Photon Width: What Have I Missed?

[ZapperZ]

Not so I can make a wavepacket to signifiy its size; the fact is you yourself assume they have a size/length otherwise you'd still be sitting at your spectroscope until the end of time waiting for a photon to finish passing through the equipment. If they are finite in time (dt), they are finite in length since s=c*dt. If they are finite in length, then the simple sinusoid is incorrect since it must be at least convoluted with a profile. Even the simplest topphat profile convoluted with a sinusoid will produce a Fourier decomposition with multiple wavelengths; the longer the extent or width of the tophat function, the fewer Fourier components of different wavelengths needed. Either way, a finite packet is actually a blend of components. Since Fourier components tend to be integer fractions of the primary, they would not show up as a broadening of a line in your spectroscope and so I was wrong there - some of the cobwebs are clearing from my memory...

No I don't. I make zero assumption about its size because I'm NOT detecting it's location, but rather its ENERGY! That has been what you seem to be missing so far - that it is defined as a quanta of energy, not as a quanta of object with definite boundary in space!

Look, we don't have to drag this into utter absurdity. I can easily tell when light has a pencil-beam profile. In fact, I do laser profiling often as part of my job. And if you bother to check the papers of people who do single-photon emission "on demand", you can easily check what processes are involved in such emission to STILL produce "plane wave" states even when the emission of one photon versus another isn't a CW process. Yet, in ALL of these, no where was it ever mentioned about the actual "SIZE" of the photon. Of course, we can make narrow guesses on the PROBABILITY of where it would be within a certain time, but we do this everywhere, even with conduction electrons! Try it! Look at the Bloch wavefunction of the conduction electrons and try to find the "average position" of it at any given time, assuming you find a scheme to normalize the wavefunction in the first place.

That's what I recall when I got my degree in Theoretical Physics decades ago, so forgive me if I'm a little rusty here. The point being that if a photon is to have finite extent, and not stretch from New York to London, then you need to view it as something like a Gaussian mix of pure sinusoids. So a wave packet is actually a blend of different wavelengths even though it is assigned one through E=hc/lambda.

OK, now consider this. If I make a "wavepacket", of light, I actually make a Fourier sum of various other wavelengths, no? HOwever, this assumes that there are MONOCHROMATIC sources of single wavelengths in which I can sum up to produce that wavepacket. Where did these monochromatic sources come from? Other photons? What are the sources that produced such monochromatic sources? What exactly is "mixing"?

And we haven't exactly explore the glarring omission here where you actually produce peer-reviewed papers that support your assertion. Have you read any papers that actually have made any claims that a "photon" is actually a wavepacket consisting of a mixture of a number of different frequencies of... something?

If you think this is not requried on PF, please re-read the PF Guidelines that you have explicitly agreed to, especially on speculative personal theories.

Perhaps. But it seems to me there is some confusion in general understanding of what photons are and their properties, and the reason it's such a 'big deal' to me is that some aspects of physics have always fascinated me even after I left professional research decades ago, and recently I started thinking more about them - the double-slit experiment in particular - and was trying to come to grips with the notion of "particles" taking two different paths simultaneously - hence my interest in how wide a photon is. However, as I've grown older, I'm much less willing to settle for a "that's just the way it is" kind of argument, and I believe such arguments are frequently indications of areas that deserve further consideration.

But you also made a gross misjudgement that the rest of my profession is settling down with the "just the way it is" scenario. Nothing could be further from the truth. As physicists, we are EMPLOYED not to verify things that already work, but to study things that don't, or currently have no explanation. We know A LOT about light and photons. Do we know everything? No. But we do know what we don't know!

Ironically, I think you should listen to your own advice. Remember, I DID NOT SAY a photon has NO SIZE. I said a photon was NEVER DEFINED to have a size. YOU, on the other hand, INSISTED that it MUST have a size. It appears that in this transaction, it is you who have a priori made a decision on the property of a photon (i) before there are any evidence and (ii) before there are any theoretical development out of it. You have decided to ask and study thing with a prejudice already in mind.

I attended a seminar last week on the possible structure of a photon given by a theorist here in our division. Again, this explores the outer boundaries of light beyond what we currently know, including possible results from a photon-photon collider. You see the possibility of photons coupling to gluons via hadronic interaction even though it doesn't have any hadronic content. There are many exotica such as these being explored almost every day! And I can easily tell you that in such a picture, your "fourier sum of various frequencies" would be blown out of the water! So you don't need to tell me about all the boundaries of physics that are out there. I can easily tell you that you don't know the half of what I have come across just within the hallway of my office.

Yet, we must keep in mind of what we DO know already, because those have brought us a huge amount of understanding AND applications. We know quite a bit of the characteristics of light within the range that we work with and what we encounter. No where in any of these is the "size" of a photon is defined. You may not like that, but that is so far the reality. If you think you can make a definition for it, and come up with a measurement of its size, then you may either submit it to a peer-reviewed journal, or do this in the IR forum. It doesn't belong in the main physics forum.

Zz.

 

[padraighaz]

...
Look, we don't have to drag this into utter absurdity.
...
Zz.

Yes indeed. In any case thanks for the effort you put into your responses.

 

[Chaos' lil bro Order]

My guess is that if a photon had a definite size, it would have a rest mass and therefore its speed would be limited to sub C. Since photons travel at C in vacuo, is this not proof that photons have no dimensional size?

 

[Edgardo]

Hi padraighaz,

the photon must not be considered
as a tiny sphere as pointed out by HallsofIvy in the second post, but I think this is not what you thought of, right?

Now, with respect to your question "how wide is a photon?",
in a certain sense you could call the "coherence length" of a photon as your width.

Let me try to explain (The numbers in the brackets refer to the references at the end of my post):
A photon can be described as a single-photon wave packet (probability density, |\Psi|^2) [1,2],
and you can actually measure the width of a the wave packet. This is done in experiments with interferometers [13], where the coherence length of a photon is measured, and the coherence length corresponds to the width of the photon-wavepacket [3,4,5].

See for example this pdf (ref [3]):
http://departments.colgate.edu/physics/research/Photon/root/P371/lab2wavepackets.pdf
Galvez and his students conducted experiments and you can also view the results here (ref [5]):
http://departments.colgate.edu/physics/research/Photon/root/P371/lab2results.jpg

Basically, Galvez takes a Mach-Zehnder interferometer, which consists of
two arms with two beamsplitters. He sends photons through the interferometer and then measures the count rate. He does this several times, each time changing the length of one arm.

It is in fact possible to describe the photon wavefunction by a Fourier transformation, see [4].
And as you stated correctly, the photon does not have a definite, pre-existing energy before measurement.
You can read this in paper [1] and in other science discussion groups [6,7,8].

The photon is in a superposition of energy eigenstates [2] which implies that the photon's energy is spread and does not have definite value.
The superposition of plane waves leads to the wave-packet.

How wide is the photon actually and is its width constant?

The width \Delta x of your photon wave-packet depends on the energy spread, or better to say the spread of the k-vectors \Delta k.
See this paper by Galvez (this paper is highly recommended!):
http://departments.colgate.edu/physics/faculty/EGalvez/articles/ajpph.pdf (see ref [3]).
Galvez shows experimentally that the photon can have different coherence lengths. In his experimental setup he uses the Mach-Zehnder interferometer, in which he splits up the photon wave packet into two wave packets. These wave packets are then overlapped again at the second beam splitter. Furthermore, he uses bandpass filters, that is filters which let through only certain frequencies (or wavelengths or k-values).
Thus, by using the bandpass filter he is choosing the spread \Delta_k.
In the paper Galvez gives values for the spreads for two different bandpass filters (see right side of page 132 of the Galvez paper,
in section D):

\Delta k = 2 \pi * \Delta \lambda/ \lambda_0^2
where \Delta \lambda is specified by the two different bandpass filters as \Delta \lambda= 10 \rm{nm} and \Delta \lambda=0.1 \rm{nm}

which leads to coherence lengths of 84 micrometers and 8400 micrometers respectively.

Note that the spread \Delta k also leads to an energy spread of \Delta E = c \hbar \Delta k
(see page 132 bottom left side).

Why does this new spread of \Delta k change the length \Delta x of the wave-packet?
This becomes clear if you keep in mind the Fourier transformation. Also Galvez writes in his paper the relation between \Delta k and the spatial spread \Delta x of the wave-packet.

\Delta x = 1/ \Delta k
(see page 132 top left side, uncertainty principle)

Thus, the smaller your \Delta k, the bigger your \Delta x.

Why is it important to have a small spread \Delta k? A small \Delta k results in a great value for \Delta x, thus your wave-packet becomes long.
This is good, because in order to have interference both packets from the
two arms of the interferomter must overlapp [9,10].

In figure 3a of Galvez's paper you can see what happens if the wave-packets overlap quite well, and
in figure 3b if they do not overlap.

Let me note that another way to interpret the wave-packet of the photon is the count rate, see ref [11,12]

Hopefully, this post was helpful for you.

Cheers,

Edgardo

-----------------

References:

[1] "Heisenberg's Introduction of the Collapse of the Wavepacket into Quantum Mechanics",
Raymond Y. Chiao , Paul G. Kwiat, Fortschritte der Physik Volume 50, Issue 5-7 , Pages 614 - 623.
A preprint of the paper is available here: http://arxiv.org/abs/quant-ph/0201036

[2] "Pure-state single-photon wave-packet generation by parametric down conversion in
a distributed microcavity", M. G. Raymer and Jaewoo Noh, K. Banaszek and I. A. Walmsley.
Phys. Rev. A 72, 023825 (2005). A preprint of this paper is available here:
http://arxiv.org/ftp/quant-ph/papers/0504/0504062.pdf

[3] "“Interference with correlated photons: Five quantum mechanics experiments for undergraduates,” E. J. Galvez, C. H. Holbrow, M. J. Pysher,* J. W.

Martin,* N. Courtemanche,* L. Heilig,* and J. Spencer,*” American Journal of Physics 73, 127-140 (2005). You can download the paper here:
http://departments.colgate.edu/physics/faculty/EGalvez/articles/ajpph.pdf

[4] http://departments.colgate.edu/physics/research/Photon/root/P371/lab2wavepackets.pdf

[5] http://departments.colgate.edu/physics/research/Photon/root/P371/lab2results.jpg

[6] http://lists.nau.edu/cgi-bin/wa?A2=ind0205&L=phys-l&P=48869
[7] http://www.lepp.cornell.edu/spr/1999-02/msg0014640.html
[8] http://www.lepp.cornell.edu/spr/1999-02/msg0014733.html

[9] ieeexplore.ieee.org/iel5/9181/29129/01314185.pdf?arnumber=1314185
"Experimental test of the delayed single-photon self-interference effect", Nicklas Ohlsson,
mattias Nilsson and Stefan Kröll

[10] "Delayed single-photon self-interference", R. Krishna Mohan, Baozhu Luo, Stefan Kröll and Alois Mair,
Phys. Rev. A 58, 4348–4358 (1998) [Issue 6 – December 1998 ]

[11] "Single-photon and two-photon wavepackets in spontaneous parametric
down-conversion", Yoon-Ho Kim, ieeexplore.ieee.org/iel5/8993/28536/01276170.pdf

[12] "Measurement of one-photon and two-photon wave packets in spontaneous parametric downconversion",
Yoon-Ho Kim, JOSA B, Vol. 20, Issue 9, pp. 1959-1966

[13] "Coherence length of photons from a single quantum system", Jelezko et. al,
Physical review A 67 (2003)

 

[Chaos' lil bro Order]

Great post Edgardo, well thought out and fully referenced, a true gem!

 

[padraighaz]

Thanks Edgardo for your post. This is the kind of analysis I vaguely remember learning decades ago and the coherence length is what I had in mind for the scale length in the direction of motion, where you needed a superposition of components to generate a finite wavepacket.

My original question concerned transverse scales since I was wondering how wide is a photon and couldn't remember having learned anything about this. If it can be as wide as the slit separation, it's no big deal to point out single photon interference requires a photon to go through both slits at once etc. etc. Couldn't one argue that a double-slit single photon experiment is a detector of transverse scales? There might not be a single unique scale; there might be a distribution - in which case interference will still occur over a range of slit separations - but the existence of the distribution is interesting in and of itself, and so is the fact (if this interpretation it correct) that the photons in this case have transverse macroscopic physical dimensions. This passing through both slits at once issue becomes less so under these circumstances.

 

[ZapperZ]

Unfortunately, one needs to look at those papers cited by Edgardo VERY carefully to know what is the "wavepacket" being mentioned there. Keep in mind one very important difference here:

The "wavefuction" as obtained out of the Schrodinger equation is NOT the same "wave" that we describe light with! The schrodinger wavefuction exists in "configuration space", whereas the "wave" that we associate light with (as when you solve Maxwell equation) is a REAL wave. One can put an antenna or a pickup probe and literally see this oscillation.

Thus, it is STILL wrong to say that a photon is made up of wavepackets of light! No where in those papers will you see such a description. What is being done instead is to designate a photon as a "particle" similar to the way you solve the Schrodinger Equation for a "free particle". When you do that, you can see that you don't have any restriction on the "k" values of your solution. To make some form of "localization" of that photon, you make a superposition of wavefunction with different k. Using a priori knowledge of the source, one can make a reasonable guess at what k values one can use.

However, after you get such a "wavepacket", do you actually know the size of a photon? You don't. All the wavefuction that is represented by your wavepacket is saying is that if you make a single measurement, this is where you will find the photon. If you make another single measurement of the identical system, this is where you will find a photon... etc.. etc. In other words, the \Delta(x) is the SPREAD in the statistics of finding where that photon is! It does not correspond to the width of the photon anymore than the standard deviation of how often the number 3 comes up in a throw of a dice is the "width" of number 3!

As Mies van de Rohe used to say "God is in the details"...

Zz.

 

[markyannone]

One photon

Given the difficulty in sizing a photon, how can you send just one? The beginning is easily determined by the start of the event . . . but the end of the transmission? When is that?

 

[ZapperZ]

Given the difficulty in sizing a photon, how can you send just one? The beginning is easily determined by the start of the event . . . but the end of the transmission? When is that?

You let mother nature take care of it. Single photon sources basically are photo emitters that are "slow", or http://physics.nist.gov/Divisions/Div844/facilities/cprad/PhotonSource.htm" .

Zz.

 

[Chaos' lil bro Order]

Unfortunately, one needs to look at those papers cited by Edgardo VERY carefully to know what is the "wavepacket" being mentioned there. Keep in mind one very important difference here:

The "wavefuction" as obtained out of the Schrodinger equation is NOT the same "wave" that we describe light with! The schrodinger wavefuction exists in "configuration space", whereas the "wave" that we associate light with (as when you solve Maxwell equation) is a REAL wave. One can put an antenna or a pickup probe and literally see this oscillation.

Thus, it is STILL wrong to say that a photon is made up of wavepackets of light! No where in those papers will you see such a description. What is being done instead is to designate a photon as a "particle" similar to the way you solve the Schrodinger Equation for a "free particle". When you do that, you can see that you don't have any restriction on the "k" values of your solution. To make some form of "localization" of that photon, you make a superposition of wavefunction with different k. Using a priori knowledge of the source, one can make a reasonable guess at what k values one can use.

However, after you get such a "wavepacket", do you actually know the size of a photon? You don't. All the wavefuction that is represented by your wavepacket is saying is that if you make a single measurement, this is where you will find the photon. If you make another single measurement of the identical system, this is where you will find a photon... etc.. etc. In other words, the \Delta(x) is the SPREAD in the statistics of finding where that photon is! It does not correspond to the width of the photon anymore than the standard deviation of how often the number 3 comes up in a throw of a dice is the "width" of number 3!

As Mies van de Rohe used to say "God is in the details"...

Zz.

This might be a stupid question, but can you put a maximum contraint on the size of a photon?

 

[christianjb]

This thread seems a bit tense to me. Some people need to calm down.

I think part of the confusion is what do you define to be a photon? Is it the wave-function or is it the the result of a position measurement on that wave-function?

A photon is a point, in the sense that one photon can only set off one photo-multiplier at one point in space. However, the wave-function of a photon is presumably massively delocalized.

 

[ZapperZ]

This thread seems a bit tense to me. Some people need to calm down.

Note that this is a rather "old" thread, the last post was in Oct. 2006 before being resurrected today.

Zz.

 

[jackiefrost]

Having read through this whole thread with interest, please forgive me for keeping it alive when maybe y'all would rather it evaporate. I'm only (very slowly) working my way through classical electrodynamics ala Griffith and various other sources and I only know the very basics regarding QM. Having said that, my question is this: how should I blend the notion of a single photon in the QM sense while still regarding what I've learned about the electromagnetic field in the Maxwellian sense [and I probably make no sense ]? Thanks if anyone has a clue as to my confusion.

jf

 

[Mentz114]

Trying to define a size for the photon can lead to some weird conclusions. Consider a very high Q single mode cavity with a volume V, with a EM field inside that has the energy of just one photon. So far everything is classical. We introduce an atom into the cavity that has a suitable resonant transition, which absorbs one photon. At the time of the absorption, where was the photon and how big was it ? It must have been close to the atom one supposes. Classically energy was everywhere in volume, but in photon terms where was it before absorption ?

I'd also like to add that interference of light can be explained as a purely classical wave phenomemon with actual interference in normal 3D space, but interference of matter waves takes place in configuration space.

So the 2 slit experiment is not a good place to start.

 

[jtbell]

I'd also like to add that interference of light can be explained as a purely classical wave phenomemon with actual interference in normal 3D space,

Even at the level of single photons, going through the apparatus one at a time?

 

[christianjb]

Trying to define a size for the photon can lead to some weird conclusions. Consider a very high Q single mode cavity with a volume V, with a EM field inside that has the energy of just one photon. So far everything is classical. We introduce an atom into the cavity that has a suitable resonant transition, which absorbs one photon. At the time of the absorption, where was the photon and how big was it ? It must have been close to the atom one supposes. Classically energy was everywhere in volume, but in photon terms where was it before absorption ?

I'd also like to add that interference of light can be explained as a purely classical wave phenomemon with actual interference in normal 3D space, but interference of matter waves takes place in configuration space.

So the 2 slit experiment is not a good place to start.

OK, I need to learn something. What's the difference between 3D space and configuration space for one particle? Isn't configuration space of one particle just x-y-z?

 

[Mentz114]

jtbell

Even at the level of single photons, going through the apparatus one at a time?

There's probably no classical explanation for that, as you know, because the photon is not a classical concept. Even stranger is the Hong-Ou-Mandel experiment.

It seems though, that to model a single photon one needs a wave packet, which is a mixture of modes and seems a sort of compromise to get some kind of localisation.

Apart from the single-photon stuff, light only gets quantised when interacting with matter at which time it is also localised.

As has been pointed out already in this thread, there is no property of the photon which corresponds to the classical idea of 'size'.

Christian, I would say that configuration space never coincides with real space. Phase space and configuration space are ideas.