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Apr
17
awarded  Popular Question
Feb
17
accepted Exact meaning of “pi/2 pulse”
Feb
4
comment Atom - light field coupling and emission process
One thing that troubles me is the following: if I'm off resonance, there is still coupling of all the modes of the light field, and therefore "emission" and "population" of the corresponding modes/Fock states, right?
Feb
4
comment Atom - light field coupling and emission process
@Emilio - I understand that. It's just that my understanding of what a photon is, or rather, how it is modeled in QFT, is ... different than the "particle" I had in mind before. It seems almost useless to speak of a "photon" anymore in QFT, except if talking about a single mode of the light field maybe? The reason being that what's emitted in a transition is actually a linear superposition of Fock states. We could call that "photon" if we wanted to, but it doesn't seem useful.
Feb
4
comment Atom - light field coupling and emission process
@Emilio - so would the emitted photon be representable as a wave packet, involving the frequencies of all the modes? Further, is that equivalent to a linear combination of Fock states, one for each mode, or am I off base here (I am a beginner in a quantum optics class).
Feb
4
revised Atom - light field coupling and emission process
added 51 characters in body; edited title
Feb
4
comment Atom - light field coupling and emission process
@CuriousOne - how about we couple the atom with the vacuum state of each mode? That is, we would be looking at spontaneous emission. I am trying to understand what is emitted: a photon in each mode, or a single photon in a single mode? There has to be conservation of energy, for starters.
Feb
4
revised Atom - light field coupling and emission process
added 66 characters in body
Feb
4
asked Atom - light field coupling and emission process
Feb
4
comment Quantized light-atom Hamiltonian
Just FYI, I'm going to open a separate question centered on coupling/population of modes/Fock states. I am quite confused there.
Feb
4
comment Quantized light-atom Hamiltonian
@Mark - thanks a lot for these insights. My problem, I guess, was the summation in $\hat{H}_I$, which led me to think that all modes coupled to the atom. Am I understanding correctly that all the modes enter into the composition of the wave packet emitted?
Feb
4
comment Quantized light-atom Hamiltonian
@Mark - Daniel has an interesting comment below, that you cannot emission into an off-resonance mode, because that wouldn't conserve energy. I was imagining there could be emission of a photon in any mode, albeit with a low probability, but it seems it's more complex than that.
Feb
4
accepted Quantized light-atom Hamiltonian
Feb
4
comment Quantized light-atom Hamiltonian
Thanks! You provided a lot of good explanations here, I think I am very happy with this answer.
Feb
4
comment Quantized light-atom Hamiltonian
Thanks for all the details - I find your last comment very intriguing though - There is even more than I thought there was to it! Is there a good text somewhere that I could read, covering off-resonant mode virtual emissions?
Feb
4
comment Quantized light-atom Hamiltonian
In the case of a coherent state of the field coupling with a 2 state atom, each Fock state couples to the atom, and that's what explains the collapse/revival of the Rabi oscillations, isn't it?
Feb
4
comment Quantized light-atom Hamiltonian
In other words, your approximation has removed the summation over the k modes, but that summation is more precise and shows that even in case of detuning, there can be absorption/emission of photons, albeit with a lower probability?
Feb
4
comment Quantized light-atom Hamiltonian
Hmmm - so the coupling of a single mode is just a result of an approximation, but fundamentally, all the modes do couple with the atom, with various strengths, right?
Feb
4
comment Quantized light-atom Hamiltonian
With $\hat{H}_I$ in "my" form, you get four products of operators, of which you can eliminate too on physical grounds of non-conservation of energy. It skips the rotating wave approximation, and feels more elegant to me :-) (I didn't invent anything of course, it's a presentation in a quantum optics class)
Feb
4
revised Quantized light-atom Hamiltonian
added 5 characters in body