M5L23e.txt

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For pedagogical reasons, I will drop
all the assumptions I'm making now, but let me make them.
So let's discuss degenerate states first.

So g and f are degenerate.
And let me also discuss blue-detuned light.
And you will see in a moment why.
And let's set up this equation.
We have the stage g, f, and e.
We have a green laser beam and an orange laser beam.
And we know already from what we have just
learned that this should be transformed into--
and let me just be more specific here.
I said I want to use blue-detuned light.
So now we do what we just learned.
We're expressing as the dark state and the bright state,
and here we have the excited state.
And the beauty of degeneracy is the dark state
and bright state are superposition states,
but since it's superposition states
of two states with the same energy,
I can draw them without twisting my hand
or doing sort of a double line.
Anyway, but now what happens is the following.
The bright state is coupled to the excited
state by the two laser fields.
And the question is, what is the energy of the bright state
relative to the dark state.
Well, if I have a blue-detuned laser beam,
I get an AC Stark shift, which increases the energy.
So therefore, the state which sees the light which
scatters photons, scattering photon
beams, there is an excited state mixture.
An excited state mixture means there's an AC Stark effect,
and the AC Stark effect is positive.
So therefore, the dark state is the uncoupled state,
is the lowest state in the ground state manifold.
And even if you would not generalize it
to multiple levels and all that, if there is one dark state,
it's not upshifted by the AC Stark effect,
whereas every state which sees the light
is upshifted by the AC Stark effect, which
provides a blue shift.
So the dark state is the lowest quantum state.
So therefore, we can now use the general concept
in quantum mechanics of adiabatic state transfer
to achieve a perfect 100% transfer from one ground
state to the other one by tailoring as a function of time
our laser fuse as follows.
We start out in a situation where
the only beam which is on this-- I
want to change that to orange.
Yeah, it's the orange laser.
And when the orange laser is on, and then the dark state is g.
Then we then down the orange laser,
but we ramp up the green laser.
And we have the situation that initially g
and eventually f is the dark state.
So this is the picture behind the rapid adiabatic passage
from state g to f.
I want to point out that the application of the two laser
pulse, first orange and then green,
is called the counter-intuitive sequence.
Because if you asked yourself the problem,
you started out in state g, and you want to go over to state f.
Which laser would you first switch on if you're in state g?
Well, if you want to get out of state g,
you would say first the green laser
to go up and then the orange laser to go down.
So what I just said, first the green and then the orange,
is called the intuitive sequence.
But STIRAP works with a counter-intuitive sequence.