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M3L17b.txt
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M3L17b.txt
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#
# File: content-mit-8-421-3x-subtitles/M3L17b.txt
#
# Captions for 8.421x module
#
# This file has 85 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------
I realized after class that it may
be useful to quickly state what I have
said using the photon picture.
If we have circular polarization,
we have for given frequency, annihilation and creation
operator.
But let's assume that the mode we are considering
is right-handed circularly polarized.
So the operator creates a photon at frequency omega
with this right-handed circular polarization.
So that means now if we start from a level m,
and we have now light atom interaction, the operator which
annihilates a photon with circular polarization,
because of angular momentum conservation,
can only take us to a level where the magnetic quantum
number is n plus 1.
The operator a [INAUDIBLE] creates a photon
through stimulated emission, and so this is now
our two-level system.
And now, we should ask the question,
in terms of rotating wave approximation
is necessary or not, are there counter rotating terms?
Well, the counter rotating terms are the non-intuitive terms
where you start out in the lowest state.
But now, instead of absorbing a photon, you emit a photon.
And the operator for emission is this one.
So I can now ask is there another term
that there is a term which is driven
by the operator a [INAUDIBLE] circularly polarized?
Well, the answer is there may be such a term,
but the state we need has now and magnetic quantum number
over of m minus 1, because of angular momentum selection
rules.
So this here is the counter rotating term,
which you may or may not neglect,
depending whether you want to make the rotating wave
approximation or not.
So therefore, if you got a little bit confused
about the different cases I considered
at the end of the last lecture, then
you may just summarize the many examples
I gave you in the lecture just as a note, which you should
keep in the back of your head.
Namely, let me first phase it in verse,
and then I write it down.
If you have circular polarization and angular
momentum selection rules, then the counter rotating term
may require a third level, and is not
part of two-level physics.
So if you have a situation where the third level does not exist,
you do not have a complicating term.
However, in all situations I've encountered in the lab,
this third level does exist.
OK, so let me just write that down.
Counter rotating term for circularly polarized radiation
requires a third level, which may not exist.
And then, you don't have this term,
but it does exist in most cases.
Anyway, just an additional clarification to the topics
we had on Wednesday.
Any questions about that?
Yes?
Are there cases other than a spin one half
system where it doesn't exist?
Well, I gave you the example.
I mentioned the example last class.
If you do spectroscopy of an s to p transition
in the magnetic field of a neutron star.
Then the z1 splitting is so huge that-- well, you
can assume that this has been shifted so far away that it
has been completely suppressed.
Other than that, well we have the trivial situation,
which we discussed in NMR.
If you simply have spin one half,
then the total number of levels is only two,
because we're talking about spin up and spin down.
Or I constructed in the last class the forbidden transition,
a tuplet s to tuplet s state.
So that's two pairs of s equals one half,
and then we're missing the state to couple any counter rotating
term into the system.