Question

“Fundamentalrelation of Resonance Fluorescence” - How can it be?

Answer 1

This formula is derived making some assumptions on the frequency of the fields (resonant fields, and the rotating wave approximation for interactions with the atom), and only holds if it acts on a state that evolved from the starting state |0⟩|g⟩|0⟩|g⟩.

Answer 2

Hello mate here is your answer.

In my quantum optics lecture, I was given the formula:

d⃗ egE⃗ ^(+)=iκℏ2|g⟩⟨e|d→egE→^(+)=iκℏ2|g⟩⟨e|

Here, d⃗ eg=⟨e|d⃗ ^|g⟩d→eg=⟨e|d→^|g⟩ is the dipole matrix element of the dipole operator d⃗ ^d→^, acting solely on the "atom" part of the Hilbert space, spanned by |e⟩|e⟩ and |g⟩|g⟩. E⃗ ^(+)E→^(+) acts solely on the field part of the Hilbert space. This formula is derived making some assumptions on the frequency of the fields (resonant fields, and the rotating wave approximation for interactions with the atom), and only holds if it acts on a state that evolved from the starting state |0⟩|g

Hope it helps you.