M5L22s.txt

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Let me connect special effects in a three-level system
to something which is very basic.
And you've heard about it.
And this is optical pumping.
So if you set up a system which has a ground-- two ground
states, g and f, you may just think
about two hyperfine states in your favorite atom.
And then they are only coupled through an excited state.
You can now drive the system with laser fields
omega 1 and omega 2.
And we also use that example of optical pumping
to introduce some notation which I
will need to describe the system with a few equations.
So we will use energy level diagrams.
And the energy is referred to the lowest ground state,
so here we have an energy splitting which is omega gf.
And the excited state has a splitting of [? eg ?].
We will call the photons in one laser
the photons created and annihilated
with the operator [INAUDIBLE].
And for the photons for the other laser beam, we use c or c
[? dega. ?]
Now, there is a very simple solution
for this situation, a very simple equilibrium situation
if you have only one laser beam.
If you have only one laser beam, omega 1 or omega 2,
well, it's clear what happens is if you have only one laser
beam-- let's say omega 1-- it doesn't
talk at all to the atoms in the state f.
They are left alone.
But the atoms in this state g are
excited to the excited state.
And then there may be a certain branching ratio
for fluorescence.
Spontaneous emission, but let's rather
call it fluorescence to photon scattering.
So there may be a branching ratio to go back to that state,
or to go to the state f.
If the latter happens, the atom doesn't interact
with the laser light anymore.
If it goes back to the original state,
the atom will try again and again until, after a while,
all the atoms have optically pumped into the state f.
And the same would happen if you have a laser omega 2.
Then you would pump all the atoms into the state g.
So if you have only one laser beam omega 1 and omega 2, then
an equilibrium, the equilibrium population
is 100% of the atoms in state f or g respectively.
And this is nothing else than the phenomenon
of optical pumping.