# Double-slit experiment and watching the electrons

1. Dec 9, 2013

### forcefield

double-slit experiment and "watching the electrons"

I'm trying to build a picture of what is happening in the double-hole experiment when you are "watching the electrons" (http://feynmanlectures.caltech.edu/III_01.html#Ch1-S6). It's mostly clear to me but I do have some questions: if you use a strong light source at the holes (so that you can see every electron at the holes), can you in that case use a long wavelength for the light source so that when you see a flash of light you can't tell which hole is closer to the flash of light ? If you can, is there interference in that case ?

(My hypothesis is that you can use such a long wavelength also in the case of strong light source and then there is no interference.)

2. Dec 9, 2013

### Mentz114

If there is no interaction between your probing light and the electrons, you can get no information and the interference persists. If there is an interaction, the interference will not be present.

3. Dec 10, 2013

### naima

Suppose that you have two receptors behind the slits and near them. Light interact with electrons and one of the receptors clicks.
Now close the right slit and send electrons to the left slit. The clicks will depend on the wavelength of light.
There is an amplitude "a" for a left clik and an amplitude "b" to a right click. (you have the same a and b by symmetry when you exchange the slits.
If a = 1 and b = 0 you will have a perfect which path information.
When two slits are open the probability for the electron to hit the screen at x is:
|aL(x) + b R(x)|² + |bL(x) + aR(x)|²
if a = 1 and b = 0 the probability is |L(x)|² + |R(x)|²
if a = b (with |a|² + |b|² = 1) you get
|L(x) + R(x)|²
So you see that here photons always interact but the result is not a yes/no interference
You have intermediate patterns depending on the quality of the which path information (the a and b) you get.

4. Dec 11, 2013

### forcefield

So I have two answers that seem to disagree. Mentz114's answer was in line with my expectations whereas I can't follow naima's reasoning. Can we build a consensus here ?

Also I'd like to know if this experiment has been done with strong light source of long wavelength and what was the result ?

5. Dec 12, 2013

### naima

I found the calculation in an old book of L Tarassov (1980)
Surprisingly i did not see it in another book nor online.

Last edited: Dec 12, 2013
6. Dec 13, 2013

### naima

We can write P(x) = |L(x)|² + |R(x)|² + k (L(x) R*(x) + R(x) L*(x)) where k (= ab* +ba*) is a real number which can be chosen between 0 and 1.

Is there an experiment (in any quantic domain) where one can vary a parameter of the setup so that the intensity of interference vary?

7. Dec 13, 2013

### Claude Bile

Both Mentz114 and Naima's explanations are compatible.

Mentz114 explains in "photon-by-photon" and "electron-by-electron" terms. If photon interacts with electron; coherence between the two slits is lost and interference is lost...on the other hand if the photon does not interact, the interference persists. Clearly, on average, this is a situation where there is partial coherence - which Naima outlines in more explicit terms.

Claude.

8. Dec 13, 2013

### naima

I do not believe that this is the correct way to see what happens.
We have not a mixture of interacting electrons and of not interacting ones.
|a|² is not the probability of an interaction giving the which-path information:
We would have P(x) = |a|² (|L(x)|² + |R(x)|²) + |b|² |L(x) + R(x)|²
This is not the formula tarasov gives.
We have a source of photons between the slits.
Remember that when the right slit is closed electrons pass through the left slit , then |b|² is the probability that the right photon receptor clicks. Giving you a wrong which-path information.
You may have interference with always interacting electrons and photons but giving you an unreliable information.

9. Dec 13, 2013

### naima

I am confused.

P(x) = |a|² (|L(x)|² + |R(x)|²) + |b|² |L(x) + R(x)|² =
(|a|²+ |b|²) (|L(x)|² + |R(x)|²) + |b|² (L(x)R*(x) + L*(x)R(x))
As |a|² + |b|² = 1 we get something like Tarasov formula.
Can we say that an unreliable information interaction is just like no interaction in this case?

10. Dec 13, 2013

### EskWIRED

I think (hope?) that there exist experiments in which low energy photons have been used to detect "which-slit" information. I'd love to read the papers.

I'd even more love to see a similar experiment using massive projectiles through the slits - buckyballs perhaps - in conjunction with RF detection of the path information. I am wondering whether such methods would yield BOTH a proportion of interference patterns and "one-slit" patterns, depending upon the nature and magnitude of the individual detections. I would be fascinated if the results varied depending upon the frequency used, especially if the results shifted rapidly from one state to another as the frequency is swept.

11. Dec 13, 2013

### Cthugha

Experiments similar to that have been done as early as 1988. See Greenberger, D. M.; Yasin, A., "Simultaneous wave and particle knowledge in a neutron interferometer". Phys. Lett. A 128 (8): 391–394 (1988).

Unfortunately I am not aware of any free copy. It turns out that you get a duality relation between which-way information and interference pattern visibility called Englert-Greenberger duality relation. See the Wikipedia entry for the fundamental journal references: http://en.wikipedia.org/wiki/Englert–Greenberger_duality_relation.

12. Dec 13, 2013

### 1832vin

try frensel lens

13. Dec 14, 2013

### naima

I found another easy experiment.
photons pass through two slits. a polarizer stands behind each slit.
When the polarizers are parallel (sin² = 0) there is no which-path information and fringes are well seen.
we can rotate one of the polarizer. fringes progressively disappear.
Here photons allways pass and interact through the polarizers. So fringes are not a question of yes/no interaction.

14. Dec 15, 2013

### forcefield

I'm not convinced in the case of this thread where we are sending electrons through the slits.

15. Dec 16, 2013

### Cthugha

By using a double slit and a reasonably narrow photon or electron source you prepare a scenario with reasonably well defined relative phases. The question of whether you see fringes at the detection screen or not depends on whether this phase gets messed up along the way. The extreme cases of no phase distortion and complete phase randomization correspond to perfect and no fringes, but there are always ways to distort the phase just a bit or inside a narrow range of values which just gives you reduced fringe visibility (and of course little which-way information).

16. Dec 16, 2013

### naima

Suppose that the screen is shuttered when photons are not detected by the detectors near the screen. we will have a pattern due to the only electrons that are observed. they all interacted with photons.
Now let the photons wavelength greater than the distance between the slits. we cannot see details smaller than that distance. so we have no which path information.
In this case all electrons interacted but we have interference.

17. Dec 16, 2013

### forcefield

Does that mean that if you prepare the electrons with complete phase randomization, you get no interference ?

Is that because your experiment is different from the one explained by Feynman ?

18. Dec 16, 2013

### naima

Did feynman say something about watching the electrons?

19. Dec 16, 2013

### Cthugha

No. What matters is the phase difference you get from the two paths via the two slits. Even if you prepare the electrons with random initial phase the phase difference between the paths via the two slits is independent of the initial phase.

What you can do is randomize this phase difference. With light the easiest way to achieve that is using a large light source and place it directly in front of rather broad slits. If the possible paths from all the positions on the surface of the light source to all the possible positions at one slit differ by way more than one wavelength of the light you will not get an interference pattern as the relative phases get randomized. That works for electrons, too, of course.

20. Dec 16, 2013

### forcefield

Check the link I posted in post #1.