M5L25a.txt

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And today we're going to talk about coherence between atoms.
So this is now, I think for the first time in this course,
that we really have more than one atom.
Well, maybe we discuss some collision or thwarting or we
discuss the Vondermals interaction between two atoms.
But, usually, atomic physics is one atom at a time.
But now we want to understand one important phenomenon, which
happens when we have many atoms.
And the phenomenon is called superradiance.
So, I left something good for the end.
And superradiance has in common the word
super with superconductivity and superfluidity.
And it really represents that many atoms act together.
And the word super also means coherence among atoms.
Superfluidity and superconductivity
have macroscopic wave function where all the atoms, the matter
waves are coherent.
The phenomenon of superradiance, as we will see,
has not so much to do with coherent atoms,
it has more to do with coherent photons.
So it's more-- some people regard superradiance as a laser
without mirrors.
But you'll see where the story leads us to.
So, just to set the stage for many atoms,
we should first talk about single atoms and all
that is described in this landmark paper
by Vicke, 1954, which is posted on our website.
So, if you have a single atom prepared in the excited state,
it's decays to the ground state.
And we want to characterize the system by an emission rate
as a function of time.
So, the emission rate, initially, is gamma.
Gamma-- they're natural alignments
of the excited state.
And then, of course, the emission rate
decays, because we don't have any atoms left.
Similarly, the probability to be in the ground state
is zero, initially.
And then, with an exponential approach,
it eventually goes to unity after awhile,
after we have only atoms in the ground state.
So, this is rather straightforward.
But now we want to bring in a second atom.
And, I'm asking what happens when we have not
one atom but two atoms-- one is in the ground state,
one is exciting.
So pretty much what we have added to the original situation
with one excited atom was we have brought in one
ground state atom, which now, if you would think, does nothing.
But that's not the case, we will drop the assumption later.
But we assume for now that all the atoms obviously in
of the wavelengths.
What we then realize is for two atoms--
and I will show you that in its full beauty--
that the initial rate of light, which comes out of the system
is the same.
So, the extra ground state atom does not
change the initial emission rate.
But, it goes down faster.
And if we ask what is the probability that the atom is
in the ground state, we find that it's only one half.
So, in other words, normalized per our system
we have a ground and excited state atom.
And what comes out is only half a photon, half of the atoms
do not decay.
So it's not the same rate and the same decay.
Something profoundly has happened.
And this is what you want to understand.
So let me give you the correct answer.
So, the rate of emission is a function
of time for this situation.
We start out with gamma, but then the emission
decays not with gamma but with two gamma.
And, the probability that both atoms are in the ground state,
or that the second atom, so to speak, is in the ground state
will only assume toted equal to one half.
And it does so exponentially, but, again,
with a time constant, which is two times faster
than for the single atom system.
So we have the same initial emission rate, but only
but only probability of one half to emit at all.