M5L23p.txt

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How can this be realized?
Let me just give you the first possible realization,
and then I think we should stop.
We could, in principle, realize it with high torsion and the DC
electric field.
Remember, hydrogen has the 1s level, has the 2s level,
and the 2p state.
And you all had a nice-- did a nice homework assignment that's
when you have a DC field, you actually coupled 2s and 2p.
And if your DC field is stronger than the Lamb shift,
you actually create a superposition
of 2s and 2p states.
And now, if you tune your laser right in between,
you have a dark resonance.
So, the situation is if I would now
plot the absorption versus frequency,
you would find that if you're in resonance with the upper state
you absorb.
But then in between there is this notch
where you have zero absorption.
So, for this simple case with hydrogen
in a DC electric field, the dark resonance
occurs when you have equaled the tuning for the atom
with respect to the two states.
And, I like to connect it to classical physics.
You know that absorption is related when you
absorb your light scattering.
The photons are not disappearing.
They're just scattered into other modes.
That's what absorption is about.
And clasically, lights scattering
comes because you've been oscillating dipole moment.
But what happens is if you have this coherent superposition
and you are right in between-- you
have a positive detuning with one harmonic oscillator
and a negative detuning with the other harmonic oscillator.
So if you drive a harmonic oscillator-- and this is one
and this is the other-- with positive
detuning with ready tuning, the dipole moment
is in phase with the electric field.
In the other case, it's out of phase.
So now you have to the two excited states,
and you're driving two equal but opposite dipole
moments in those two states.
And, therefore, the two dipole moments add up to zero.
Therefore, the laser just using our understanding
of a simple harmonic oscillator is not
creating any dipole moment.
Therefore, we're not scattering any light.
And, therefore, we're not absorbing any light.
So this is how you can now realize in the hydrogen atom
using DC magnetic field and creating this level structure.
You can create lasing without inversion.
But, I will tell you on Wednesday--
no today is wednesday-- next Monday,
next week that we don't have to deal with the difficulties
of hydrogen atoms in the laboratory.
We can just use our favorite alkalies
and dress the alkalies up with laser beams.
And, eventually, create the same situation
with an atom, which is experimentally
much simpler to address.
Any questions?

OK, one more week to go.