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M3L17g.txt
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M3L17g.txt
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#
# File: content-mit-8-421-3x-subtitles/M3L17g.txt
#
# Captions for 8.421x module
#
# This file has 106 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------
Can you think of a very intuitive argument
why for spectrally broad radiation,
all the properties of the atoms cancel out?
If you think about one physical example
for, let's say black-body radiation,
this is spectrally broad.
So you're going to atom in a black-body cavity,
and the atom experiences a very broad spectrum.
How would we for-- for what number of photons,
black-body photons per mode, would we find saturation?
Think about it, it's a simple criterion
you can formulate for black-body radiation,
to saturate your transition, in terms
of-- the number of photons per mode.
You crank up the temperature in your cavity,
how high do you have to go with the temperature
in order to saturate an atom, which is inside
your black-body radia-- inside your black-body cavity?
One photon per minute.
Pretty close.
1 over [? degeners. ?]
[? Degeners ?] OK, no [? degeners ?].
I hate [? degeners ?].
That's your private homework, to put in [? degeners ?]
afterwards.
The answer I came, was n equals 1/2 I think.
Because you I underestimated of by factor of two now,
but the argument was that--
The rate equals endogenous by n by gamma,
so if the rate equals--
Gamma over--
--gamma over that means it's [? degeners ?] by n equals 1/2.
And if [? degeners ?] equals 1, n equals 1/2.
Yes, OK.
So spontaneous emission-- we know
that spontaneous emission, from our derivation
of spontaneous emission, corresponds
to 1 photon per mode.
And we want to cut a-- and our criterion now
is if we want to have an absorption
rate, or stimulated rate, which is gamma over 2.
So we get sort of half the effect
of spontaneous emission, when we have a half a photon per mode.
So therefore spontaneous emission absorption
is proportionate to n, and I think if n equals 1/2,
then we have the unsaturated rates equal to gamma over 2.
So this is a very physical argument.
When we put an atom into a black-body cavity,
and we have half a photon per mode occupation number,
then we saturate, any atom we put in.
Because using Einstein's argument, we have now the rate
coefficient for absorption emission
is just-- for stimulated emission and absorption-- is
just 1/2 of the rate coefficient for spontaneous emission.
And that explains that all atomic properties
have to cancel out.
So now the question for you, we talked about the fact
that if we have hyperfine transitions,
that it would take-- what was the value, 1,000
years for spontaneous emission?
So that we can completely neglect spontaneous emission.
On the other hand, we've just learned that saturation only
comes from spontaneous emission.
Without spontaneous emission we wouldn't have saturation.
But now I'm telling you that any atom should really
be saturated if you put it in a black-body cavity,
where n bar is 1/2.
So what is the story now, if we put an atom into a cavity-- so
into a black-body cavity, and we're asking about,
will we saturate the hyperfine transition?
Will we eventually have-- saturation means we have
[BLOWING]
--a quarter of the atoms in the excited state, 3/4
in the ground state, so
[BLOWING]
The delta n has been reduced form 1, which it was initially
3/4 minus 1/4, which is 1/2.
What will happen, I mean, this was almost
like a thermodynamic argument.
Will we equilibriate and saturate hyperfine transitions
in a black-body cavity?
Based on this argument, that 4n bar equals 1/2,
we should really saturate everything.
Yes, but it's going to take a long time?
Yeah.
So for those conditions, if your black-body cavity with n bar
equals 1/2, you should saturate any two level system completely
independent of what gamma is.
And if the gamma is 10 nanoseconds or 10,000 years,
you re-saturate it.
The value of gamma has completely
dropped out of the argument.
But of course, if you want to reach any kind of equilibrium,
it will take a timescale, which is 1 over gamma,
and then we are back to 1,000 years.