M1L1c.txt

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The next thing I want to discuss is the analogy-- but also
the differences-- between an harmonic oscillator
and a two-level system.

So, what is a two-level system?
Well, it's a system with two levels.
What is an harmonic oscillator?
Well, it's a system which has an infinite number
of equidistance levels.

I will tell you later in this course, when
we talk about the AC and DC Stark Effect,
when we talk about the polarizability and light
scattering, that you can regard the atom-- or the electron
in the atom-- as an harmonic oscillator.
An atom scatters light exactly in the same way
as a charge, which is connected to some support
structure with a spring, how a charge-- how an oscillating
charge-- would scatter light.
Well, you know of course, the atom is a two-level system.
And, this sort of model I make for the electron
as an harmonic oscillator, at a single resonance frequency.
Which is 100% exact in the limit of low laser power.
Well, this realizes an harmonic oscillator.
So, therefore, what I'm telling you,
by this example, that there are situations
where a two-level system and an harmonic oscillator
are the same.
Or, create the same observance.
Create the same physics.
Do you have any idea when the two systems may look the same?
Or, when the two systems react exactly in the same way
to-- for instance, external radiation?
I'd like to give you the answer before I give you
the full explanation, which now comes.
If you start out in the ground state,
you can see at zero temperature, we
have mainly all of the population there.
If you start now driving the system,
we put-- and I will say a bit more about it--
a little bit into the excited state.
But, it is the nature of an harmonic oscillator,
when you put something into the excited state,
that immediately, a little bit, goes
into the second excited state.
And, this is of course something which you can only do
in an harmonic oscillator, but you cannot do a level system.
So, to the extent that we have weak excitation,
and we can neglect the excitation in higher
levels, to that extent a two-level system
and harmonic oscillator are identical.
Actually, what I'm saying appears trivial,
but I really want you to think about it.
It's actually a very profound statement
that when can you describe the quantum mechanical system
as an harmonic oscillator?
For weak excitation, then all of what matters
is that you have put a small fraction of the system
to the first excited state.
And, you immediately realize that the feature which
distinguishes the two-level system
from an harmonic oscillator, is the phenomenon of, let's say,
saturation.
You cannot go higher.
If you do not saturate a two-level system,
it behaves like an harmonic oscillator,
and therefore, it behaves completely classical.