Double-Slit Experiment: Does rate of photon emission matter?

[Mr Fallspring]

TL;DR Summary

I'm curious whether the rate of photon emission has any noticeable effect on the diffraction pattern generated by the double-slit experiment.

Hi there!

High school physics teacher hoping to pick the brains of people who know more than I do here.

I'm curious whether the rate of photon emission has any noticeable effect on the diffraction pattern generated by the double-slit experiment.

To be clear: I understand a diffraction pattern remains in evidence even when we send only a single photon through, my question is whether we see any changes at all to that pattern depending on the rate of emission.

Also to be clear: This is pre-supposing that such experiments have been done. I've been looking to find such an experiment, figuring it must have been done, but I may not know the best language to use to find the experiments along these lines.

Finally, if such experiments have not been done, I'd appreciate any insight into why such an approach is either problematic or theoretically confused.

Thank you for your time!

 

[PeterDonis]

I understand a diffraction pattern remains in evidence even when we send only a single photon through

Some care is required in how this is described.

If you only send one photon through the apparatus, ever, you will see a single dot on the detector, not an interference pattern. ("Interference" is the correct term for the double slit result; "diffraction" implies a single slit or pinhole or other small aperture.)

If you send one photon through at a time, very slowly (by turning the intensity of the source down very, very low), you will see single dots on the detector each time a photon is sent, and over time, if you record the locations of all the dots, they will gradually build up an interference pattern.

If the only thing you change about the photon source is its intensity, then the pattern you end up with will not depend on the intensity; the only change will be how long it takes for you to have enough dot locations to see the pattern. At high intensity, the dots all appear on the detector so quickly that you can't see them individually, you can only see the pattern itself.

 

[PeroK]

If the only thing you change about the photon source is its intensity, then the pattern you end up with will not depend on the intensity; the only change will be how long it takes for you to have enough dot locations to see the pattern. At high intensity, the dots all appear on the detector so quickly that you can't see them individually, you can only see the pattern itself.

Does superposition hold precisely for the quantized EM field? If we take the one photon at a time to be the baseline, are there any minor changes to the pattern when there are many photons in the experiment at the same time? And, if so, is the difference significant enough to have been experimentally observed?

 

[Mr Fallspring]

Some care is required in how this is described.

If you only send one photon through the apparatus, ever, you will see a single dot on the detector, not an interference pattern. ("Interference" is the correct term for the double slit result; "diffraction" implies a single slit or pinhole or other small aperture.)

If you send one photon through at a time, very slowly (by turning the intensity of the source down very, very low), you will see single dots on the detector each time a photon is sent, and over time, if you record the locations of all the dots, they will gradually build up an interference pattern.

If the only thing you change about the photon source is its intensity, then the pattern you end up with will not depend on the intensity; the only change will be how long it takes for you to have enough dot locations to see the pattern. At high intensity, the dots all appear on the detector so quickly that you can't see them individually, you can only see the pattern itself.

Thank you for you prompt and patient reply Peter!

I do understand that each photon is detected as a single dot and that the pattern we discuss only emerges as more dots are recorded.

I'll take care in my parlance of diffraction vs interreference going forward. Thank you for your guidance.

You've answered my main question precisely I think - that intensity, which determines emission rate, has no effect on the pattern. I am curious though when this was most rigorously studied. Perhaps it's so clear as to be obvious to those working with the data first hand, but between the fact that a) the results were so counter-intuitive, b) the technology was so limited a century ago, and c) the central role of nondeterminism in what they encountered, it seems to me like something calling out for precise methods of statistical analysis at some point along the study.Matt

 

[Grinkle]

@PeroK

To answer that, is it necessary to state what one means by one interference pattern being the same or different as another interference pattern? It seems to me that if one creates some number of interference patterns one dot at a time or many dots very quickly for a relatively rapid pattern emergence, none of them will be purely identical to another one, so to say that they are the same must refer to a macro-level property of the pattern, is this right? The ones I have seen are all blurry at the edges.

 

[Mr Fallspring]

@PeroK

To answer that, is it necessary to state what one means by one interference pattern being the same or different as another interference pattern? It seems to me that if one creates some number of interference patterns one dot at a time or many dots very quickly for a relatively rapid pattern emergence, none of them will be purely identical to another one, so to say that they are the same must refer to a macro-level property of the pattern, is this right? The ones I have seen are all blurry at the edges.

Indeed. To me this is something that would likely require a statistical lens, and in current times might benefit from a machine learning approach. ("Given this particular pattern, predict the emission rate (or whatever makes more sense".)

Anyone aware of any work done along these lines? Is the data available to do it?

 

[PeterDonis]

Does superposition hold precisely for the quantized EM field?

I think "linearity" would be a better term than "superposition" here. See below.

If we take the one photon at a time to be the baseline, are there any minor changes to the pattern when there are many photons in the experiment at the same time?

My response assumed that the answer to this is no, i.e., that the quantized EM field is exactly linear. Strictly speaking, this is not correct since, while there is no direct photon-photon vertex in QED, there are higher-order Feynman diagrams that can, in theory, produce a net photon-photon interaction.

However...

And, if so, is the difference significant enough to have been experimentally observed?

At intensities that we are capable of producing in experiments, no. We would have to achieve intensities many orders of magnitude higher to have a chance of seeing any effects of nonlinearities such as I described above.

 

[Devin-M]

You may find this experiment interesting… he uses a single photon setup and makes the two possible paths unequal length such that the time of flight of one of the paths should guarantee a single photon can’t interfere with itself… & yet a single-photon interference pattern is still observed…

(7:37)

 

[PeterDonis]

You may find this experiment interesting

Is there a published paper on this experiment? A video is not a valid source by itself.

 

[Devin-M]

No paper, Its just a video showing the experiment— he sets up an optical table and uses neutral density filters on a laser to get the beam power down to single photon levels. Then beam splitters separate the beam and recombine it before entering a camera. One of the beam lengths is significantly longer than the other. He then shows when either beam path is covered the interference pattern disappears, but when both paths are open the interference pattern is plainly visible. How would you explain his results?

 

[PeterDonis]

No paper, Its just a video showing the experiment

Then it's not a valid reference. You would need to find an experiment documented in a peer-reviewed paper. That's how valid, reproducible scientific experiments are documented.

 

[PeterDonis]

He then shows when either beam path is covered the interference pattern disappears, but when both paths are open the interference pattern is plainly visible. How would you explain his results?

Assuming that there have been properly documented experiments done that show similar results, the explanation is simple: the single photon that makes a dot on the detector does not have a definite time of emission. Heuristically, it is in a superposition of having been emitted at two different times.

The way to test this would be to only have the source on for a time shorter than the difference in travel times between the two paths. Doing this should eliminate the interference pattern at the detector.

 

[Rene Dekker]

Assuming that there have been properly documented experiments done that show similar results, the explanation is simple: the single photon that makes a dot on the detector does not have a definite time of emission. Heuristically, it is in a superposition of having been emitted at two different times.

The way to test this would be to only have the source on for a time shorter than the difference in travel times between the two paths. Doing this should eliminate the interference pattern at the detector.

I have been interested in (and surprised by) this experiment as well, ever since I saw the video. Does it make a difference for the outcome that it is a laser that is being used? That is, what does the QM theory state that should happen when an incoherent light source is used instead?

 

[PeterDonis]

Does it make a difference for the outcome that it is a laser that is being used?

Yes. You need the state to be coherent in order for interference and diffraction effects to be observable. An incoherent mixture of many wavelengths would give you an incoherent mixture of interference and diffraction patterns with many different spacings between the peaks--which ends up just being a blob that tells you nothing useful.

It's not impossible to get a reasonably coherent source without using a laser--for example, you could use a sodium arc lamp--but nowadays lasers are much easier to work with and control.

 

[Rene Dekker]

Yes. You need the state to be coherent in order for interference and diffraction effects to be observable. An incoherent mixture of many wavelengths would give you an incoherent mixture of interference and diffraction patterns with many different spacings between the peaks--which ends up just being a blob that tells you nothing useful.

It's not impossible to get a reasonably coherent source without using a laser--for example, you could use a sodium arc lamp--but nowadays lasers are much easier to work with and control.

Thanks for the answer, Peter.
But I always thought that a sodium arc lamp is a typical example of a light source that emits light of a single frequency, but incoherent. I thought "coherent" refers to light in which the photons not only have the same frequency, but also aligned phases of their wave functions. That should allow interference between two photons in laser light, while not in sodium arc lamps
Is my use of terminology incorrect?

 

[PeterDonis]

I always thought that a sodium arc lamp is a typical example of a light source that emits light of a single frequency, but incoherent. I thought "coherent" refers to light in which the photons not only have the same frequency, but also aligned phases of their wave functions.

The term "coherent" as applied to light, strictly speaking, refers to a coherent state of the quantum electromagnetic field:

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

Lasers are basically the "canonical" type of source that emits a coherent state. However, while I have not seen a quantum model of the light from a sodium arc lamp or similar source, I would expect it to also be modeled fairly well by a coherent state, particularly if it were passed through a narrow pass filter, since the sodium emission is actually not one spectral line but two closely spaced ones; without the filter the lamp light might be modeled as a mixture of two different coherent states with slightly different wavelengths, so it would not give interference or diffraction patterns quite as sharp as those from a laser, but probably still observable. By contrast, a source like an incandescent bulb would be modeled as a mixture of many different coherent states with widely varying wavelengths.

The concept of "phase" is actually somewhat problematic in quantum field theory; AFAIK there isn't a well-defined operator for it. It appears in the math of a coherent state, as can be seen in the article I linked to above, but its physical meaning is not straightforward.

 

[dlgoff]

Is there a published paper on this experiment? A video is not a valid source by itself.

@PeterDonis
Got it. I deleted that post. The post I'm referring to is the YouTube video I posted.