What is the quantum picture of laser field accelerating free electrons?

[gaiussheh]

Free electrons can not absorb photons. Otherwise, the 4-momentum will not be conserved. That is what I understood from the very first lecture of QED.

However, we do have the semi-classical picture for HHG - electrons are kicked out from the atom and get accelerated by the radiation field. I have no question about the classical picture with pondermotive force etc.

But really, how is this process possible in the photon picture?

My first thought is that electrons do not absorb photons after they are ionised - they only gain energy from Keldish ionization. But this is not possible for very large n - the electrons must have already been ionised at some point.

Also, the pondermotive energy looks strange from the photon perspective. if the maximum energy scale as $\omega^{-2}$, does that mean lower energy photons are way more likely (scale as $\omega^{-3}$) to be absorbed than higher energy ones?

 

[PeterDonis]

Free electrons can not absorb photons. Otherwise, the 4-momentum will not be conserved. That is what I understood from the very first lecture of QED.

Then your understanding was incomplete. A more complete statement would be: there is no process permitted by QED (even more precisely, in QED specialised to analyze scattering processes) in which the only external lines are an incoming electron, an incoming photon, and an outgoing electron.

how is this process possible in the photon picture?

Because "the photon picture" is not as simple as your (incomplete, see above) understanding is telling you. The process you describe is not a scattering process to begin with, so the correct version of what you were taught in the very first lecture of QED doesn't even apply. To the extent the process you describe can even be modeled using "the photon picture", the photons would have to be virtual photons, which correspond to internal lines in Feynman diagrams, not external lines in a scattering process.

The rest of your post simply compounds your basic error described above.

 

[gaiussheh]

Then your understanding was incomplete. A more complete statement would be: there is no process permitted by QED (even more precisely, in QED specialised to analyze scattering processes) in which the only external lines are an incoming electron, an incoming photon, and an outgoing electron.


Because "the photon picture" is not as simple as your (incomplete, see above) understanding is telling you. The process you describe is not a scattering process to begin with, so the correct version of what you were taught in the very first lecture of QED doesn't even apply. To the extent the process you describe can even be modeled using "the photon picture", the photons would have to be virtual photons, which correspond to internal lines in Feynman diagrams, not external lines in a scattering process.

The rest of your post simply compounds your basic error described above.

Sure, you have as many virtual photons as you want in your Feynman diagram, but in HHG, the photons are real photons from the laser, and they do get absorbed as you really get $n \hbar \omega$ energy?

 

[Vanadium 50]

Why are you bringing in virtual photons?

 

[Vanadium 50]

In fact, why don't you show us the calculation. Not an argument on what the calculation would show if you actually did it. Show us the calculation.

 

[PeterDonis]

in HHG, the photons are real photons from the laser

No, they're not. A laser does not emit photons. It emits a coherent state of the quantum electromagnetic field, which is not an eigenstate of photon number. This state interacts with the electron and gives it energy and momentum, but that interaction is nothing like "a free electron absorbing a photon".

 

[Vanadium 50]

I really would like him to write down equations - we have words, words, words, and they are all problematic. There are lots of misconceptions.

I hope a calculation will show the probelms, or if not, allow us to point to these problems.