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M5L24n.txt
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M5L24n.txt
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#
# File: content-mit-8-421-5x-subtitles/M5L24n.txt
#
# Captions for 8.421x module
#
# This file has 155 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------
Let me just say a few words about the fact
that we have a large derivative of the index of refraction.
This, of course, is used for generating
what is called slow light.
The group velocity of light is the speed to light,
but then it has a denominator which
is the derivative of the index of refraction
with respect to frequency.
And towards the end of the last century,
there were predictions that electromagnetically-induced
transparency would give you very sharp features which can
be used for very slow night.
And what eventually triggered major developments in the field
was this landmark paper by Lene Hau where
she used the Bose-Einstein condensate to eliminate
all kinds of Doppler [INAUDIBLE].
There are other tricks how you can eliminate it,
but this was the most powerful way,
to just take a Bose-Einstein condensate where
atoms have no thermal velocity.
And in this research, she was able to show
that light propagated at the speed of a bicycle.
So it was a dramatic reduction of the speed of light,
and this showed the true potential of EIT.
There have been other demonstrations
before where light has been slowed by a factor of 100
or a few hundred, but eventually combining
that with a Dopplerless feature, because the atoms don't
move, in the BEC it created a dramatic effect.
So we have now two ways how we can get a large derivative,
d and d omega.
I've discussed here the general case,
that we have a narrow feature, a broad feature, because we
have the coupling light detuned form the excited state.
But let me just point out that even if you have the coupling
light on resonance, you can actually get an even--
it depends what you really want, but you
can get an even stronger feature in the index of refraction
versus frequency.
This is now the situation where we have the strong absorption
feature.
But then we have the EIT window.
So we have this superposition of a positive Lorentzian
and a negative Lorentzian.
And if I now run it through my [INAUDIBLE] calculator
and I take the dispersive shape, I
can sort of do it for the broad feature in this way,
and for the narrow feature in this way.
And now you have to add up the two.
And what you realize is, at this point,
you have a huge d and d omega.
So what I'm plotting here is on the left, the absorption
of the Lorentzian, and you can regard this sharp nudge
as a second Lorentzian.
So you have the positive Lorentzian, negative
Lorentzian, and then you take the dispersive feature
and you add them up with the correct sign.
So whether you are-- you're just realizing now
for quite general situation whether you have
a single photon detuning, which I discussed before,
or whether you are on the single photon resonance,
you can have extremely sharp features.
So now you can take it to the next level.
You have a light pulse which enters the medium,
and now the light pulse slowly moves through the medium.
But while the light pulse moves through the medium,
you reduce the strengths of the coupling laser.
What happens?
So you do now an adiabatic change of your system.
You do an adiabatic change of the control field, omega 2,
while the probe pulse is in the medium.
Well, that means that under idealized conditions--
assumptions which we have discussed,
this feature gets narrower and narrower and narrower.
If omega 2 goes to 0, the control field,
the strengths of the control field,
this feature becomes infinitesimally narrow.
And therefore, this feature becomes infinitely sharp.
And that means that the group velocity goes to 0.
And this is now-- well, in the popular press it's called
stopped light or frozen light because the light has
come to a standstill.
Well, what really happens is the following.
We have our coupling laser, omega 2,
and we have our probe laser, omega 1.
When we do what I just said is that omega 2 goes through 0,
then the dark state-- originally for very strong omega 2,
remember the dark state for very strong omega 2,
the dark state was g.
But now if we let omega 2 go to 0,
the dark state will become f.
And that means that, in a way, every photon in the probe pulse
has now pumped an atom from g through to photon [INAUDIBLE]
process into f.
So therefore, what it means to stop light
or to freeze light means simply that the photons of the laser
have turned into an atomic excitation,
an atomic excitation where the excitation is now the state f.
In other words, you've written the photon has now put the atom
into different hyperfine state.
So if this is done adiabatically--
and I can't do full justice in this course,
but this means that the light is coherently
converted into the atomic-- well, when I say coherently
and into population, I mean all the quantum phases, everything
which was in the quantum nature of the light,
has now been converted into-- has
been written into the state f.
And this is often called, because g and f are
hyperfine states, this means that you have coherently
converted the photon or the electromagnetic wave
in the probe beam into a spin wave, or a magnon.
Anyway, I just want to show you the analogy,
the fact that you can put the quantum information of light
into an atomic state and back and forth.
We've discussed that.
When we had the situation of cavity QED,
we prepared a superposition of ground and excited state.
And exactly the same quantum state which we had in the atom
we later found in the cavity as a superposition of the 0
photon and the 1 photon state.
So from those general concepts, it should be clear to you
that it is possible to coherently
transform a quantum state from light to atoms
and back to light.
And here you see a different realization.
We have a quantum state of the photon in the probe laser.
And by switching-- and we can now
describe the excitations in the system
in a sort of parametrized way.
And what it means is, for the strong probe laser,
for the strong coupling laser, the excitation in the system
travels as a photon in the field 1.
But when you reduce the coupling in the coupling laser,
the excitation becomes less and less photon-like.
It becomes more and more magnon-like, spin wave-like.
And the moment you reduce the power in the coupling laser
to 0, what used to be an excitation
in the electromagnetic field has now been turned adiabatically
into a spin excitation, into-- coherence has
been written into the hyperfine states of your atoms, g and f.
All of this is done coherently, and therefore reversibly.
You can read out the information by simply
time-reversing the process.
You ramp up again the coupling laser,
and that adiabatically turns the spin excitation back
into an excitation of the electromagnetic field.
Any questions?