Double-slit experiment with momentum entangled pair of photons

[Christian Thom]

TL;DR

Naively one could figure that making a double slit experiment with a photon coming from an entangled pair could determine which slit the photon is coming through by looking at its entangled twin. From some papers, it appears in my understanding that no interference pattern is observed, even if the twin is not measured.

In Kaur, M., Singh, M. Quantum double-double-slit experiment with momentum entangled photons. Sci Rep 10, 11427 (2020). https://doi.org/10.1038/s41598-020-68181-1 and in C. K. Hong and T. G. Noh, "Two-photon double-slit interference experiment," J. Opt. Soc. Am. B 15, 1192-1197 (1998) it is shown that in this situation, no fringes are visible. Have I well understood ? What kind of photon is that ?
Another paper seems to show different conclusion, but it describes only a thought experiment : Entangled Photon Pairs and Young’s Experiment Lewis Nash Marietta, GA, USA. DOI: 10.4236/jqis.2021.114011, so it is maybe less convincing...

 

[StevieTNZ]

Have I well understood ? What kind of photon is that ?

From what I've read in the literature, yes. And it would be a normal photon.

I believe in 'Sneaking a Look at God's Cards' (https://press.princeton.edu/books/paperback/9780691130378/sneaking-a-look-at-gods-cards), the author discusses this experimental setup. Unfortunately I am traveling so don't have the book at hand otherwise I would indicate which specific pages to check in that book.

With regards to the alternative paper, you'll need to check whether the paper has been peer reviewed to see if it has any standing.

 

[Nugatory]

TL;DR Summary: Naively one could figure that making a double slit experiment with a photon coming from an entangled pair could determine which slit the photon is coming through by looking at its entangled twin.

This is Kim's delayed-choice experiment, is it not?
https://arxiv.org/abs/quant-ph/9903047

 

[Christian Thom]

From what I've read in the literature, yes. And it would be a normal photon.

I believe in 'Sneaking a Look at God's Cards' (https://press.princeton.edu/books/paperback/9780691130378/sneaking-a-look-at-gods-cards), the author discusses this experimental setup. Unfortunately I am traveling so don't have the book at hand otherwise I would indicate which specific pages to check in that book.

With regards to the alternative paper, you'll need to check whether the paper has been peer reviewed to see if it has any standing.

Thank you.
If it is a normal photon, why can't it interfere with itself ?

 

[PeroK]

Thank you.
If it is a normal photon, why can't it interfere with itself ?

It's difficult to know where to start with a question like that!

The system comprises an entangled pair of photons. Not a single photon.

 

[Christian Thom]

This is Kim's delayed-choice experiment, is it not?
https://arxiv.org/abs/quant-ph/9903047

Thank you.
It is certainly a similar experiment, but it lacks the clarity brought by the momentum entanglement, which can correlate directly to the slits position.

 

[Cthugha]

Thank you.
If it is a normal photon, why can't it interfere with itself ?

The double slit is a momentum measurement. You get a different result for each different value of particle momentum in the plane of the slits. Or putting it more simply: A light field arriving at an angle will show a shifted interference pattern compared to a light field arriving at normal incidence. Accordingly, you will see different interference patterns when putting a light sourceat different positions. Also, as a consequence of that you will see no interference pattern (or more precisely a sum over many different ones) when you have a spatially large light source. You can try that your self. A standard light source will show an interference pattern in a cheap home-made double slit if you place it far away from the double slit, but it will not show an interference pattern when you place it in front of the slit: the range of angles reaching the slit in these two scenarios differs significantly.

How is this related to momentum entangled photons? When you have momentum-entangled photons, they will necessarily have a momentum distribution. If you always get the same momentum on one side, you can only get classical correlations which do not violate bell inequalities. Here, the same reasoning as above applies: You have a wide range of momenta, so the bare pattern you will see behind the double slit is just a sum of many different interference patterns that sum up to no interference at all.

Does this mean that this light source can show no interference? No, of course you can just perform momentum filtering by placing the light source far away from the double slit, placing a pinhole or doing something similar. However, if you want to reach full visibility of the interference pattern, the subset of photons that makes it through this filter will not have the necessary width of the momentum distribution to violate Bell inequalities anymore. This subset will not show entanglement. Alternatively, you can measure the momentum of the entangled partners, find out about the momentum of each photon at the double slit and create histograms where you can plot the resulting patterns for each individual momentum. These will be interference patterns, but they show up only in coincidence counting because you need the information from the partner photon.

A more formal explanation why you can have either single-photon interference or entanglement has been given here:
https://arxiv.org/abs/quant-ph/0112065Btw: The scenario you imagine is more or less similar to this double slit quantum eraser setup:
https://arxiv.org/abs/quant-ph/0106078

 

[Christian Thom]

Thank you for this thorough explanation that I have now to process !