M5L24k.txt

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Let me first give you a drawing which
may illustrate or summarize what I've just said.
So what we try to understand is, what happens
when we detune the probe laser.
And until now, we had always the EIT feature.
The EIT window, was completely overlapping
with the one-photon resonance.
But now, because the laser, the coupling laser,
has a detuning of gamma two, we have
to use with the probe laser-- so the Raman detuning was big
Delta two minus big Delta one.
And if the detuning Delta is chosen to be Delta two,
we have the simple situation that we
go from the ground state right to the excited state.
And we have the feature which has a width of gamma.
This is what you would call the single-photon resonance.
It is the single-photon resonance.
It is [? due ?] by resonantly coupling into this continuum.
And the only feature of the coupling laser
is that there is an AC Stark shift to it.
Now, we have a second feature which can be very sharp.

This is when we do the two-photon Raman process
into the other ground state.

Due to photon scattering, this resonance
has a width of gamma scattering.
And the position is not at zero at the naked Raman resonance.
It also has an AC Stark shift.
Because the coupling laser does an AC Stark shift
to both the excited and the ground state.
The coupling laser, the AC Stark shift
pushes ground and excited state in opposite directions.
So therefore, we find that at the Rabi frequency
of the coupling divided by gamma over two.
So the name of this feature is the two-photon Raman resonance
plus the AC Stark shift.
Which actually means it's a four-photon process.

The questions is now, where is the electromagnetically induced
transparency?

We have introduced now, specifically, the absorption
feature.
We have identified a one-photon absorption feature
plus AC Stark shift, a two-photon absorption
feature plus AC Stark shift.
But where is electromagnetically induced transparency?

Here-- electromagnetically induced transparency
is always at delta equals zero.
You have to fulfill the Raman resonance.

And this resonance is not affected by any AC Stark shift.
So it's always at delta equals zero.
So therefore, what that means is,
you have two absorption features.
And you would think these are two Lorentzians.
But they interfere and they go to exactly zero
at delta equals zero.
And this is our EIT feature.
So there is an interference effect between a broad feature
and a narrow feature.
And this is found in many different,
I want to say parts of spectroscopy.
But you also find it in nuclear physics
whenever you have a narrow feature embedded
into continuum.
What we have here is a narrow feature and, well,
a broader feature.
But a narrow feature in something
which is broader or continuum is called a funnel resonance.
You actually have the same situation
when you look at scattering of atoms.
Many of you are familiar with Feshbach resonances.
Well, a lot of people call it funnel Feshbach resonance.
And what you have is, in a funnel Feshbach resonance,
is two atoms can scatter off each other.
This is sort of the continuum.
This would be your broad feature.
But then they can also scatter through a molecular state.
And this is a narrow feature.
And what we have identified now, for electromagnetically
induced transparency, are the two features.
One is the single-photon absorption.
One is the Raman resonance.
But in general, the concept is much more general.
You have a narrow feature.
You have a broader feature.
It's responsible for scattering two atoms.
Or it's responsible for scattering a photon.
And once the photon or the atoms have been scattered,
you have no way of telling which intermediate state was
involved.
And therefore you get interference.
And what I just said, what is EIT for light,
is the zero crossing over scattering lengths
that the atoms do not scatter of each other.
Because the two different processes complete
the destructively interfere.
OK, so what I've shown here is sort of two
Lorentzian, two absorption, features.
Let me now replot it and plot the index
of refraction minus one.
Here was EIT, zero detuning.
We have the sharp feature here at the two-photon resonance.
We have a broad feature here at the single-photon resonance.
And if I now transform the Lorentzian
into a dispersive feature-- well, I use freehand.
So this is the dispersive feature
for the broad transition.
The narrow transition has a much, much sharper
dispersive feature.
And the important part is now at the EIT,
at the condition delta.
At the detuning delta is zero, where
we have electromagnetically induced transparency.
We have an index of refraction which is exactly one.
Because it's a dark state.
You have no absorption.
You have no light scattering.
You have no reaction to the light.
And therefore, the index of the refraction of the material
is like the index of refraction of the vacuum.
So you have n equals one.
It looks like vacuum in terms of index of refraction.
It looks like vacuum because you have no absorption.
But what you have is, you have a large derivative
of the index of refraction with the frequency detuning.
And that affects-- and that's what
I want to tell you now-- the group velocity of light.
So anyway, this is maybe as far as I want to push it.
And I was actually wondering if this is a little bit too
complicated to present in class.
But on the other hand, I think it's sort
of also wraps up the course.
We have with three-level system.
And we find a lot of things we have studied separately before,
two-photon Raman feature, single-photon light scattering.
But now they act together, and they
interfere, and have this additional feature