Does a single photon have a wavelength?

  • #1

Main Question or Discussion Point

I may be mixing things up terribly, but since the energy of a photon (or any particle for that matter) is related to its frequency, does a single photon have an associated wavelength and energy, or do those terms make sense only when considering a stream of particles?
 

Answers and Replies

  • #2
f95toli
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Yes, sort of.
In experiments in e.g. cavity Quantum electrodynamics single (or a few) photons are routinely trapped in high-quality microwave cavities. These cavities are designed using "classical" physics, meaning the distance between the walls on is e.g half a wavelength. Hence, there is some correspondence between the classical notion of a wavelength and QED in this case.
Note that the field is in a number state, meaning one can really talk about a definitive number of photons (i.e. it is not just a case of the intensity being very small).

It is perhaps worth mentioning that it IS possible to quantize a cavity (and more generally a transmission line) meaning a "pure" QM description is possible, but the resonance conditions are -not surprisingly- the same in the both the QM and classical description.
 
  • #3
clem
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I may be mixing things up terribly, but since the energy of a photon (or any particle for that matter) is related to its frequency, does a single photon have an associated wavelength and energy, or do those terms make sense only when considering a stream of particles?
Yes. It's energy, frequency and wavelength are related by:
E=hf=hc/lambda.
 
  • #4
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I Bragg-diffracted a few x-rays per hour in my Ph.D. thesis, and counted them individually in a sodium-iodide detector. So wavelength is a property of individual photons. Also, there was no obvoius correlation of "streams of photons".
 
  • #5
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The diffraction pattern shows up when a lot of photons are measured. I don't think the wavelength of a single photon has ever been measured before. So all this is just "quantum fairy tales"
 
  • #6
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The diffraction pattern shows up when a lot of photons are measured. I don't think the wavelength of a single photon has ever been measured before. So all this is just "quantum fairy tales"
The temperature of the Sun's interior has never been directly measured using a thermometer either.
 
  • #7
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If you think it's just "quantum fairy tales", how do you explain that the results persist when individual particles are sent through the apparatus one at a time?
 
  • #8
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If you think it's just "quantum fairy tales", how do you explain that the results persist when individual particles are sent through the apparatus one at a time?
But each individual particles do not show interference pattern, interference pattern only show up as more particles arrive, so you can't say that each individual particles have definite wavelength
 
  • #9
f95toli
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The diffraction pattern shows up when a lot of photons are measured. I don't think the wavelength of a single photon has ever been measured before. So all this is just "quantum fairy tales"
As I pointed out above: In cavity QED single photons are trapped in resonant cavities; and the resonance condition is just lambda/2. If you send in photons of other energies they just decay immediately.
I'd say this is a pretty good way of measuring wavelength (adjusting the length of a resonator while looking for a resonance is a pretty common technique for measuring wavelength in microwave engineering, this is essentially the same thing).
 
  • #10
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But each individual particles do not show interference pattern, interference pattern only show up as more particles arrive, so you can't say that each individual particles have definite wavelength
In a sense. You can't say you've ever measured the wavelength of an individual photon in such an experiment. But can you provide an explanation of Bob S' PhD without reference to this idea?

If you want to attribute wavelike behaviour to the aggregate of photons rather than them individually, you'd have to espouse a principle by which the dynamics of a photon going through the apparatus now can be influenced by the presence of those going through the apparatus half an hour later. Do you really want to do that?

Furthermore, suppose you send a single electron through a two-slit setup. Just one, before you pack up and go home. It won't straight go through the slits like a bullet, but will travel to a region of your detector associated with one of the predicted interference fringes, most probably the one in the middle of the screen. How would you describe that trajectory without reference to some kind of diffraction effect?
 
  • #11
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The energy of the quanta of a given field is given by the frequency of the field itself, which is indeed periodic as long as it does not interact exchanging. However the concept of single particle, especially for the photon whose Compton wave length is infinity, is not not correct. A field in the quantum limit is a stream of particle.
 
  • #12
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The diffraction pattern shows up when a lot of photons are measured. I don't think the wavelength of a single photon has ever been measured before. So all this is just "quantum fairy tales"
Not quite true. If a crystal diffraction (or reflection) spectrometer crystal is "rocked" over a narrow x-ray line, the rocking curve is a few seconds of arc wide, independent of the x-ray intensity. Because the Bragg angle is directly related to the x-ray wave length, single photons all exhibit the same wavelength, independent of counting or accumulation rate.
 
  • #13
The diffraction pattern shows up when a lot of photons are measured. I don't think the wavelength of a single photon has ever been measured before. So all this is just "quantum fairy tales"
Imagine this. I shoot a photon at your head. It is emitted back to me. So, I give it more energy. It still gets reemitted. So, I take a bigger machine and I shoot a very high energy gamma ray photon at you. It penetrates your body this time. How come? I gave the photon more energy, and so it was able to penetrate smaller spaces.

The diffraction pattern is not seen when a single photon is emitted because by definition the diffraction pattern is a pattern, and can not be seen from one particular outcome. However, its trajectory is still determined by probabiliy, which means that a wave function must be present, which means that wave interference is not neglegible.

BTW, I was just kidding about shooting you in the head with a photon. :smile:
 
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  • #14
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If a single photon has a wavelength, would it violate Heisenberg Uncertainty principle?
Since photon is a particle, that means it can be represented by a wave packet. But wave packet can not have definite wavelength, only pure wave can have wavelength
 
  • #15
If a single photon has a wavelength, would it violate Heisenberg Uncertainty principle?
No, of course not.

"Since photon is a particle, that means it can be represented by a wave packet. But wave packet can not have definite wavelength, only pure wave can have wavelength."

Are you trying to say that a particle's wave packet is poorly defined, or doesn't exist?
 
  • #16
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No, of course not.

"Since photon is a particle, that means it can be represented by a wave packet. But wave packet can not have definite wavelength, only pure wave can have wavelength."

Are you trying to say that a particle's wave packet is poorly defined, or doesn't exist?
A particle's wave packet is well-defined, it's just the sum or superposition of many pure wave,
So it can not have a single wavelength, like a square-wave does not have wavelength. If the wave packet does not have a definite wavelength, then how can a particle have wavelength?
 
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  • #17
A particle's wave packet is well-defined, it's just the sum or superposition of many pure wave,
So it can not have a single wavelength, like a square-wave does not have wavelength. If the wave packet does not have a definite wavelength, then how can a particle have wavelength?
The wavelength is not a pure wavelength for a wave packet. It must be a range of wavelengths, because the wavelength varies over the distance of the wave packet. The range in wavelength corresponds to the range in energy, since the energy of a particle cannot be definitely determined (the velocity of the particle is never knwon to 100% accuracy). So, the wavelength is ill-defined, yes, but that does not discard its existence. I could find a mean wavelngth, could I not?
 
  • #18
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Yes a single photon has a precise wavelength and energy. A single photon is a particle not a wave-packet. A single photon moves at the velocity c.
 
  • #19
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"....does a single photon have an associated wavelength and energy"

Of course it does. otherwise it would not "know" what color it should be....would a single photon radiated from a star through a gravitational field change frequency and wavelength...would it be red shifted??? Of course....

It would be strange indeed if two (or more) photons had different properties when traveling together relative to traveling separately....

Can you imagine how confusing it would be to identify particles if they changed their nature every time another particle was nearby???? That would be one crazy universe and we would not be here....
 
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  • #20
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A field is has a given wavelength as long as it does not interact. The quanta related to this field has momentum given by the wavelength of that fields times the planck constant. Thus to quanta with the same momenta it is associated a wavelength. However the number of quanta is not an observable since it is not well defined for distance smaller that the Compton length.
 

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