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M5L25e.txt
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M5L25e.txt
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#
# File: content-mit-8-421-5x-subtitles/M5L25e.txt
#
# Captions for 8.421x module
#
# This file has 117 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------
OK.
Now we understand the basic of superradiance in two atoms,
and therefore we can now generalize it to N particles.
But before I use the spin algebra to describe
N particles, I want to glean some intuition, where we just
consider-- and this takes us back
to the beginning of the course-- where we consider
N spins in the magnetic field.
So, and I really invite you to think now completely
classically.
We'll describe the quantum mechanic in a moment,
but I've often said in this course, if in doubt,
if you have a classical description and a quantum
mechanical, and they seem to contradict,
usually there is more truth in the classical description.
It's so much easier to fool yourself
with the formalism of quantum mechanics.
So, let's take N spins in a magnetic field,
and ask what happens.
So we have N spins.
So these are now real spins, they [? are real ?]
magnetic moment.
These are tiny little bar magnets.
And we do a pi over two pulse.
And after we've done a pi over two pulse,
the spins are aligned like this.
Let's assume we had our magnetic field.
And now what happens is, these spins will precess
at the Larmor frequency.
So now you have your N spins.
They precess together.
And if you have a magnetic moment which oscillates,
the classical equation of electromagnetism
tell you that you have now a system which radiates.
But compared to a single atom, the dipole moment
is now, N times, the single-atom dipole moment.
So therefore, what do we expect for the radiated power?
Well, if the electromagnetic radiation
by an oscillating electric, or an oscillating magnetic,
dipole moment scales with a dipole moment squared.
So therefore, we would expect that the power radiated
is proportional to N square.
And that means, I have to take the perfect of N now apart.
This means, this is N times higher
than if you assume you have N individual particles.
And each of them emits electromagnetic radiation.
So what I'm telling you is, if you
scatter N spins through your laboratory, you excite them,
pi over 2 pulse.
They radiate.
They radiate a power which is proportional to N.
But if you put them all together, localize them better
than the wavelengths, their radiated power
is proportional to N square.
Which is an N enhancement.
So the way how I put it for N spins-- and this
is a situation of nuclear magnetic resonance--
this is the completely natural picture.
But if I would have asked you the question,
let's take N atoms which are excited
and put them close together, you'll
say, oh well, each atom does spontaneous emission.
And If you have N atoms, we get N times the intensity.
You would have gotten a different result.
So we are so accustomed to look at spins in NMR
as a coherent system.
Look that all the spins add up to one giant antenna,
to one giant oscillating dipole moment.
Whereas for atoms, we are so much
used to say each atom is its own particle does its own thing.
So for N excited atoms, they are usually
regarded as independent.
However-- and this is the message of today--
that there shouldn't be a difference.
All two-level systems are equivalent.
Side remark-- for NMR N spins, it is much, much easier
to observe the effect because the condition
that all the spins are localized within one wavelength
is always fulfilled if the wavelengths is
meter or kilometers.
But if you have atoms which radiate
at the optical wavelengths, this condition becomes non-trivial.
That is partially responsible for the misconception
that you treat the two-level system, which
is a spin, in your head differently
from the two-level system which is an atom.
So the important difference here is lambda.
And we have to compare it with the sample size.
And usually the sample size is much larger
in the optical domain and is much, much smaller
in the NMR domain.
However, and that's what we will see
during the remainder of this class,
some of the traumatic consequences of superradiance
will even survive, under suitable conditions,
in extended samples.
So when we have samples of excited atoms much,
much larger than the optical wavelengths,
we can still observe superradiance.
So therefore, for pedagogical reasons,
I first completely focus on the case
that everything is tightly localized.
We derive some interesting equations.
And then we see how they are modified
when we go to extended samples.
But I want to say, the intuition from spin systems,
the intuition from classical precession
and nuclear-magnetic resonance will help us
what happens for electronically excited atoms.
So we want to use this other spin 1/2
system as a powerful analogy to guide us.