R_{0j}$, which represents all photons detected with $D_0$, you'll find no two-slit interference pattern.

The intriguing thing with the entangled photons is that you can by choosing the 4 subensembles, decide whether you look at situations, where you know from which of the two slits the original photons came. E.g., if you take the ensemble, where one of the "blue" photons which is registered by $D_3$, then you know for sure this photon was parametric-downconverted from a photon which came from the lower slit ("which way information"). This in turn ensures that the photon state for the photon registered at $D_0$ is due to an incoherent mixing of two independent photon sources, and thus there is no double-slit interference pattern (plot for $R_{03}$). Interestingly, however, theres the single-slit interference pattern (i.e., the sine-like curve shown in this plot). That's because the photons being produced from the photon coming through the upper slit are a coherent source for themselves and thus show the single-slit interference pattern and so are the photons being down-converted from the photons coming through the lower slit, showing the same single-slit interference pattern. Their incoherent addition thus shows the single-slit interference pattern.

The same holds true if you use the subsensemble where one of the "red photons" was registered by detector $D_4$, because then this photon for sure originated from one of the entangled photons created by parametric downconversion of a photon that came through the upper slit. Correspondingly, you know that the photon state for the photon registered at $D_0$ for this subensemble is described by an incoherent mixing of two independent photon sources and thus there's no interference pattern (or rather only the single-slit interference pattern).

If you look at the ensembles prepared by looking only at photons where $D_1$ registered a photon, the situation is very different: Now you don't know, whether this photon orinated from one of the photon pairs which was created by the upper or the lower slit, i.e., for this ensemble there's no which-way information. Due to the entanglement of the pairs (12) and (34) now the photon state at detector $D_0$ is a coherent superposition of indistinguishable photons, and thus an interference pattern is observed (see the plot for $R_{01}$). The same argumentation holds for the ensemble, where one of the photons has been registered with detector $D_2$. You have again an interference pattern, as seen in $R_{02}$, but it's anticorrelated to the one of $R_{01}$, i.e., where you have constructive interference in $R_{01}$ you have destructive interference in $R_{02}$ and vice versa. Adding up $R_{01}$ and $R_{02}$ thus doesn't show any interference pattern (or, as shown in the original paper, the single-slit interference pattern).

Now all the manipulations of the equipment you took out of the picture do not causally influence the photons registered at $D_0$, and thus you can expect that in your experiment you don't see a double-slit interference pattern. That is, however, also explained independently as written in the first paragraph.

The paper by Kim et al is really very nicely readable:

https://arxiv.org/abs/quant-ph/9903047

Also ref. [14] therein is a very detailed explanation of the theory of parametric downconversion:

https://doi.org/10.1103/PhysRevA.50.5122

 

[Athraxin]

I see. Then, if you simplify the setup as you do, of course no interference patterns occur (neither on Screen 0 nor on Screen 1). That's, because the photons that interfere on Screen 0 and Screen 1 are from uncorrelated sources since the preparation of entangled photon pairs through parametric down conversion is an entirely spontaneous, i.e., completely random process. So the two entangled pairs used in the experiment are completely uncorrelated with each other, i.e., you superimpose two completely incoherent light sources at Screen 0.

That's also confirmed, BTW, by the original setup: If you take all 4 subsensembles together, i.e., add the 4 plots for $R_{0j}$, which represents all photons detected with $D_0$, you'll find no two-slit interference pattern.

The intriguing thing with the entangled photons is that you can by choosing the 4 subensembles, decide whether you look at situations, where you know from which of the two slits the original photons came. E.g., if you take the ensemble, where one of the "blue" photons which is registered by $D_3$, then you know for sure this photon was parametric-downconverted from a photon which came from the lower slit ("which way information"). This in turn ensures that the photon state for the photon registered at $D_0$ is due to an incoherent mixing of two independent photon sources, and thus there is no double-slit interference pattern (plot for $R_{03}$). Interestingly, however, theres the single-slit interference pattern (i.e., the sine-like curve shown in this plot). That's because the photons being produced from the photon coming through the upper slit are a coherent source for themselves and thus show the single-slit interference pattern and so are the photons being down-converted from the photons coming through the lower slit, showing the same single-slit interference pattern. Their incoherent addition thus shows the single-slit interference pattern.

The same holds true if you use the subsensemble where one of the "red photons" was registered by detector $D_4$, because then this photon for sure originated from one of the entangled photons created by parametric downconversion of a photon that came through the upper slit. Correspondingly, you know that the photon state for the photon registered at $D_0$ for this subensemble is described by an incoherent mixing of two independent photon sources and thus there's no interference pattern (or rather only the single-slit interference pattern).

If you look at the ensembles prepared by looking only at photons where $D_1$ registered a photon, the situation is very different: Now you don't know, whether this photon orinated from one of the photon pairs which was created by the upper or the lower slit, i.e., for this ensemble there's no which-way information. Due to the entanglement of the pairs (12) and (34) now the photon state at detector $D_0$ is a coherent superposition of indistinguishable photons, and thus an interference pattern is observed (see the plot for $R_{01}$). The same argumentation holds for the ensemble, where one of the photons has been registered with detector $D_2$. You have again an interference pattern, as seen in $R_{02}$, but it's anticorrelated to the one of $R_{01}$, i.e., where you have constructive interference in $R_{01}$ you have destructive interference in $R_{02}$ and vice versa. Adding up $R_{01}$ and $R_{02}$ thus doesn't show any interference pattern (or, as shown in the original paper, the single-slit interference pattern).

Now all the manipulations of the equipment you took out of the picture do not causally influence the photons registered at $D_0$, and thus you can expect that in your experiment you don't see a double-slit interference pattern. That is, however, also explained independently as written in the first paragraph.

The paper by Kim et al is really very nicely readable:

https://arxiv.org/abs/quant-ph/9903047

Also ref. [14] therein is a very detailed explanation of the theory of parametric downconversion:

https://doi.org/10.1103/PhysRevA.50.5122

So you mean that I'm going to see a single-slit interference pattern on both dedectors in my new setup like in Kim's setup for D3 or D4?

 

[vanhees71]

I guess, you rather see a flat line as in Fig. 4 in the published version of the paper. I attach it here, because the paper is not open access.

 

[Athraxin]

I guess, you rather see a flat line as in Fig. 4 in the published version of the paper. I attach it here, because the paper is not open access.

View attachment 330474

I guess, you rather see a flat line as in Fig. 4 in the published version of the paper. I attach it here, because the paper is not open access.

View attachment 330474

Thanks for sharing this result with me sir. However, Dr. Jeffrey H. Boyd has said the opposite in his youtube video.

- this link must redirects you to the exact time of the video.

He says we will see an interference pattern. Right now, I'm really confused. I believe you are right sir but at least that guy in the video needs to be corrected otherwise people like me may misinterpret the results.

 

[vanhees71]

Hm, but the experiment shows a flat line. If you just look at all photons registered by $D_0$ you see this flat line in the original setup. Now, when you take out the setup as you wrote in the OP, you still nothing changed for what's observed with $D_0$. In this setup you just register photons from two completely uncorrelated sources, and the photons are thus incoherent and don't interfere. That's why you don't even see a singel-slit interference pattern, let alone a double-slit intereference pattern. I'd not rely on arbitrary Youtube videos!

 

[Athraxin]

Hm, but the experiment shows a flat line. If you just look at all photons registered by $D_0$ you see this flat line in the original setup. Now, when you take out the setup as you wrote in the OP, you still nothing changed for what's observed with $D_0$. In this setup you just register photons from two completely uncorrelated sources, and the photons are thus incoherent and don't interfere. That's why you don't even see a singel-slit interference pattern, let alone a double-slit intereference pattern. I'd not rely on arbitrary Youtube videos!

I agree with you sir, I think published results must be more accurate to rely on. Anyway I wanna thank you for your answers.

But I'm still not able to comprehend why they are coming from uncorrelated sources, there is only one source for pump photons in the experiment, after splitting pump photons into twin photons (with the assistance of SPDC) their frequencies and wavelengths still should be the same except their phases (after double slit operation) and also we know that interference pattern only happens if there is an out of phase situation in that case we should still see an interference pattern.
Am I missing something here?
Because we see a line in D0 not patterns in the real experiment as you showed. Quantum world is really weird If you ask me.

If they are uncorrelated after SPDC that means this crystal doesn't split photons into entangled photons only random and different photons.

I guess I'm about to get downconverted by quantum physics itself.

 

[vanhees71]

The point is that indeed the laser illuminating the double slit is a coherent source, i.e., you'd get nice double-slit interference fringes just using this double slit.

Now the photons coming from the slits are parametrically downconverted in the BBO, and you produce two pairs of entangled photons. In each pair the down-converted photons are also coherent, but photons from different downconversion events are completely uncorrelated, because the downconversion is a spontaneous process. Thus photons from a different pair are not in a fixed phase relation. That's why you see neither double-slit nor single-slit interference patterns when looking at all photons registered at $D_0$. That you get single-slit and double-slit interference patterns when using the apparatus of the original experiment I've tried to explain in my postings above, and it's also well described in the Wikipedia article. See also the paper, which is not too hard to understand.

Maybe also the slides from my habilitation talk may help. The English version is here:

https://itp.uni-frankfurt.de/~hees/publ/habil-coll-talk-en.pdf

It's however discussing a different delayed-choice quantum-eraser experiment, which is maybe a bit easier to understand. The principles are, however, the same.

 

[Athraxin]

The point is that indeed the laser illuminating the double slit is a coherent source, i.e., you'd get nice double-slit interference fringes just using this double slit.

Now the photons coming from the slits are parametrically downconverted in the BBO, and you produce two pairs of entangled photons. In each pair the down-converted photons are also coherent, but photons from different downconversion events are completely uncorrelated, because the downconversion is a spontaneous process. Thus photons from a different pair are not in a fixed phase relation. That's why you see neither double-slit nor single-slit interference patterns when looking at all photons registered at $D_0$. That you get single-slit and double-slit interference patterns when using the apparatus of the original experiment I've tried to explain in my postings above, and it's also well described in the Wikipedia article. See also the paper, which is not too hard to understand.

Maybe also the slides from my habilitation talk may help. The English version is here:

https://itp.uni-frankfurt.de/~hees/publ/habil-coll-talk-en.pdf

It's however discussing a different delayed-choice quantum-eraser experiment, which is maybe a bit easier to understand. The principles are, however, the same.

I suppose I got it now. It seems like we splitting photons in the real experiment but in reality we actually get random entangled photons from slits without knowing other random entangled photons coming after them (in phase or out of phase). That's why we can't get an interference pattern because there is no other photon to interfere for each photon comes to dedector due to uncorrelated relation. All mystery suddenly gone now. I'm really lucky to come across you on this thread sir. Have a nice day.