M5L25j.txt

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Let's maybe try to shed some light on it.
One way how you can intuitively learn this in superradiance
is really with a classical antenna picture
that you have n spins, which form a macroscopic dipole
moment which oscillates.
And this is a very nice picture to understand the n times
enhancement when we have half of the atoms excited,
and the other half de-excited.
Let me now give you a nice argument
which explains why a single excitation in the system
now leads to an n times enhanced decay.
The situation is that the initial state
for this last photon is we have an excited atom,
and all the atoms are in the ground state.
However, we could also have, in this nomenclature,
the second atom excited, or we could have the third one
excited, and so on.
So therefore what we have is because we
are in the left-most Dicke ladder, which has the maximum S
spin [INAUDIBLE] number of n over 2,
that means everything is fully symmetrized so therefore we
have to fully symmetrize by summing over the n
possibilities.
And our final state is, of course, the fully symmetrized
count state.
And now you'll realize that you have
a coherent summation over-- you have n contributions.

So therefore the matrix element has n contributions
compared to single atom.
The normalization is only square root n,
so therefore the matrix element is square root n times larger
than for an atom.
So by simply having one atom excited and n
minus 1 atom not excited, but if you now
have the fully symmetrized state,
you don't know for fundamental reasons which atom is excited.
Tou have a superposition state where the excitation can
be with either of the atoms.
This state, which has a single [INAUDIBLE]
of excitation radiates n times faster than a single atom
would.