M5L23b.txt

#
# File:   content-mit-8-421-5x-subtitles/M5L23b.txt
#
# Captions for 8.421x module
#
# This file has 117 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------

So when we shine on the light, atoms
may be in some initial state.
They will sort of scatter light.
But then after some [? transient, ?]
the state which is stable against further illumination
is the dark state.
That's like optical pumping.
So we'll optically pump into the following state, which
I'll write down for you and then we can inspect that indeed it
is a dark state.
It is a coherent superposition of the two ground states,
and the coefficient involves the Rabi frequency,
omega 2 of laser two, omega 1 of laser one.
And we just normalize it by taking the [INAUDIBLE] some
of the two Rabi frequencies.
This state is indeed a dark state.
So let me show that to you by looking at what happens when
we expose it to this operator.
This operator V in the Hamiltonian
is the operator which couples the atoms
to light, which couples the atom to the excited state.
And this causes spontaneous emission.
What I want to show you that it's a dark state since,
if you take this operator, apply it to the dark state, and ask
is there any possibility how you can
excite to the excited state.
And the answer is it will be 0.
The dark state has a component on f,
and it has one component in g.
Sometimes it's easier to say it in words
than to write down a long equation.
The light-atom interaction couples
the component of the ground state to the excited
state with a Rabi frequency omega 1, and for the state
f with omega 2.
However, in the construction of the dark state,
I've made sure that the amplitude of the component g
is omega 2.
So therefore, when we apply this operator,
we have omega 1 from the operator and omega 2 here.
And here we can also get omega 1 and omega 2,
and this minus sign means the two effects cancel.
So therefore, I have shown you that even
in its full frame with [? second ?] quantization
photon operators and all this, this coupling is identically 0.
And therefore, we have a dark state.
So this phenomenon of having a dark state
and populating the dark state by light scattering,
you have spontaneous emission into the dark state
until the scattering light [INAUDIBLE] stops.
And no matter what the initial state of the atom were,
the dark state is now 100% populated.
This is called coherent population trapping.

Let me mention that this coherent population
trapping can be some good thing if you want to pump atoms
into a certain state and then they stop scattering light,
they're not heated up anymore.
But sometimes, you want the atoms to scatter light.
For instance, in current laser cooling experiments
with molecules, there is a problem
that the multiplicity of the angular momentum states which
are suitable for laser cooling in molecules
is such that you always have a dark state.
So if you irradiate the atoms with laser light,
they will not be on a cycling transition.
The cycling transition will stop.
So then you have to play additional tricks.
One is to apply a transverse magnetic field,
that the axis of the laser and the quantization axis given
by the magnetic field are in two different directions,
and then once the atom is pumped into a dark state,
it really actually [INAUDIBLE] out of the dark state.
Or, magneto-optical traps for molecules
use a magnetic field gradient which is rapidly switched.
Because when you are in a dark state for one
value of the magnetic field, you just change the sign quickly
and then the atoms are no longer in the dark state
for the new situation you have created.
So in other words, to have this wonderful dark state, which
is a major intellectual accomplishment
and eventually was used-- was exploited in many experiments,
for a number of experiments it's a real nuisance.
And you have to find ways around it
to make sure that the atoms are not stopping scattering light,
and don't stop scattering light.
I gave you the simple example that the dark state
exists for resonant excitation.
But as you can immediately show, the dark state also exists
for [? the ?] [? tuning ?] of resonance.

The only thing which is important, as long
as the two lasers fulfil the two photon resonance condition.

So you want that the difference between the two lasers
is the energy difference between the two states.
Also remember if we had two lasers which
are very different in power-- so let's say one Rabi frequency is
much smaller than the other one-- then
the dark state, the superposition
which is the dark state, the dark state
is now predominantly which one?
The state with the stronger coupling,
or with the weaker coupling?

Well, it's the state with the weaker coupling.
The dark state has always a larger amplitude
in the state for which the coupling is weaker.
And that, of course, immediately makes a connection
to optical pumping.
For instance, if omega 1 of the Rabi frequency is 0,
then the dark state is what we started out
with a trivial example as state g.
So you see that actually what I taught you
about coherent population trapping
is nothing else than an extension of the concept