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M1L1c.txt
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#
# File: content-mit-8422-1x-captions/M1L1c.txt
#
# Captions for 8.422x module
#
# This file has 98 caption lines.
#
# Do not add or delete any lines. If there is text missing at the end, please add it to the last line.
#
#----------------------------------------
I always like to start the course
by talking to you in a lighthearted but hopefully
profound way about a system which
helps you to showcase, what are we doing in this course?
And until a few years ago, I would
have started with the simplest example of laser cooling,
simply beam slowing or optical molasses in the simplest
possible picture, just to give you
a taste of what we will be doing together in doing the semester.
But as I said, [INAUDIBLE] physics is moving along.
And what I now want to use as an example, which really
synthesizes many aspects of this course,
are atoms in an optical lattice.
So let me make some connections to different topics
of this course by using as a starting point a very
simple system but very, very rich and profound.
And these are atoms in optical lattice.
So the situation I want to use here
is that you have two laser beams which interfere.
And those laser beams form an optical standing wave.
So next week we will learn how this electromagnetic wave
interacts with atoms.
So we have to put a few atoms into the system.
And we will derive from first principles
the QD Hamiltonian, which after a lot of manipulation
and eliminating complicated terms,
will be the dipole interaction.
But of course, each symbol here's an operator,
and there's a long story behind that.
In about two months, we will describe light atom interaction
with the formalism which uses the block
vector and the optical block equations.
There is vector with three components which describes what
is the state the atom is in.
One component will tell us if the atom
is in the upper or the lower state,
whereas the other components tell us
whether the dipole moment of the atom
is in phase or out of phase with a driving
electromagnetic field.
Well, if there is part of the dipole moment,
which is in phase with a driving electric field,
then the suitable expectation value, defiance
and mechanical potential.
And if the electric field is a standing wave,
then we generate, through light atom indirection,
a periodic potential for the atoms.
We will learn everything which we
have to know about this potential in a simple case.
It is simply the Rabi frequency divided by the detuning
of the electromagnetic wave.
But we will be able to find it very interesting
to look at it from a very different point of view.
And maybe let me use this example
to point out that I am really a big friend of explaining
the same physics from very, very different perspectives.
And when we talk about optical standing waves,
we will use a picture of a classical potential
like a mechanical potential when the atom is just moving around.
We will use the photon picture that every time the atom
feels the force, photons are involved.
You don't see them in the classical potential,
but photons are behind it and ultimately
the forces of the classical potential
come from stimulated absorption emission of photons.
I may go down to the microscopic level, and I may ask you.
But in the end, it's an atom.
But the atom consists of electrons.
And the electrons are simply oscillating
because it's driven by the electromagnetic field.
It's actually something that most people are not aware of.
But you can ask the question now,
is the force in the optical lattice on the atom,
it's ultimately a force on the electron.
Well, if you have a charged particle,
you can have two kinds of forces-- an electric force
or the Lorentz force.
And I don't know if you would know the answer,
but an atom is in an optical lattice.
Thus, is the force just the roller
coaster potential, which the atom experiences,
is that fundamentally due to the Coulomb force exerted
by the electric field of the light?
Or is it due to the Lorentz force
exerted by the magnetic part of the light?
Who knows the answer?
Who doesn't know the answer?
OK, great.
I was actually surprised when I derived it
a few times for the first time.
And it's not in the standard textbooks.
So anyway, I hope even for many of you who know already
a lot about the subject.
I hope I can sort of add other perspectives for you.