M5L22q.txt

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Now we are ready to do the next step,
namely to talk about coherence in three level systems.

And if we had three levels, we could think about it--
we have terms which connect kind of level one to two,
level two to three, and level three to one
in all possible ways, but that's not
what we want to assume here.
The situation where we can discuss some fundamentally new
effects is when we have two states connected
through a third state.

In other words, if you have two levels,
we are not allowing any transition matrix element
connecting the two, they are only
connected through a third state.
This is for obvious reasons called the lambda-type system.
You can turn it upside down and you have the v-type system.
Or if the intermediate state is between the first
and the second state, you have a ladder type system.
But once you start driving it, it may not really matter.
There may be a dressed atom description
where if you drive two states coherently in the dressed atom
picture, you've degeneracy between this level
and one more photon in this level.
And then in the dressed atom picture,
which includes a number of photons,
the two levels have become degenerate.
So therefore, it's very important
for practical applications or how
to implement it in an atom, what kind of system you have.
But for the description of those systems,
some of the differences may simply
disappear if you formulated in the dressed atom basis.
Of course, there is an important practical reason.
Usually the lower states are ground states,
the upper states are excited states.
And here you have the opportunity--
and that's why the lambda-type system is the most important
one-- to have some coherent superposition mediated
by the third state.
And the coherent superposition is stable,
because it's equivalent to a position of ground states.
If any form of coherent superposition
involves an excited state, then you have short lived states