What causes the collective emission in Dicke Model? Dicke model is a collection of two level atoms prepared in the excited state, when the wavelength of the light absorbed or emitted is very large compared to the distance between the atoms, the rate at which radiation emitted is proportional to $N^2$. My question is if we have a collection of $N$ atoms, if they independently emit radiation the maximum radiated intensity goes as $N$.  In Dicke model, there is no interaction between atoms, all $N$ atoms interact with common light field only.  How does the $N$-atoms emit collectively?
 A: I have a bit of intuition for some of these concepts, so maybe this will help a bit.
First let's start with collective absorption. If you have a cluster of atoms that are close together, and you send a single photon into this collection. Only a single photon can get absorbed a single atom. But the photons wavefunction spatially overlaps with multiple atoms. What happens is that you end up with a wavefunction of all the different possibilities of exactly one atom each absorbing a photon. so you a superposition of all of the configurations of individual states where exactly one atom absorbed a photon: $|0\rangle |0\rangle |0\rangle |0\rangle ... |1\rangle ... |0\rangle$
If you send a second photon into this, there's a chance that the 1 states will emit a photon through stimulated emission. In the circumstance that stimulated emission is created because the photon that triggered the emission talks to all of the atoms simultaneously, and they each have a component of having absorbed a previous photon - they can all emit their probability simultaneously.
Now why is the collective emission enhanced when more atoms are added? I think it's just that it increases the chance of interaction (more atoms means you have more shots to interact with an atom), and when they are bunched together, this behavior happens simultaneously and they interfere constructively.
