Delayed choice quantum eraser experiment

[Jayjay]

So, in the delayed choice experiment as far as I've understood from numerous youtube videos I've watched, you take the basic double slit experiment, but add prisms (?) that split the photons in two entangled pairs. One photon in the pair goes to the screen, another either is or isn't checked by a detector that tells which slit it went through.

Now the part I don't get is this: when in this experiment does the inteference pattern from the double slit experiment disappear?

Is it when you split the photons, regardless of what you do with them afterwards? What if the other pair also goes to a screen, does it show the same interference pattern or not?

Is it when you add the detectors to the system?

Or is it when you add the quantum eraser part?

 

[phands]

The YouTube videos are generally poor.

The generally accepted view is that it's a superposition of states situation, and there's no time paradox. Experiments so far confirm this.

 

[Jayjay]

The YouTube videos are generally poor.

The generally accepted view is that it's a superposition of states situation, and there's no time paradox. Experiments so far confirm this.

Yes I get that there is no time paradox. But I'm not quite sure what you see on the screen at each phase if you start with double slit experiment (interference pattern) and end with the full quantum eraser experiment (a blotch that has "hidden" interference patterns). So does the interference pattern disappea as soon as one splits the photons, or is it crucial to have those additional detectors or the eraser? I'm assuming the former, because if not, you would have a time paradox in your hands.

 

[barbos]

Interference pattern disappears when you detect through which hole photon went.

 

[Jayjay]

Interference pattern disappears when you detect through which hole photon went.

So if you split the photons, but have identical screens on both sides, and no detectors for which way they went, do you see two interference patterns, or just blotches? That's what I'm not quite getting.

 

[steve_bank]

So, in the delayed choice experiment as far as I've understood from numerous youtube videos I've watched, you take the basic double slit experiment, but add prisms (?) that split the photons in two entangled pairs. One photon in the pair goes to the screen, another either is or isn't checked by a detector that tells which slit it went through.

Now the part I don't get is this: when in this experiment does the inteference pattern from the double slit experiment disappear?

Is it when you split the photons, regardless of what you do with them afterwards? What if the other pair also goes to a screen, does it show the same interference pattern or not?

Is it when you add the detectors to the system?

Or is it when you add the quantum eraser part?

Propagating EM waves are both a wave and a particle in them model. As a wave it is subject to constructive and destructive interferemce .A prisim amd cancelation remind me of interferomters.

Can you link to an optical diagram of the setup?

See the diagrams.

https://en.wikipedia.org/wiki/Interferometry

Wavefront splitting versus amplitude splitting
A wavefront splitting interferometer divides a light wavefront emerging from a point or a narrow slit (i.e. spatially coherent light) and, after allowing the two parts of the wavefront to travel through different paths, allows them to recombine.[6] Fig. 5 illustrates Young's interference experiment and Lloyd's mirror. Other examples of wavefront splitting interferometer include the Fresnel biprism, the Billet Bi-Lens, and the Rayleigh interferometer.[7]....An amplitude splitting interferometer uses a partial reflector to divide the amplitude of the incident wave into separate beams which are separated and recombined. Fig. 6 illustrates the Fizeau, Mach–Zehnder and Fabry–Pérot interferometers. Other examples of amplitude splitting interferometer include the Michelson, Twyman–Green, Laser Unequal Path, and Linnik interferometer.[14]

 

[Jayjay]

So, in the delayed choice experiment as far as I've understood from numerous youtube videos I've watched, you take the basic double slit experiment, but add prisms (?) that split the photons in two entangled pairs. One photon in the pair goes to the screen, another either is or isn't checked by a detector that tells which slit it went through.

Now the part I don't get is this: when in this experiment does the inteference pattern from the double slit experiment disappear?

Is it when you split the photons, regardless of what you do with them afterwards? What if the other pair also goes to a screen, does it show the same interference pattern or not?

Is it when you add the detectors to the system?

Or is it when you add the quantum eraser part?

Propagating EM waves are both a wave and a particle in them model. As a wave it is subject to constructive and destructive interferemce .A prisim amd cancelation remind me of interferomters.

Can you link to an optical diagram of the setup?

If this is the "complete" quantum eraser experiment:



Then what I'm wondering is what happens if there is a splitter after the slits, but instead of coincidence detectors just two screens like this:



And why?

(In all fairness, I nicked these off another forum where someone else asked exactly the same question. But I'm still reading and trying to understand the answer so I'm sharing them here for your enjoyment.)

 

[steve_bank]

Thanks, a picture is worth a thousand words. It will take me a while to think through it. If you would save me the trouble of looking it up, what is the point of the experiment.

 

[barbos]

Interference pattern disappears when you detect through which hole photon went.

So if you split the photons, but have identical screens on both sides, and no detectors for which way they went, do you see two interference patterns, or just blotches? That's what I'm not quite getting.

Yes, and that's what you should be getting.

 

[Jayjay]

Interference pattern disappears when you detect through which hole photon went.

So if you split the photons, but have identical screens on both sides, and no detectors for which way they went, do you see two interference patterns, or just blotches? That's what I'm not quite getting.

Yes, and that's what you should be getting.

A blotch you mean? Because nothing else makes sense. Anyway I'm now getting the hang of it, will post my findings soon and you can rip them apart then...

 

[Jayjay]

I played around a bit with Quirk (http://algassert.com/quirk), a simple quantum computer simulator. With some help from this article, I think I finally get what's happening.

To simulate a double slit experiment / interference I did this:



So basically, there is first a Hadamard gate that's the "slit", i.e. it generates a superposition that has 50/50 chance of being one or zero (up or down, or whatever). Then I do a pi/8 phase shift, which puts the two states in different phase. And finally, another Hadamard gate that shows interference, simulating the waves in the double slit interfering with each other.

For clarity, I left out actual measurements and just used the simulator's own diagnostics to show the probability densities in the green boxes. Of course in reality it's impossible to peek a superposition like this, but for purposes of explaining just imagine that there is one measurement at the end and the other green boxes are just for show, and that we run the circuit enough times to see different probabilities. The three dots are just spacers so that the pictures align properly.

So, in the above case, there is interference. But if we add another entangled cubit (i.e. the prism in the quantum eraser experiment that creates another entangled photon) like this:



The interference pattern disappears. That black dot and the cross is a CNOT gate: if the bit in the line where the dot is is ON, then the value in the line with the cross is flipped. This is basically the picture with nothing but two screens in the double slit experiment. They both show just blotches and no interference pattern because we've extracted the "which-way" information from the double slit and even if we don't use it, that counts as an observation!

Next step:



Here we erase the information by unentangling (is there a better term?) the two cubits with another CNOT gate. Interference pattern re-appears. No time travel or faster than light communication, because we have to do the unentangling before any measurement. If we were to measure the top cubit then the entanglement would be lost.

But there is also another way to get the interference pattern: the delayed choice and using the measurement info from the other cubit/photon.



In this case we measure the cubits. The original pattern on the screen is a blotch, no interference pattern. But if we condition the measurement on the which-way info, then we can split it into two interference patterns. Pretty neat. In this case the cubits or photons could be lightyears apart, but we need to transmit the information of one measurement to the next to extract the pattern.

So, I hope I'm on the right track here. Next step is to try run this on an actual quantum computer (IBM cloud) but that'll have to wait until another day.

 

[barbos]

Cool, did you get the answer to your interference/blotch question using this simulator?

These increasingly more and more convoluted experiments don't really bring anything new compared with original double-slit experiment.

 

[Jayjay]

Cool, did you get the answer to your interference/blotch question using this simulator?

These increasingly more and more convoluted experiments don't really bring anything new compared with original double-slit experiment.

Basically what I didn't understand was what counts as an "observation" that collapses the wave. So in this scenario:

View attachment 16634

The "collapse" is due to the prism. When another entangled photon is created, then you get a blotch instead of an interference pattern. What my experiments, while a bit more convoluted, did show is that if the entanglement is "unentangled" without measuring the which-way information, then interference pattern can be seen again. But alternatively, one can measure the which way info, and use that to recreate the interference pattern from the "blotch" as in the delayed choice experiment. But even then the information has to move from one point in spacetime to another, so sadly no time machines or faster than light communication...

Of course, this is probably obvious to physicists, I'm simply trying to wrap my own head around it.

 

[barbos]

These illustrations are pretty useless for someone who is not doing these experiments. You should not even be trying to decode them.
And they are truly horrible. I mean lens and photon pass part is simply wrong.

Basically what I didn't understand was what counts as an "observation" that collapses the wave. So in this scenario:

That's essentially a million dollars question. But there is a technical answer. Measurement/collapse is interaction between wavefunction and macroscopic apparatus which basically cause entropy to jump. In practice it's when photon hits the screen and cause cascade of interactions which end up with large macroscopic effect like counter incrementing.
As long as such thing is not happening and entropy stays the same you have pure quantum mechanical wavefunction evolution described by Schroedinger equation. So what it means is, until collapse happened it stays uncollapsed and all these manipulations in order to determine which way or whatever are utterly meaningless. "Decision" to "behave" as a particle or wave happens at the time of the collapse.

 

[Jayjay]

These illustrations are pretty useless for someone who is not doing these experiments. You should not even be trying to decode them.
And they are truly horrible. I mean lens and photon pass part is simply wrong.

What do you mean? The picture is modified (not by me but that was exactly what I was looking for) from actual setup described here:

 Delayed_choice_quantum_eraser

If you were referring to the quantum computer diagrams, sure, they don't match 1-1 to the double slit experiment, they just show the same basic principle. And the notation is widely used (except by "pi/8" I meant the T-gate, my ignorance).

Basically what I didn't understand was what counts as an "observation" that collapses the wave. So in this scenario:

That's essentially a million dollars question. But there is a technical answer. Measurement/collapse is interaction between wavefunction and macroscopic apparatus which basically cause entropy to jump. In practice it's when photon hits the screen and cause cascade of interactions which end up with large macroscopic effect like counter incrementing.
As long as such thing is not happening and entropy stays the same you have pure quantum mechanical wavefunction evolution described by Schroedinger equation. So what it means is, until collapse happened it stays uncollapsed and all these manipulations in order to determine which way or whatever are utterly meaningless. "Decision" to "behave" as a particle or wave happens at the time of the collapse.

So how do you explain the results, that you get two blotches instead of two interference patterns if you add that prism after the double slit?

 

[barbos]

What do you mean? The picture is modified (not by me but that was exactly what I was looking for) from actual setup described here:

 Delayed_choice_quantum_eraser

Yes, I mean that. It's horrible and wrong and does not describe well what is happening in the experiment.
One has to go and read description and even then wikipedia is often written by people who don't understand the problem well enough.

If you were referring to the quantum computer diagrams, sure, they don't match 1-1 to the double slit experiment, they just show the same basic principle. And the notation is widely used (except by "pi/8" I meant the T-gate, my ignorance).

That's essentially a million dollars question. But there is a technical answer. Measurement/collapse is interaction between wavefunction and macroscopic apparatus which basically cause entropy to jump. In practice it's when photon hits the screen and cause cascade of interactions which end up with large macroscopic effect like counter incrementing.
As long as such thing is not happening and entropy stays the same you have pure quantum mechanical wavefunction evolution described by Schroedinger equation. So what it means is, until collapse happened it stays uncollapsed and all these manipulations in order to determine which way or whatever are utterly meaningless. "Decision" to "behave" as a particle or wave happens at the time of the collapse.

So how do you explain the results, that you get two blotches instead of two interference patterns if you add that prism after the double slit?

That one easy, with prism there is no interference
You don't even need quantum mechanics, you can simply treat the problem as an classical electrodynamics/optics.
As I said original double slit experiment is all you really need.