I Incomprehension of a simple interferometer?

[desertshaman]

Hi people :)

On an electronics forum, I began a discussion of laser interferometers.
A correspondent's theoretical analysis of the Mach-Zehnder interferometer contains the following assertion:

"The scattering of a photon into one or other arm at BS1 induces by reaction a fluctuation in the re-radiation field,& it is this that interferes with the photon at BS2."

Everything else that my correspondent said seems to make good sense to me, but this particular assertion troubles me because it seems to call firstly for the collapse of the photon in 1 and only 1 path from the first beam splitter, and secondly this collapsed wave interferes itself as a non-collapsed entity.

... I'm confused?

(I guess you can see why I thought it might be better to take this question to a physics forum.)

Mark

 

[.Scott]

You may be thrown off by the word "scattered". BS1 will pass and reflect each photon. So each photon is directed to both M's.

Also, the way that is phrased, you might think that something other than the path is different for those two paths. In particular, is it saying that a re-radiation field is interfering with a photon? To be clear, however you describe the photon that reflects from one of the M's is a suitable description for the other - because, after all, it's the same "re-radiation field" or "photon". Only the path is different.

 

[desertshaman]

:) Thanks...
Yes, thanks Scott. I think that my correspondent might not have expected the forum to understand his rather purple jargon at all - and was carried away by the joys of raconteur-ship.
If I'm right ~
The "light beam" is a coherent stream of disturbances in space which transfers units of energy from the source at c in a very specific direction.
I simplify, in order to try and get an understanding of the phenomena.
I imagine that disturbances in the electromagnetic medium which is free space propagate in some respects like chirps of sound.
For sound, the simultaneous emission of chirps from very many emitters spread half a wavelength or less apart on a plane results in a 2 dimensional wavefront moving away fron the plane.
For light, the emitters are atoms, separated by picometers, which radiate their energies through nanometer scale electromagnetic waves. Since there are billions or trillions of little emitters all emitting at once on the same plane, the wavefront that they generate together is very flat.
This wavefront is the sum of the discrete waves emitted from each source. This is the electromagnetic wave which passes through the interferometer and is divided; polarised; attenuated and summed at the detector.
I think that the collapse of the wavefunction (the realisation of its transmitted energy) at the detector is only relevant at the detector, and is irrelevant to the previous stages of workings of the interferometer.
Whew I hope that's right
Mark

 

[.Scott]

The "light beam" is a coherent stream of disturbances in space which transfers units of energy from the source at c in a very specific direction.
I simplify, in order to try and get an understanding of the phenomena.
I imagine that disturbances in the electromagnetic medium which is free space propagate in some respects like chirps of sound.

And you also seem to provide ample purple prose to your physics as well.
Thinking of the behavior of light as similar to the behavior of sound has it's limits. I don't think photons will easily fit into your model.

For sound, the simultaneous emission of chirps from very many emitters spread half a wavelength or less apart on a plane results in a 2 dimensional wavefront moving away fron the plane.
For light, the emitters are atoms, separated by picometers, which radiate their energies through nanometer scale electromagnetic waves. Since there are billions or trillions of little emitters all emitting at once on the same plane, the wavefront that they generate together is very flat.
This wavefront is the sum of the discrete waves emitted from each source. This is the electromagnetic wave which passes through the interferometer and is divided; polarised; attenuated and summed at the detector.

You will be using a laser in you interferometer. What the atoms are emitting are photons of a particular wavelength - small packets of energy of uniform size. If you were trying to understand simple optics, your notion of photons teaming up to for a wavefront would be fine. But your interferometer will do its thing even when the photons are produced at very slow rates - like a few per second - too few to team up to form anything.

Each of these photons is a wave front - and once it passes through the first beam splitter, it is two wave fronts.

After the second beam splitter the fronts recombine. Our detector should be a surface - when the wave front reaches the screen, the location of the photon will be at one of the lighter spots of an interference pattern. The interference pattern itself can only be seen after many photons have gone through this process - each one picking some random brighter spot on the screen.

 

[desertshaman]

Thank you very much for all you have said, .Scott :)

BTW Can there be laser light at a photon rate of say 1 photon per second, or is laser light entirely a phenomenon of photon teamwork?

 

[.Scott]

Thank you very much for all you have said, .Scott :)

BTW Can there be laser light at a photon rate of say 1 photon per second, or is laser light entirely a phenomenon of photon teamwork?

A 1-photon-per-second laser could probably be engineered. But it is much easier to take a regular laser and filter it down until it is that dim.

 

[desertshaman]

Thank you, .Scott
So a 1 photon/second laser could be manufactured.
Alright, that makes good sense in the end. Still, I find it to be rather wonderful :)

 

[Baluncore]

A 1-photon-per-second laser could probably be engineered. But it is much easier to take a regular laser and filter it down until it is that dim.

LASER = Light Amplification by Stimulated Emission of Radiation.
Why would you amplify one photon, to get one photon?
Surely that would simply be, the emission of one photon.

 

[desertshaman]

I purposely asked a edge case question.
It appears that a single photon might be collimated with itself, and sent with high directionality, at least.
:)
and it's wonderful, innit.

 

[weirdoguy]

A 1-photon-per-second laser could probably be engineered.

Photons and lasers do not get along, since E-M filed created by laser is not the one where one can meaningfully talk about number of photons.

 

[desertshaman]

So a laser EM field could be indefinitely weak? It's hard to believe in a laser whose output energies are less than, say, a single quantum over the lifetime of the universe.
Yet, with attenuators, and I don't know why you'd want to, I guess such a device could be constructed. What a project. Just a few coats of marvellous Stewart Semple 4.0 Black over the lens of a perfectly good laser and you're done :)
There are, quite likely, more interesting questions to sneak up on.

 

[Lord Jestocost]

Can there be laser light at a photon rate of say 1 photon per second, or is laser light entirely a phenomenon of photon teamwork?

https://en.wikipedia.org/wiki/Single-photon_source

 

[.Scott]

Thank you, .Scott
So a 1 photon/second laser could be manufactured.
Alright, that makes good sense in the end. Still, I find it to be rather wonderful :)

Wow! You've jumped from my "could probably be engineered" to "could be manufactured".
I definitely share some of the skepticism expressed - especially from @weirdoguy .
The experiment I had in mind when I said "could probably..." was with a laser that is in the process of creating a hologram.

So can a laser be made such that the film plate is only exposed at a rate of 1 photon per second. I think the answer is "yes" or "at least in theory".

Now, I could to take a shot at trying to explain how that works - but I would rather leave it up to others more practiced with QM.
Let me ask @weirdoguy in particular: Would it be fair to say that in the situation I described (ie, holography), 1 photon-per-second is mostly a description of the energy level of the EM field and less a description of the timing of the photon emissions?

 

[PeterDonis]

Would it be fair to say that in the situation I described (ie, holography), 1 photon-per-second is mostly a description of the energy level of the EM field and less a description of the timing of the photon emissions?

The issue with the "1 photon per second" description, as a description of anything except detections, is that the state of the quantum EM field emitted by a laser is a coherent state, and a coherent state is not a eigenstate of photon number. So with a laser, you can't count "photon emissions", because there aren't any: that's not how a laser works (although pop science descriptions often mistakenly describe it as if it is).

With any light source, however, you can count photon detections if you use an appropriate detector. (Note that I'm not saying a holographic film is such a detector; I don't know whether it is or not. But there are such detectors.) With an appropriate detector, and a light source whose intensity is low enough, the detector will show individual dots at discrete intervals (not the same interval each time, the time distribution will depend on the source). With a simple light source like an incandescent bulb, the brightness of the dots will vary; but with a laser, the dots will all have the same brightness, indicating that the laser is emitting light of a specific frequency--which means a specific "photon energy" at the detector. But you cannot describe the state of the light before detection in terms of "photons", because, as above, the coherent state emitted by the laser is not an eigenstate of photon number.

The link @Lord Jestocost gave in post #12 describes light sources (which, as the article notes, are not lasers) that do emit "photons" in the sense that (in the idealized case) the state of the quantum EM field they emit is an eigenstate of photon number. Light emitted from such sources can have properties on detection that are quite different from those of laser emitted light, as the article describes.

 

[hutchphd]

1 photon-per-second is mostly a description of the energy level of the EM field and less a description of the timing of the photon emissions?

To me this is a very confusing statement. The energy state of the field depends comprehensively on the setup as you rightly point out. As has been much discussed before, the language of photons is ill-suited here. What does 1 photon per second mean? It does not lead to understanding unless one knows the nuances.
I really don't understand the references to holography. To me holograms are very complicated interference patterns and much more difficult to parse. Perhaps I am not seeing something here.?.

 

[desertshaman]

Wow! You've jumped from my "could probably be engineered" to "could be manufactured".
I definitely share some of the skepticism expressed - especially from @weirdoguy .
The experiment I had in mind when I said "could probably..." was with a laser that is in the process of creating a hologram.

So can a laser be made such that the film plate is only exposed at a rate of 1 photon per second. I think the answer is "yes" or "at least in theory".

Now, I could to take a shot at trying to explain how that works - but I would rather leave it up to others more practiced with QM.
Let me ask @weirdoguy in particular: Would it be fair to say that in the situation I described (ie, holography), 1 photon-per-second is mostly a description of the energy level of the EM field and less a description of the timing of the

Hey that "jump" from "could probably be engineered" to "could be manufactured" wasn't so bad, was it? Optical attenuators could certainly reduce energies of a powerful beam to any arbitrary value... is a laser of low power equivalent to a laser of reduced power?

 

[Baluncore]

An attenuated laser can deliver low numbers of photons, but it does not prevent emission of two or more photons together.
"For example, a mean value of μ = 0.1 leads to a probability of 90% for zero photons, 9% for one photon and 1% for more than one photon." https://en.wikipedia.org/wiki/Single-photon_source#Faint_laser

To separate photons, requires some "antibunching" mechanism.
https://en.wikipedia.org/wiki/Photon_antibunching

 

[desertshaman]

Anti-bunching mechanism for photons; quantum hairbrush?
Thanks for your patience, you good fellows.
:)