Analytical proof of LASER production

[SteveHowe73]

TL;DR Summary

A question on the analytical proof on LASER production, perhaps using Feynmann diagram.

Is there analytical proof that a photon Pe will be emitted by an excited atom Ae when another photon Pp of the same frequency is passing by Ae in LASER production? I tried using Feynman diagram to show a high probability of this event. I failed (most likely because I am not an expert in QFT), perhaps due to my misconception that Pp does not interact with, but rather just passes by, Ae. If the proof exists (I believe it does), I would highly appreciate it if you can provide me with the citation.

 

[DrClaude]

This should be covered in any book on advanced QM or on Quantum Electrodynamics. For instance, see section 14.7 in Townsend, A Modern Approach to Quantum Mechanics.

When deriving the coupling between atoms and the electromagnetic field, one finds a term $\sqrt{n_{\mathbf{k},\lambda }+1}$ in the emission rate of the atom for a photon of wave vector $\mathbf{ k }$ and polarization $\lambda$, with $n_{ \mathbf{ k } , \lambda }$ the number of photons already in that mode. In other words, the emission rate increases with the presence of photons of the same mode in the EM field, which is what we call stimulated emission.

 

[SteveHowe73]

Thanks a lot.

 

[bob012345]

This was predicted by Einstein starting in 1916 decades before the Maser or Laser. If you want to get into the details here is a MIT open course Quantum Physics III, where lecture 12 goes through atom/photon interactions. There are five parts to lecture 12.

https://ocw.mit.edu/courses/8-06-qu...-lectures/time-dependent-perturbation-theory/