M3L15s.txt

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In many situations, we may decide that the off shell
terms of the interaction just create level shifts,
Lamb shifts, Bloch-Siegert shifts,
and we may simply absorb those Lamb shifts
in our atomic energy levels, omega e and omega g.
So therefore, for the dynamic of the system,
if you include all those Lamb shifts
in the atomic description, we do not need those off shell,
counter intuitive terms.
These are actually also the counter rotating terms
in the semi-classical approximation.
We only keep the intuitive terms.
And that's called, again, the rotating wave approximation.
Just to remind you, we do not have rotating waves here.
Everything is operators.
But the same kind of physics, co- and counter-rotating,
appears here that we have four terms.
Two are the fully quantized version
of the co-rotating terms, and the other two, the off shell
terms, are the quantized version of the counter rotating term.
So therefore, if you neglect those two off shell terms,
we have now the fully quantized Hamiltonian in the rotating
wave approximation.
So let me just write it down, because it's also
a beautiful line.
We have the electronic system.
We have the interaction Hamiltonian,
which has now only two terms.
When we raise the atomic excitation,
we lower the photon excitation and vice versa.
And we have the Hamiltonian for the photon field a dagger a.
And this is apart from those Lamb shift terms,
the full [INAUDIBLE] description of the system.