# Single photon and the double slit

1. Sep 3, 2008

### IlyaZ

If you send a photon towards some wall it will bounce back (or in some cases be absorbed), why don't the photons bounce back if you shoot photons at the middle of the double slit experiment? Do the photons have to be released at "random", and not in the middle? How's the experiment performed?

And how do we know that it isn't the slit wall that generates the pattern?

2. Sep 6, 2008

### andrewm

What if you used a beam splitter that divided the laser 50-50 into each slit?

3. Sep 6, 2008

### DrChinese

"Slit wall"? There is the double slit, and the "wall" behind which is the target (may be film actually if the pattern is being built up a photon at a time). Are you referring to the physical shape/edge of the slit itself? If so, it is a factor but has nothing to do with the diffraction effect. (Because, if one slit is covered the diffraction pattern disappears.)

4. Sep 6, 2008

### f95toli

The "beamsize" has to be bigger than the two slits; if the beam is focused to a small spot between the slits the photon will be reflected/absorbed.
In real experiments they test this by first shining a laser on the two slits, if the optics is set up correctly the beam will hit both slits and the result is a "classical" diffraction pattern (in the sense that you do not need QM to explain the result). Once that is done the laser is replaced by the single photon source.

(I don't know much about practical quantum optics, but I actually attended a seminar where this exact question was discussed yesterday).

5. Sep 10, 2008

### IlyaZ

Sorry, my explanation of the "slit wall" wasn't very precise. I mean the space between the two gaps/slits.

If you perform the single photon experiment, how can the beam size be bigger than the "slit wall"?

The photon seems to go through both slits at the same time. I just can't imagine that one particle disappears and knows which way it (they) should go to go through the slits. I understand that this all can be "explained" in terms of probability, but hasn't the possibility that the single photon is absorbed by the "slit wall" and somehow split into two photons (or other unknown particles) that propagate to the edges of the material and thus to the position of the slits and out, been considered? Sure it sounds improbable and maybe even absurd, but the other explanations (or the lack of them by purpose) also do.

I also have another question; if you make a device that detects the position of this single photon it will naturally affect the experiment (heissenberg) (at least with all current knowledge and methods). But won't the diffraction pattern still show, as long as you don't view the detector results? (What if a computer prints the results, you don't look at them, but take a photo of the diffraction pattern (maybe once for each photon), and look at the detector results afterwards?).

If I get this right, the pattern will be gone if you know the path of the photons before they hit the film/wall? So one man's knowledge changes the probability just like in that famous TV-show problem? And by looking at the pattern an outsider can see if at least one mind knows (or doesn't know) which way the photon is going without asking these people if they know?

6. Sep 10, 2008

### DrChinese

Split into 2? Don't you think that would be pretty noticeable?

What difference would that make anyway? It wouldn't explain the interference pattern. There are plenty of ways to isolate things so you can see what is what. In every version, the only thing that matters is that the interference pattern disappears if you know which of the 2 slits the photon goes through.

In reality, this has been looked at many ways already. There are lots of similar effects in QM and they all follow QM predictions and violate classical analysis.

7. Sep 10, 2008

### peter0302

What is a "beam" except a wide spread of photons? Even if you send one photon at a time, the possible spread of that photon - i.e. the possible places it might "go" - has to be wider than the two slits. Obviously.

8. Sep 11, 2008

### IlyaZ

The Feynman "path integral formulation"-interpretation of the problem states that the photon takes every possible path. Letting the particle go through both slits at the same time creating interference maybe could be used to "explain" the pattern.

Alright, in that case I understand. My text-book explanations and pictures don't mention any spread, they just show a photon hitting the area between the slits perpendicularly.

9. Dec 26, 2008

### JCBoyce

I have a question about the interference pattern disappearing if you know which slit the photon goes through:

What if you measure the time taken from the generation of the photon, to the time when the detector receives it? For most spots on the screen, the path length through Slit 1 will be different than the path length through Slit 2.

Assume the experiment takes place in a vaccuum, and further that the path length from source to the point where the photon hits, through Slit 1, is 1 meter, and that the path length through Slit 2 is 2 meters.

If the photon arrives at the time light would take to travel 1 meter, the photon must have gone throught Slit 1. else it would have to travel faster than light to get there through Slit 2, an impossibility.

Equally, if the light arrives at the screen at some longer time than it takes light to travel 1 meter, it can't have gone through Slit 1, because light can't travel slower than c in a vaccuum (as far as I know).

But the collection of the information about how long the photon is in flight occurs after it has struck the detector, so it couldn't affect the interference pattern that builds up over many photons (could it??) It seems to me this is materially different than putting some kind of detector in the space between the source and screen to figure out which way the photon went.

I would guess that my argument above is faulty, although I do not see where. If it is faulty, can anyone tell me what the actual measured flight times of the photons are? are they equal to the 'short' time, the 'long' time, or some blended value?

10. Dec 26, 2008

### msumm21

So by measuring how long (DT) the photon travels, and knowing that it travels at fixed speed (C), we can determine how far (L) it traveled, and therefore through which slit it passed. A potential problem might be that there is some uncertainty in DT, which means you'll have some uncertainty in your computed value of L and, for this experiment to work, the distance between the two slits must be small enough that the time difference attributed to traveling through one slit or the other is within the aforementioned uncertainty. However, I do not know if what I'm saying is correct at all and I hope someone else more knowledgeable can let us know because it seems like a really good, interesting question.

11. Dec 26, 2008

### Staff: Mentor

I suggest that you calculate the difference between the two paths for a realistic double-slit experiment, and the time difference that this implies.

12. Dec 27, 2008

### msumm21

Even if the time difference associated with going through the two different slits is too small to measure with existing technology, do you know if it's theoretically impossible to distinguish the which-way information using DT? Is there some QM principle that outlaws this?

13. Dec 27, 2008

### JCBoyce

I am sure there are better or worse ways of setting up the physical experiment, depending on current technology etc, as jtbell indicates. But there is the fundamental problem I quoted from DrChinese, which is that knowing the photon's exact path is supposed to destroy the interference pattern. In my scenario, does the pattern get destroyed, or is the data I need to infer the photon path unobtainable? If so, in what way? What are the elapsed times of the photon's relative to c and the path lengths?

14. Dec 28, 2008

### DrChinese

Welcome to PhysicsForums, JCBoyce!

I am sure you know about the Heisenberg Uncertainty Principle. This prohibits us from knowing as much about the photon as you are trying to learn. Once you learn enough to determine absolutely "which slit", there will be no interference pattern at all.

Now, keep in mind that the interference pattern can be made to disappear completely or partially. If you loosen the precision which controls your "which slit" information, the pattern will gradually re-appear! Once you loosen the test for "which slit" sufficiently that you no longer have any knowledge about the path traversed, the pattern will be back to the normal double slit.

All of this consistent with the great HUP.

15. Dec 28, 2008

### JCBoyce

DrChinese: Based on your statements about HUP, you appear to suggest that I could not know the time that the photon left the source, the time that it hit the screen, and it's position on the screen, with sufficient precision to determine the photon flight time and hence its path length.

This suggests that if I had extremely precise time measurements for each photon, each flashpoint on the screen would grow larger in diameter, in order to 'prevent' me from knowing the position precisely. It's size would have to be such that the photon could have come through either slit and still landed within the flash's footprint on the screen. In fact, I guess that the energy of the photon would have to be spread out over the entire flash footprint. Is this what actually happens experimentally? Such flashpoint spreading would also degrade the 'dual slit' interference pattern, I imagine.

16. Dec 28, 2008

### Cthugha

No, the important point DrChinese raised here is:

As soon as you are able to know the photon flight time with sufficient precision to determine the path, the interference pattern will be gone. The HUP in this case corresponds to the complementarity of having which-path information and having interference fringe visibility.

From the experimental point of view it is indeed extremely difficult to determine the photon flight time. Most measurements will destroy the photon. Measurements of the recoil of the emitter are possible, but very complicated. Additionally photons emitted just a short time after each other (inside the coherence time) are indistinguishable, so you will not be able to determine, which photon arriving at the detector corresponds to which photon emitted, so even this method will only work for small mean photon numbers.

17. Dec 29, 2008

### JCBoyce

I appreciate that the experimental difficulties may be extraordinary at this time. It's the principles I am largely interested in.

Cthuga suggests that recoil measurements are possible, even though complicated. I believe all I need is recoil measuments at the source and at the detector to determine the time accurately. Perhaps the flash from the detector screen is recorded by another detector, or recorded directly, I don't know. But I don't see anything in principle that prevents sufficiently accurate time measurements.

To prevent the problem of indistinguishable photons, I imagine sending one photon at a time is possible to do, even if you have to ignore a large number of multiple photon emissions to get enough data.

The only other variable that I can see in this thought experiment is the location of the detector flash. If the flash location can be known precisely along with the photon flight time, then it appears to me that HUP is violated. If the required time measurements are possible in principle, then it seems to me HUP implies an indeterminate location. The only thing I can imagine that makes the location indeterminate is a larger flash footprint.

18. Dec 29, 2008

### DrChinese

You can make successive different (and non-commuting) measurements of a particle to any level of precision without violating the HUP. However, those measurements do NOT tell you information about the particle at a single point in time (i.e. simultaneously) to any greater precision than the HUP allows.

Particle behavior will always respect the HUP. Now, let's think through your example once again:

You want to place a detector at a spot where an interference fringe will appear and measure delta T (time) as a way to get the distance traversed. You assume that the photon travels at c in a straight line and want to deduce its path as being through one slit or the other.

Now, do you expect the answer to tell unambiguously "which slit" info? That does not make sense on 2 levels I can think of:

1. Assuming you got an answer indicating that the particle went through one slit - let's say slit L - you would be able to cover up slit R without changing the outcome for at least some trials. But wait! That has been done experimentally millions of times and guess what: that doesn't happen. If you cover up slit R, there are no flashes at all at the fringe spots.

2. More importantly: A photon exhibiting self-interference is traveling as a wave, not a point particle. So the answer cannot ever point to one slit or the other. Regardless of precision involved, the answer will be a value that reflects wave propagation rather than a direct single path as you imagine.

So this provides both experimental and theoretical evidence why your idea cannot work.

19. Dec 29, 2008

### JCBoyce

DrChinese:

I accept that my thought experiment, if actualy performed, would not yield results overthrowing established quantum theory ! I am interested in how, in principle, the results would present themselves.

Your point 2 is interesting, since I am not specifying how the light travels, merely that it acts as a (point) photon when released from the source, and received at the detector. My time measurements do not rely on the apparent character of the light at any other time/location (as far as I know). They could infer a path traveled, however.

If I am allowed unlimited precision in the time measurements, then there may be something about the flash location that preserves uncertainty. Possibilities:

1. Enlargement of the flash footprint so that both paths remain possible. If the footprint enlarges, I will not be able to calculate the path length precisely enough to say Slit 1 or Slit 2 was traversed. The ordinary photographs of any kind of interference pattern always show point flashes, but they are not taken under the condition that precise time measurements are being done.

2. The overall flash pattern changes to the non-intereference pattern, but the flashes themselves remain the same size (generated at points whose position can be precisely defined). In this case, I can tell which slit a single photon came through, but I believe quantum theory states that the pattern is not different than if I mount detectors at the slits that allow the photon to proceed, while also indicating its passage. (I understand such detectors exist).

Is there some theory that suggests whether the individual flashes smear out (Possiblity 1) or alter their overall pattern (Possibility 2), when precise time measurements are being taken?

20. Dec 29, 2008

### Cthugha

No, the position is not a problem. However another problem will arise. The key property, which allows an interference pattern to show up is coherence. Coherence implies several things: coherence time is the time, over which an emitted light field still has a well defined fixed phase relationship. It is also the timescale over which photons emitted are indistinguishable. It is also the timescale, which determines how well you know the exact emission time.

Think for example of the usual double slit. If you put the slits further and further apart at some point the interference pattern will start to vanish as at some point the photon travel time difference betweeen the two possible paths will be on the order of the coherence time of the light or above. Michelson interferometers measure the coherence time of a light field in a similar way.

Now imagine what happens if you measure the exact emission times using only single emitted photons. At first using only single photons means that you filter the light field. You have a coherent state beforehand and afterwards you will be somewhere near a n=1 Fock state. This drastically alters the coherence time. Measuring the recoil is even worse. Each time you determine the emission time, you also change the state of the light field. The atom-photon-system is entangled as well and measuring the atomic recoil is the same as measuring the emission time and emission angle of the photon. If you measure the emission time with high enough precision, the light field amplitude at some point in space will be maximal at some moment and will fall to zero on a timescale comparable to the temporal resolution of your recoil measurement. This also means automatically that the coherence time will also be reduced to this timescale, so the interference pattern will not be visible anymore.

You could in principle also measure the photon emission angle with high precision in a recoil measurement. If the precision is high enough, this will give you direct evidence of which path the photon takes and you will also not see an interference pattern.