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M3L16b.txt
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#
# File: content-mit-8-421-3x-subtitles/M3L16b.txt
#
# Captions for 8.421x module
#
# This file has 160 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------
Experiments are done in the microwave regime.
The leading groups are-- well, in the older days,
Dan Kleppner, Herbert Walther, and Serge Haroche.
And this involves Rydberg atoms.
Rydberg atoms in superconducting high Q
cavities.
And those Rydberg atoms because things scaled
with n and n squared, the principle quantum number--
have a fantastically strong coupling
through the electromagnetic field.
And there is homework assignment on Rydberg atoms
in such cavities.
The other example is in the optical domain.
And this really involves the D line of alkali atoms.
You drive them on the D line.
Rubidium and caesium are often used.
And the work is enabled by the development
of so-called super mirrors, which
have an extremely high reflectivity,
and you can realize an excellent Q factor.
And the leaders in this field is Jeff Kimble and Gerhard Rempe
at the Max Planck Institute.
So let me just discuss an example
taken from the optical domain.
So the generic situation is that you have two mirrors which
define a single mode cavity.
Usually you have a stream of atoms
traditionally in atomic beams, then
in some experiments in slowed atomic beams,
more recently in atoms which are falling out of the MOT,
and only very recently, the single atoms
with the help of other laser beams where
trapped inside the cavity.
So they are streamed in such a way
that only one or few atoms in the mode volume
interact with the single mode of the cavity at a given time.
And then you want to figure out what is now happening.
And you have a probe laser.
You send it through the cavity.
And then you record the transmission
with a photo diode.
Yeah, [INAUDIBLE]?
What is the mirror made of [INAUDIBLE].
The mirror is made of a glass substrate,
but then you have a dielectric coating.
And the mastery is really to put coatings
on which are very few pure; but then also-- I think
using ion sputtering, you make sure
that the coating is extremely smooth
and does not have any surface irregularities which
would scatter a tiny fraction of the light.
I know there are some people in Ike's group
and Vladan's group who work with high Q mirrors.
What is a typical example for the reflectivity, or the Q
factor you can reach?
Five ninths, and a finesse of maybe 500,000.
So finesse of about a million, and that means the mirror
has 99.9999 percent reflectivity.
And the super polishing is-- I think that was the last step.
People had controlled the materials,
but then they found ways to make a super polish
and avoid even one part per million
scattering by surface roughness.
OK, so if do that experiment, what would you expect?
Well, it's a Fabry-Perot experiment,
so if you would scan the probe laser,
and there is nothing in it, what you would expect
is-- you would just expect transmission peak
at the cavity resonance.
And if you tune much further, you get the next peak
at the free spectral range.
Let me just indicate that.
So this is the case for zero atoms in the cavity. l
If you put one photon in the cavity,
you're no longer-- sorry, on atom in the cavity-- you're
no longer probing a cavity.
You're really probing a system which is
no longer the cavity by itself.
It's an atom photon system-- it's a coupled system--
and we know it's described by our 2 by 2 Hamiltonian.
And this Hamiltonian has two solutions.
And the two solutions are split by one photon Rabi frequency.
So the two eigenvalues of our Hamiltonian
are a plus minus omega 1 photon.
So therefore, for n equals 1, we have a situation
that we have two peaks split by the single photon Rabi
frequency.
Of course I have assumed that great care has
been spent to make sure that the cavity resonance is right
where the atomic resonance is.
So this is now for one.
If you have 10 atoms, remember the 2 by 2
Hamiltonian looks the same, but it has a square root
n plus 1 factor.
So neglecting the 1 roughly when we have 10 atoms in the cavity,
it's square root 10, larger Rabi frequency, and therefore
we would expect that we have now a splitting
of the two modes, which is square root 10 plus 1 larger.
Actually I didn't-- sorry-- I have to correct myself now.
I showed you that the Rabi frequency,
you can see it scales with square root
n plus 1 in the photon field.
But you should realize that everything
is here symmetric between photons and atoms.
It's the complete coupling between photons and atoms.
And if you would now look-- but I don't want to do it now--
if you would now look what happens if several atoms are
present in the mode volume, you would also
get a scaling, which is n plus 1 in the atom number.
Because the atoms couple coherently, it
is actually an effect of super radiance,
which we discuss later.
So just take my word-- you have the same scaling with the atom
number, but I have to give you my word
now, because in the experiment, this is what people varied.
How would you draw this observation
if you were changing the photon numbers?
I don't want to go into line shape.
It will probably be a Lorentzian.
I mean all I want to discuss here is if that we have a 2
by 2 Hamiltonian which is split.
And if you have one atom and one photon,
it is split by the single photon Rabi frequency.
If we have one atom and 10 photons,
the atom can absorb and emit only one.
As i derived on the previous page,
we would have now a Rabi splitting, which
is square root n plus 1, n being the number of photons.
But if you would start in an empty cavity
with 10 atoms in the excited state,
because all the atoms are identical,
they would spontaneously emit together.
And then you would have 10 atoms in the ground state.
And then you would have 10 photons.
And so maybe this helps you.
If you start with 10 atoms in the excited state,
they do everything together.
You have 10 atoms in the ground state with 10 photons,
and now you have 10 photons and it's clear
that 10 photons lead to Rabi frequency, which
is proportional to the square root of 10
or the square root of 11.
So therefore what you will observe
is you will now observe a splitting
of the single mode of the cavity which goes
by the square root of n plus 1.
I don't want to discuss the line shape and the strengths.
I just want to sort of discuss, in a way, the eigenvalues
of the Hamiltonian, and the eigenvalues
are the positions of the transmission peaks
[? of ?] the cavity.
And this has been observed.