Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Atomic-S on 21/05/2015 06:44:37
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Consider a barrier (plate) having two parallel slits close together. Is there any way to measure their spacing using only one photon?
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No
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What if we were to do the following: Set up the source of light having a narrowly defined wavelength, then the slits, and then the detector such as photographic film. Then insert, immediately in front of the film, a piece of energized light-amplification material such as neodymium laser glass. Now do the experiment by allowing a low power of the source send one photon through the apparatus. The photon passes through the slits as usual, diffracting. It reaches the light-amplification glass -- and then what happens?
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Consider a barrier (plate) having two parallel slits close together. Is there any way to measure their spacing using only one photon?
No. However, if you have an ensemble of such experiments and execute each experiment only one time with one photon for each experiment then the answer becomes yes. You'd be able to obtain the width of the slit by analyzing the collection of data from all experiments.
What if we were to do the following: Set up the source of light having a narrowly defined wavelength, then the slits, and then the detector such as photographic film. Then insert, immediately in front of the film, a piece of energized light-amplification material such as neodymium laser glass.
What is a light-amplification material?
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Then insert, immediately in front of the film, a piece of energized light-amplification material such as neodymium laser glass.
You could inject a single incoming photon into an optical amplifier (http://en.wikipedia.org/wiki/Optical_amplifier). Using the principle of the laser*, it would turn into a group of photons with the same frequency and phase. This would illuminate the slit nicely, producing a clear interference pattern; however, you would no longer be illuminating the slit by a single photon (which was the original premise).
*Or several other optical effects
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You could inject a single incoming photon into an optical amplifier (http://en.wikipedia.org/wiki/Optical_amplifier). Using the principle of the laser*, it would turn into a group of photons with the same frequency and phase.
It's extremely important to keep in mind here that no device can turn one photon into multiple photons. What happens is that one photon goes in and multiple photons come out. This is not the same as splitting one photon into more than one and one should bear this in mind.
When I was studying optical electronics I studied such devices. They're used in the NOVA laser fusion center. It was confusing at first until I realized what I just said was happening. Hence the reason why I mention it.
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You could inject a single incoming photon into an optical amplifier. Using the principle of the laser*, it would turn into a group of photons with the same frequency and phase. This would illuminate the slit nicely, producing a clear interference pattern; however, you would no longer be illuminating the slit by a single photon (which was the original premise).
The idea is to place the optical amplifier between the slits and the target (film), not between the source and the slits.
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The idea is to place the optical amplifier between the slits and the target (film), not between the source and the slits.
If that's what you want to do then the quantum effects of diffraction has already occurred by the time it gets to the amp.
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The idea is to place the optical amplifier between the slits and the target (film)
If you had a number of optical amplifiers at various points behind the slit, then a single photon would illuminate just one of the optical amplifiers, producing a brighter image of that photon on the photographic film. But you cannot identify a diffraction pattern from a single point of light, so you will be left with a large number of possible slit configurations.
There are some points in a diffraction pattern that have zero intensity (at least in theory). So you cannot determine what slit arrangement is present, but you can identify a few slit arrangements that are not present.
In practice, it takes a few photons to hit the same grain of film before you will develop a spot on a photographic plate. Historically, photomultiplier tubes have been used to convert a single photon into a cascade of electrons, providing an amplified electrical signal. CMOS detectors have a fair chance of detecting single photons, and superconducting detectors are very efficient at detecting single photons.
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If that's what you want to do then the quantum effects of diffraction has already occurred by the time it gets to the amp.
That is correct, and is the desired phenomenon. The theory here is that the amp will magnify the strength of the original photon by adding many more, but in such a way as to match each to the original photon's wave function.
If you had a number of optical amplifiers at various points behind the slit, then a single photon would illuminate just one of the optical amplifiers
Is that actually true? The breadth of the diffraction pattern says that the photon has a certain probability of illuminating each of them, and until we measure which one, all amplifiers must be considered to be viable options. The original wave function is available for amplification in each amplifier simultaneously. If there is, say, a .01% chance that the photon is being amplified by a certain amplifier, and if the amplifier has a gain of 106, then each of the 106 photons that would emerge has a .01% chance of existing, a situation that says there are about 100 photons that actually emerge. The number of photons likely to emerge from different amplifiers would, of course, vary in proportion to the input probability applicable to each amplifier, which would vary depending on its position in the diffraction pattern. Whatever emerged from an amplifier would make one pixel on the diffraction pattern, and the number of photons coming out of this process would be large enough that it ought to be easily recordable. But the result is expected to appear as a diffraction pattern rather than a bright spot because no attempt was made to find the photon in a particular amplifier during the amplification, but only afterward, by which time the photon had been cloned into many copies of itself.
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Historically, photomultiplier tubes have been used to convert a single photon into a cascade of electrons, providing an amplified electrical signal. CMOS detectors have a fair chance of detecting single photons,
These are different devices than laser amplifiers, and would not be expected to give the same results.
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The breadth of the diffraction pattern says that the photon has a certain probability of illuminating each of them, and until we measure which one, all amplifiers must be considered to be viable options.
Yes, but we humans are not the only certified observers in the universe.
An optical amplifier is a perfectly good photon detector, and putting a photon into a laser amplifier "collapses the wave function", so that the photon appears in one and only one optical amplifier, which will multiply it up to (say) 106 photons.
This is one of the principles of quantum cryptography - if someone attempts to copy the entangled photons by means of beam splitters or optical amplifiers, the entanglement is lost. It is also why quantum cryptography is a nuisance, because you have to use "dark" fiber, which severely limits the range of the encrypted stream.
As I understand it, just because the gain of an optical amplifier can be 106 does not mean that a 1 in 106 chance of detecting a photon will be multiplied up to just 1 photon.
What it means is that if you make 106 trials with different single photons, there is an even chance of detecting a burst of 106 photons from this particular optical amplifier.
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putting a photon into a laser amplifier "collapses the wave function", so that the photon appears in one and only one optical amplifier, which will multiply it up to (say) 106 photons.
If this is correct, then photons in a laser can be held in coherence only because they are forced to interact over a distance shorter than their wavelength. Because otherwise, the collapsed wave function created when each photon interacts with the medium would cause it to become a "point source" there, spreading out in many directions from that point, much as in a conventional gas discharge tube. That would end coherence. In a laser as we generally know it, we are usually assured of the required density of photons and also of the amplifying medium; however, the concept seems to require that for coherence to be possible, a minimum density is necessary, with the consequence that it would not be possible to create a coherent beam from a medium whose molecules were further apart than the wavelength of light in question. This brings up the question of Mars' atmosphere. Mars' atmosphere is known to generate a narrow wavelength of radiation due to stimulated emission which produces laser action within the atmosphere. A check of certain data seems to indicate that Mars' atmosphere is dense enough at the surface that the mean distance between molecules is substantially less than infrared wavelengths, so that requirement seems to be satisfied, but raises the question: How high above Mars' surface does this action take place? Has that altitude ever been measured? If it is known, is it consistent with these concepts? Of course, there is undoubtedly a limit to the altitude at which the action occurs, but that limit could be due not just to low density of CO2 but also due to the limits on the available energy due to the lesser cross-section per cubic meter of the atmosphere for absorbing solar radiation to power the process. That requires, for a proper evaluation of the altitude limit of coherence, that we ask what the altitude limit would be in the hypothetical cases of different intensities of driving radiation. Is there any intensity of driving radiation that would allow coherence to be maintained even when the intermolecular distance were larger than the wavelength of interest? What you have said would suggest "No, that would never be possible." However, I am not completely convinced of that, and would wish to find definitive information, especially experimental data, on the possibility of impossibility of generating coherent radiation within a medium whose molecules are separated by a distance greater than the wavelength.
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Actually, the question of molecular density is not essential to our present question. The essential point is not the density of amplifying molecules, but the density of photons. Consider a light amplifier of the stimulated-emission type. A coherent beam goes in, and a stronger coherent beam comes out. Now what happens if the brightness of the input beam is lowered to the point that the average distance between photons in it becomes larger than the wavelength? According to your prior comments, the photons are now entering the amplifier "individually", and as such, proceed on the basis of each's collapsed wave function from the point of impact within the amplifier. But that would end the photon's ability to continue traveling in the original manner or to synchronize with any other photon coming through, meaning that the output from the amplifier must lose coherence as soon as the input beam drops below a certain minimum intensity. Is this phenomenon actually observed in practice?
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a "point source" there, spreading out in many directions from that point, much as in a conventional gas discharge tube
This is what happens with spontaneous emission.
However, for stimulated emission (http://en.wikipedia.org/wiki/Stimulated_emission#Overview) (the "se" in laser), the emitted photon is coherent with the incoming photon.
held in coherence only because they are forced to interact over a distance shorter than their wavelength
A traditional laser, with a mirror at each end*, bounces the laser light backwards and forwards within the cavity, building up a coherent wave within the cavity.
You can no longer consider it a bunch of individual photons bouncing backwards and forwards, but as a Bose-Einstein Condensate (http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_correlations#Bose.E2.80.93Einstein_correlations_and_quantum_coherence) which fills the entire volume of the cavity. The length of the cavity can be less than a milimeter or up to a meter - the lasing medium interacts with this coherent wave over a distance far larger than the wavelength of the light.
*Some optical amplifiers are like a laser without a mirror.
putting a photon into a laser amplifier "collapses the wave function"
The scenario here is that we have a bundle of optical amplifiers is spread out behind the dual slits, to detect the photons which pass through the slits, one photon at a time.
As I understand it, in "deciding" which one of these optical amplifiers the photon will enter, the wavefunction has already collapsed even before it reaches the gain medium. The "descendents" of this photon will emerge from just one optical amplifier.
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*Some optical amplifiers are like a laser without a mirror.
OK, let's look at the problem from the following perspective: We have a laser shining at the slits. Following them, we have an interval of empty space such that a diffraction pattern would be able to form within it, then a laser amplifier, then the recording screen. We expect that the screen will record a really bright fringe pattern. But now let us imagine that we reduce the input intensity from the source laser, such as by moving it further and further away (laser beams will diminish over distance due to spreading if the distance is large enough, as has been demonstrated from Earth to Moon). We keep moving it farther away until the average time betwen photons arriving at the slits is substantially less that the length of the apparatus/c . In fact, we will keep moving the laser away so that the rate drops arbitrarily low -- it could eventually reach a matter of hours between photons. The question to be answered is, what will appear on the recording screen as the source power diminishes to arbitrarily low values? Will we see the fringe pattern get dimmer and dimmer but always being like it would have been if the laser amplifier had been on the input rather than the output side of the slits, or will we see patterns composed of a very few but really bright spots? The latter situation corresponds to what I understand you to be saying, namely, that a photon is either amplified extensively or not at all, so that either it generates a shower or nothing. But if it generates a shower, then, since its wave function has "collapsed", that shower cannot contain the fringe information, and we would record only a single bright spot for it, or a spray of random spots over the screen. (Which would it be?) If, however, the wave function does not collapse within the amplifier, so that the entirety of its possible motions are all amplified together, so that when it finally does collapse at the screen there are enough clones of it to depict it extensively, then the fringes would still be visible. So, what exactly happens to the screen as the source laser is dimmed arbitrarily dim while the diffracted light passes through the amplifier?
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will we see patterns composed of a very few but really bright spots?
Yes, this is what I expect to see.
If you wait a long time for enough photons to pass through the slits (one at a time), you will see a bright interference pattern.
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As for Atomic-s question: Is there any way to measure double slit spacing with a single photon; yes there are several.
There are a lot of lasers that can produce single photons and at least one that can produce them on command. If the laser is far enough away from the slits so that both paths are probable for the photon then a sequential stream of photons hits will build up an interference pattern. There are videos on the internet where you can actually watch this happen.
If you are asking about a sole hit from a single photon, I think it can still be done. The single photon can only actualize at the detector at an anti-nodal position associated with the interference pattern for those slits.
If a series of lenses are position to spread out the possible interference patterns so that they do not overlap or converge then a determination can be made.
I have done some experiments with barriers or baffles with the edges placed in the dark nodal lines that isolated the path to one specific anti-nodal ban; but I knew the slit size and width ahead of time. Once set up a single photon can be used to confirm the spacing.
Pmbph: I am disappointed at your comment that no device can split a photon into multiple photons. Usually you are right on. What about parametric down converters, the main stay of quantum optics. Maybe it is the meaning of split that is tripping me up.
A down converter in front of the double slit would create two photon hits that would enable the calculation of the slit spacing if the frequency of the photon and the distance to the target were known. But then you would be using two photons. Putting the down converter after the slit would complicate the possible path directions.
I am sure there other ways to achieve the desired results available if I took the time to research it.
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Pmbph: I am disappointed at your comment that no device can split a photon into multiple photons.
I'm very sorry to hear that. I didn't have the time to carefully explain myself when I posted that and don't have the time now. But I'll get around to posting a very clear explanation for you. For now just know that I'm right. If you hear people claim that In Spontaneous parametric down-conversion, one photon may produce two photons with half the energy. then know that they don't have a clue about what they're talking about. Just because one photon goes in and two come out each having half the energy it doesn't mean that one photon split into two.
If you really need to hear it from an authority on quantum mechanics the read Alastair Rae's text Quantum Physics: Illusion or Reality? On page 75 the author writes
https://books.google.com/books?id=kccLAQAAQBAJ&pg=PA75&lpg=PA75&dq=a+photon+cannot+be+split&source=bl&ots=32jaXA0Yy-&sig=_L5Wb3EwhtZo5RuZg8aAIyrpscg&hl=en&sa=X&ved=0CFoQ6AEwCGoVChMIid3I9aGGxgIVgSysCh0TggD_#v=onepage&q=a%20photon%20cannot%20be%20split&f=false
In contrast, photons cannot be split, but they can be considered to be in a superposition state until a measurement "collapses" the system into one or other of its possible outcomes.
You'll also find the same thing stated in Laser Physics by Peter W. Milonni, Joseph H. Eberly
Usually you are right on.
Gee! Thanks. That's awfully kind of you to say. [:)]
You should go to all those other forums where there are a few crackpots who've been harassing me for years because I've proven them wrong so often and tell that to them. Lol!! What about parametric down converters, the main stay of quantum optics. Maybe it is the meaning of split that is tripping me up.
A down converter in front of the double slit would create two photon hits that would enable the calculation of the slit spacing if the frequency of the photon and the distance to the target were known. But then you would be using two photons. Putting the down converter after the slit would complicate the possible path directions.
I'm sorry but I don't know what that device is. I'm going by theory only. I'm too busy to get to it tonight but I will later. I've contacted some friends who are also authorities in the field of quantum mechanics so I'll report what I hear from them. After all, I may not a lot but nobody knows everything, right? :)
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Once again Pmbphy you are somewhat correct. Stating that the photon is in a superposition state until a measurement collapses it is closer to prevailing theory than saying the photon is split.
In the prevailing, orthodox, interpretation of quantum theory, the Bohr interpretation, a photon does not actually travel a path; does not pass through the slits, does not enter the down converter or exit it. It is not until an interaction occurs ( could be a measurement ) where the quantum field collapses from multiple abstract mathematical probabilities into a limited set of mathematical properties associated with the actualized photon.
In the Bohr interpretation the interference pattern in a double slit is not the result of wave interference but the result of the intersection of time distance intervals that correspond to the highest mathematical probability for photon actualization to occur. However, in all but the most theoretical experiments, wave frequency, paths traveled, devices enter, photons split, and photons entangled are commonly used to describe the experiment for simplicity.
I noticed in the past that members on this forum have trouble with the mind boggling concept of photons not propagating through space and not coming into existence until tested for, including some of the phds.
Of course the Bohr interpretation is not the only interpretation in contention. In the Bohm interpretation an actual photon would inter the down converter and be split and the photon core would pass through only one of the two slits while its broader field would pass through both.
I favor a model of light similar to the Bohm interpretation but favor a view of ultimate reality similar to that of Bohr. I have been doing experiments that I think show how these two concepts along with some others together can be brought together. But this is not the place to discuss them.
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Once again Pmbphy you are somewhat correct.
I'm very glad to hear that but am confused about the "somewhat."
In the prevailing, orthodox, interpretation of quantum theory, the Bohr interpretation, ...
I'm not familiar with anything called the Bohr interpretation. The only thing that's close to that which I'm aware of is the Bohr model and that's from the old theory of quantum mechanics which is wrong. Perhaps you're thinking of the Copenhagen interpretation, formulated under Bohr's leadership, which is defined as follows:
http://en.wikipedia.org/wiki/Copenhagen_interpretation
The fundamental axiom of the Copenhagen interpretation is the "postulate of the quantum", that subatomic events are only perceptible as indeterministic physically discontinuous transitions between discrete stationary states.
I noticed in the past that members on this forum have trouble with the mind boggling concept of photons not propagating through space and not coming into existence until tested for, including some of the phds.
I agree. That's one of the hardest things for people to grasp. I've had a devil of a time trying to help people learn this correctly. David Griffiths explains this extremely well in his quantum mechanics text.
I case anybody is a bit confused about what we're talking about it's as simple and hard as this: Before you observe a particle it really isn't anywhere.
Consider the following quote from the article Is the Moon There When Nobody Looks? by N. David Mermin, Physics Today, April 1985, page 38. It's online at: http://maltoni.web.cern.ch/maltoni/PHY1222/mermin_moon.pdf
Mermin quotes Pascual Jordan on this saying
Observations not only disturb what is to be measured, they produce it ... We compel (the particle) to assume a definite position.
Mermin quoted this from Max Jammers book The Philosophy of Quantum Mechanics, (1974) p.151.
Of course the Bohr interpretation is not the only interpretation in contention.
While not the only one it has survived close to 100 years with no problems with it so far, and with surprising results, whereas the other interpretations either have serious problems or can't be tested. I ignore them myself.
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photons cannot be split, but they can be considered to be in a superposition state until a measurement "collapses" the system into one or other of its possible outcomes.
I know terminology can get tricky in the quantum world, but I'll dip my toe in the water...
- When photons travel through a vacuum, air, or glass, the photon that comes out has the same frequency as the photon that went in (it is a linear medium).
- In a more exotic scenario, when photons enter a calcite crystal, light with different polarisations take a different path*. But the photons still come out with the same frequency they went in.
- In an even more exotic scenario, when photons enter a non-linear crystal, most of the photons come out with the same frequency they went in - the really interesting case is the rare event where a pair of entangled photons come out at different frequencies than the photon which went in.**
So would you rather say:
(a) The photon originally generated with a single frequency (eg by a laser) is in an entangled state consisting of many possible pairs of photons with different frequencies - but you never see this after passing through linear materials like a vacuum, air, glass or calcite
OR (b) There is something about the nonlinear crystal in a parametric down-converter which (rarely) causes a single-frequency incident photon to exit as two entangled photons of different frequencies.
Essentially: is the entanglement in the frequency domain a property of the original, single-frequency photon, or is it something which is produced or revealed only after passing through a non-linear crystal (ie it is a behavior of the crystal)?
*The quotation from Alastair Rae is in the context of splitting a beam of polarised light into two possible paths with different polarisations, and is merely making the point that in a linear material, one photon in=1 photon out. This would seem to have no bearing on the results for a non-linear optical material, which can have 1 photon going in and 2 photons coming out.
**Photons can also be totally absorbed (by an opaque material), or be absorbed and re-emitted later at a different frequency, at a later time in a fluorescent material. But this can be ascribed to different mechanisms than you see with mostly-transparent materials.
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photons cannot be split, but they can be considered to be in a superposition state until a measurement "collapses" the system into one or other of its possible outcomes.
I know terminology can get tricky in the quantum world, but I'll dip my toe in the water...
- When photons travel through a vacuum, air, or glass, the photon that comes out has the same frequency as the photon that went in (it is a linear medium).
- In a more exotic scenario, when photons enter a calcite crystal, light with different polarisations take a different path*. But the photons still come out with the same frequency they went in.
- In an even more exotic scenario, when photons enter a non-linear crystal, most of the photons come out with the same frequency they went in - the really interesting case is the rare event where a pair of entangled photons come out at different frequencies than the photon which went in.**
Under no circumstances can you ever say that a photon that goes in a substance is ever the same photon that comes out. Think of it as an absorption and emission process where one atom absorbs a photon and then emits a new photon in the same direction with the same properties.
*The quotation from Alastair Rae is in the context of splitting a beam of polarised light into two possible paths with different polarisations, ..
That's irrelevant because the author is basing his argument on the fact that one cannot split a photon.
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The commonly used phrase of Copenhagen Interpretation is very lose and contains many views including some conflicting ones. Bohr and Heisenberg were both members of the Copenhagen school of thought. But were Bohr thought that the quantum field was a complete mathematical abstraction Heisenberg thought that there was some, as of yet undefined, real physical oscillation.
As for the moon not being there when no one is looking, this is a reference to what is usually referred to as quantum philosophy. It is nether good science or good philosophy. Conscious observation is not required to collapse the quantum field. There has actually been a couple of experiments to test this hypothesis and it was found false.
The idea persist in the popular mediums because of its appeal, especially to the crazies. The phrase known path is used a lot, but this is really short hand for saying that the properties of the actualize photons are in agreement with only one probable path. This subject was discussed in a long thread on remote entanglement that I introduced in 25/04/2011.
I have heard the phrase that quantum theory has been around for a hundred years without contradiction a lot. That does not make it true. There are a lot of historical contradictions that have been brushed aside as unexplained anomalies. And a lot of new ones appearing currently ( this is in addition to mine ). I posted one historic contradiction on this site as the Chiao Anomaly on 9/06/2010.
In his book, Three Roads to Quantum Gravity, lee Smolin stated that whereas most physicist do not like quantum theory it is the only thing they have to work with. In a later book, The Trouble with Physics he acknowledged that this was not the case.
To describe the results of the down converter in Bohr's terms you might say that at the target the quantum probability field collapses into two actualized photons with properties associated with a down converter inserted into the probable path.
We are getting away from the original question about determining slit spacing with one slit. If the reason for that question is because of trying to come to terms with single photon interference. It has been both been demonstrated and theorised.