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M5L24j.txt
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M5L24j.txt
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#
# File: content-mit-8-421-5x-subtitles/M5L24j.txt
#
# Captions for 8.421x module
#
# This file has 99 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------
Let's now go to the more interesting case
that we have a coupling laser.
What happens now?
We have our two states.
The excited state is coupled with the laser and Rabi
frequency omega two.
Now we know that the laser omega two, if it is not on resonance,
will give us an AC Stark shift.
This AC Stark shift is, we've gone through that several
times, is the matrix element , or Rabi frequency squared,
divided by the detuning.
If we now bring in the probe laser,
what are the features we expect?
Well, there are two features.
One is, we've just discussed, the trivial case above.
If you tune to probe laser into resonance with the excited
state, we have single-photon absorption.
We get a broad feature.
It's almost like in a two-level system.
But in contrast to the case I just discussed above,
the excited state level E has now an AC Stark shift.
So the resonance is shifted.
That's now becoming a four-photon process.
Because we need two photons going up and down
with a coupling laser to create the AC Stark shift.
And now we have a laser from the probe beam.
And the photon is scattered.
So it's a four-photon process.
and it will give us a broad resonance,
which is now AC Stark shifted.
But in addition, we have a resonance,
which is the Raman resonance.
When the Raman detuning is zero, then we
absorb from the probe laser and we
emit in a stimulated way with the coupling laser.
And we have a stimulated two-photon transition.
Now, what is the Ritz of this stimulated two-photon
transition?
Well, we go from a stable ground state
to-- I wanted to say another stable ground state,
but this other stable ground state
is now scattering photons.
So because of the presence of a strong coupling laser,
you have broadened this level F by photon scattering.
You interrupt the coherent time evolution
by scattering photons.
And the photon scattering happens in perturbation theory
by the amplitude to be in the excited-- I need a little bit
more room-- the amplitude to be in the excited state
squared times gamma.
So, the scattering rate gamma scattering
is Rabi frequency divided by detuning.
This is the amplitude to be in the excited state.
We square that, and then we multiply with gamma.
And if I can trust my notes, as a factor of 2,
which I don't want to discuss further.
This is a qualitative argument.
The analytic expressions are in the reference
I've given to you.
So the situation which we have right now
can be, in a very powerful way, summarized as follows.
We have our ground state.
We have two continua we can coupling to.
We can couple to the excited state, which
has a Ritz gamma, through a single photon,
but there is the AC Stark shift.
Or we can couple through a two-photon Raman transition
to the state F. But the Ritz is much, much smaller.
Because it is only the scattering rate due
to the off-resonant coupling laser.
So G couples now to a narrow and a wide, well, excited state.
One excited state, of course, is the state F.
But the coupling laser puts some character of the excited
states into the state F.
And the most important thing now is the following.
And this is sort of the theme I've
emphasized again and again when we discuss three-level systems.
Those two states have a Ritz.
And the Ritz means, they spontaneously emit light.
But they emit light into the same continuum.
So if you start in the ground state.
Your probe laser has a photon, and the photon gets scattered.
You do not know for which channel it has been scattered.
So in general, and this is sort of as far as I
want to push it in this class.
In three-level system, we have now the interference
between those two continua.
One is narrow and one is wide.
So let me just write that down because this is important.
But both excited states couple to the same continuum.
And by continuum I mean the vacuum of all empty states
where photons can be scattered.
And this is the condition for interference.
And this is, of course, what gives rise
to electromagnetically induced transparency.