In which QED limit are Einstein's rate equations for transitions in atoms valid?

Question

I guess one has to assume low intensities? What are notable differences in a full quantum treatment?
I'm familiar with the semi-classical theory of atomic transitions (coupling classical field to quantized atom), but don't know anything about quantization of the EM field. I'm mostly interested in the consequences, no exhaustive calculations are needed. I only found confusing literature, which is beyond my scope for now.

Andrew · Answer

Einstein's argument is that in thermal equilibrium, there must be detailed balance between stimulated emission, stimulated absorption, and spontaneous emission. So long as these are the only processes describing interactions between light and the material of interest, detailed balance must hold in equilibrium.
I suppose if you look at frequencies of light away from absorption lines the detailed balance argument becomes vacuous (ie, stimulated emission and absorption will vanish). And, I suppose if you look at very high frequency light (gamma rays) you may have to worry about exciting nuclear states.
But otherwise this argument is extremely powerful and will always work so long as you are balancing these three processes.
"... if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation." - Arthur Eddington

In which QED limit are Einstein's rate equations for transitions in atoms valid?

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