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M5L24d.txt
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M5L24d.txt
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#
# File: content-mit-8-421-5x-subtitles/M5L24d.txt
#
# Captions for 8.421x module
#
# This file has 104 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------
What I first want to discuss is another aspect
of the dark state.
And this goes by the name EIT, electromagnetically-induced
transparency.
I can introduce this topic by a question to Radio Yerevan.
Is it possible to send a laser beam through a brick wall?
And, well, the answer of Radio Yerevan, if you know the joke,
is always, in principle, yes.
But you need another very powerful laser.
So in an incoherent way, of course, a very powerful laser
can drill a hole into the wall, and then the next laser
can go through the wall without absorption.
But you can be smarter if the very powerful laser,
through coherence, puts all the atoms in the brick
in the beam path of the laser into a coherent superposition
state.
And then they become a dark state.
Then your laser can go through a brick wall.
So, can a laser beam penetrate an optically thick medium.
And the answer is yes, with the help of another laser.
Original ideas along those lines were
formulated by Steve Harris, who has really
pioneered this field.
And he first considered special auto-ionizing excited states
which couple to-- there were two pathways of coupling
into the continuum.
But later work has shown that it can
be realized in a lambda system.
So let me talk about this conceptually simpler
realization in a three-level lambda system.
Let's assume we have again our normal--
our three-level system, gf, and an excited
state, which has a width gamma.
And we want to send the probe laser through a dense medium.
And it would be completely absorbed by the resonance
to the excited state.
But now we can have a strong coupling laser
with a Rabi frequency omega c.
And so if we drive the system very strongly,
we can create a situation where the coupling laser does-- well,
if it's strong enough-- compete mixing between the excited
state and the ground state.
And that means if you have two levels which are completely
mixed, they are split by the energy or the frequency
of the coupling.
So in other words, what we obtain is we
have now two states, e plus f and e minus f.
Another way how you should read it is the following.
You can just assume for a second the state
f will degenerate with gamma.
And then I put in a very strong mixing between the two.
This is exactly the example we had with hydrogen
in an electric field.
And then we get two states which have both reached gamma over 2.
They are strongly mixed.
And the splitting is nothing else than the matrix element
of the electric field.
But if you don't have two degenerate states
and we add a photon, then the photon--
I mentioned it again and again in [INAUDIBLE] atom picture--
creates a degeneracy.
You can just add a photon, draw a dashed line,
and this is your virtual state, if you want.
Or if you look at Schrodinger's equation,
you have something which oscillates
at the frequency of the state f, but now
you multiply it with an electric field which oscillates
at the resonance frequency.
And then you have something which
oscillates at the sum of the two frequencies.
And this is exactly what I indicated with a dashed line.
So that's how you create, so to speak, a degeneracy
by using the frequency of the laser to overcome the energy
splitting.
And the result is that you have created exactly
this excited state level structure.
And if we now look at the ground state
and our photon is tuned right between those two continua,
then we have a dark resonance.
And in order to accomplish this, I'm
not going into any calculations here,
but you need a sufficiently strong coupling
laser who can accomplish that.
For instance, coupling laser which
is stronger than the spontaneous emission rate or decoherence
rate gamma in the excited state.
So if we now scan the probe laser
and we look for transmission, let
me assume for simplicity that there is no relaxation
between the two ground states.
And if the coupling laser strength is 0,
then we have a broad feature, which
is simply the single-photon absorption of the probe light.
If we have an infinitesimal coupling laser strings,
we get a very, very sharp feature.
And if the coupling laser is stronger and stronger,
we get a window, a window of transparency.
And the width is given, the width delta omega
of this central feature, is given by the Rabi frequency
of the coupling laser.