M5L22j.txt

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What we have actually done is, we
have done a version of the double-slit experiment.
We have a ground state.
We had our excited states, e sub i.
And our broadband source was creating a coherent excitation.
And then we were observing the light which came out.
But we were performing a multi-slit experiment.
We had a laser pulse and then we see photons coming out.
But it is fundamentally not observable
which intermediate state was responsible for the scattering?
So therefore, we have, in the Feynman sense,
several indistinguishable paths going
through different internal states.
And therefore, we get an interference effect.
Some of what I'm saying we will retrieve
later on when we talk about three-level systems.
We will also have situations that sometimes we
go through two possibilities for the intermediate state.
And if we have no way, even in principle,
to figure out which intermediate state was involved,
we have to sum up the amplitudes.
And that's when we get a beat note.
This technique is a Doppler-free technique.
Because, even if you take a single pulse
from a light source, you have a Doppler broadening, which is k
dot v, v the thermal velocity.
And this can be much, much broader.
But you will still see the quantum beats.
Maybe I should say in principle, because a beat
note happens at the much smaller frequency, delta.
Or maybe I should say that the Doppler shift is reduced
by the splitting of the excited states over the frequency
of the excited laser.
Of course, if you have your different atoms emitting
at different frequencies, you have a Doppler shift.
But since you measure the difference frequency,
you only get the Doppler shift associated with the difference
frequency.
Now, let me come back to the previous example I had about
the spin-1/2 system.
If you assume you have a spin1/2 system,
spin up and spin down, which is excited with a laser, which
is linear polarization.
You would then create a superposition of up and down.
Which, let's say, is now a dipole moment, which
points in the x direction.
A dipole moment which points in the x direction
will not emit light along the axis
of the dipole moment because of the dipolar emission pattern.
It will only emit to the side.
But I mentioned to you that the dipole moment, or the spin,
which is originally in x, will now oscillate with the Larmor
frequency in the xy plane.
So the picture you can actually have
of such a quantum beat and quantum sleep superposition
is like the lighthouse.
You have a search light at the lighthouse.
And the searchlight is just rotating
at the Larmor frequency.
For instance, you wouldn't see light right now.
Now you don't see light.
Now you don't see light.
It's really like a classical lighthouse,
which is emitting light at the Larmor frequency.
So if you have a fluorescence detector which
looks at the atoms from a certain direction,
you will pretty much see the lighthouse effect.
That the fluorescence off this coherent superposition of atoms
goes on and off, on and off, on and off.
And this is sort of a very nice visualization.
How you obtain what I showed here,
a beat note in your detected signal.