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M5L21a.txt
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M5L21a.txt
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#
# File: content-mit-8-421-5x-subtitles/M5L21a.txt
#
# Captions for 8.421x module
#
# This file has 112 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------
I want to feature in this last big chapter of this course
coherence in all its different manifestations.
I think this is rather unusual.
I don't know of any text book or any other course
where this is done.
But this is similar in spirit to what we did on line broadening.
I felt I could create special connections
by discussing all possible line shifts and line
broadenings together.
And now I hope you will also see certain common traits
if I discuss together all the different manifestations
of coherence.
So we start out by talking about coherence in a single atom.
We can have coherence between two levels.
Usually I try to stop at the simplest
possible manifestation.
But when we talk about coherence,
I cannot stop at two levels, because there are many new
qualitative features which come into play when we have three
levels, like lasing without inversion,
like electromagnetically induced transparencies for those of you
who have heard about it.
On the other hand, I can reassure you
I don't think there is anything fundamental to be learned
by going to four, five, and six levels,
so we will stop at three levels.
So this is a single atom, but we can also
have coherence between different atoms.
And phenomenon we want to discuss
is superradiance, which is very, very
much related to the phenomenon of phase matching.
Everybody who [INAUDIBLE] laser knows about phase matching,
phase matching condition.
You have to rotate the crystal or heat the crystal
to the temperature where the whole crystal, all the atoms
in the crystal act coherently.
But it's very related to superradiance.
There is a third aspect of coherence between atoms which I
will not discuss this semester.
And this is the situation of Bose-Einstein condensates
and microscopic wave functions.
This is discussed in the context of quantum gases
in the second part of the course.
Having these very different manifestations of coherence,
I want to try now to give you a definition of coherence.
But it's a little bit difficult, because I
want to cover with my definition all the cases I know.
With those examples in mind, we have the phenomenon
of coherence.
Coherence exists if there is well-defined phase.
Well, if we have a phase, well-defined phase,
it's always a phase between quantum mechanical amplitudes.
So we need two or more amplitudes.
So coherency exists if there is a well-defined phase
between two or more amplitudes, but we can only observe it
if those amplitudes interfere.
And it can be two amplitudes describing two different atoms,
or it can be two amplitudes of two
states within the same atom.
But I will point out what is really
relevant is an indistinguishability
that those two amplitudes are involved
in two branches of a process which has the same final state.
And like in Feynman's Doppler state experiment,
you don't know which intermediate state was taken.
And that's where coherence manifests itself.
So that means when we observe an interference, that
means we observe-- and this is how we read out of coherence--
one observes a physical quantity, the population
in certain quantum state, totally electric field
admitted.
But this quantity is usually proportional to the square
of the total amplitude.
And that means we get an interference term.
So coherence is important.
Let me provide one additional motivation
that coherence is an important technique, an important tool
for measurements.
It's subtle but trivial at the same time.
Whenever we do spectroscopy, we are actually
interested in doing a measurement of, you know,
energy.
We want to measure energy levels.
And those energy levels can tell us
something about magnetic fields, for Zeeman shifts.
If you're addressing energy levels
in the gravitational field for atomic [? interferometry, ?]
the energy levels reflect gravitational fields.
Or if you're not interested, if you try to eliminate or shield
the atoms from magnetic fields and we just
want to get the most precision in a reproducible energy level,
this is the situation of atomic clocks.
So pretty much when we use atomic spectroscopy
for any application, we're interested in the energy
levels.
But this is very deeply connected
to coherence interphase, because the relative phase between two
states is nothing else than the time integral over the energy
difference between two levels.
So the phase evolved between the two levels
is the difference frequency times time or time
integrated tt.
So therefore when we are talking about coherence,
how can we maintain longer coherence
between energy levels?
Or how can we create coherence in three-level systems?
This is actually intricately related to the fact
that we can obtain more precise information about the energy