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PROFESSOR: So this first lecture
is a spirited but lighthearted
introduction into the course.
I usually never talk about
technicalities first.
I want to talk about the
excitement of the field first.
So I will talk about
technicalities a little bit
later.
So when you take a
course in AMO physics,
the obvious question
is, what is AMO physics?
What defines our field?
Actually, by far
the best definition
of what AMO physics is-- it
is what AMO physicists do,
which is defined by a
community of AMO researchers.
And this is really
characteristic for our field.
I will tell you in
the next 10 minutes
or so about these enormous
dynamics of the field, how
AMO physics has changed in
a fraction of my lifetime.
And what happened is, I
felt, whatever I was doing--
and it turned out to be
very different of what
I did 10 and 15 and
20 years ago-- has
stayed in the center
of AMO physics.
So myself and the
whole community,
we're moving, and
took the field along.
So therefore AMO physics is what
gets AMO researchers excited.
It's not a joke.
It's the way it
sort of happened.
Well, a little bit
more mechanically,
we can define AMO physics.
AMO physics is what is
made out of the building
blocks we have in AMO physics.
So defined by the
building blocks.
And in AMO physics,
we build systems
out of atoms, or molecules,
and then photons,
or light, and in general,
electromagnetic fields--
electric, magnetic fields,
microwaves and all this.
So in other words, everything
which is interesting
and we can put together
with those building blocks,
this is AMO physics now.
And this may redefine AMO
physics in the future.
Now, historically this meant
that those building blocks,
atoms and molecules, were
available in the gas phase.
So you had gases of
atoms, gases of molecules,
and you studied them.
And almost all of AMO
physics was actually
about individual particles,
individual atoms,
individual molecules,
because in the gas phase
at high temperature,
pretty much,
you learned that in
statistical mechanics
each particle is by itself.
And the partition function
of the whole system
is just factorized into
partition functions
of the individual particles.
Well, maybe with some
exception-- occasionally,
particles collide.
And the field of
collisions-- collisions
between atoms and atoms,
atoms and ions, atoms
and molecules, molecules
and photons-- this
was widely started
in AMO physics.
Well, now the field
has really moved away
from just individual
particles and collisions
between two particles.
What is in the center of
attention is few body physics.
And that of course takes
us to entanglement.
For instance, people
study entanglement
of eight ions in ion traps.
And of course this
is deeply related
to quantum information science.
Or if you want to go from
few body to many body,
this is now starting to overlap
with condensed matter physics.
And this is now widely studied
in the field of [INAUDIBLE]
atoms and quantum gases.
Now, when we talk about
many body physics,
we get, of course, into overlap
with condensed matter physics.
In condensed, I would
actually say now
a larger fraction of AMO physics
and condensed matter physics
overlap strongly, that we
speak the same language,
we study the same Hamiltonian,
a lot of theorists
apply the same methods to
topics coming from either field.
However, often in technology,
how the systems are studied,
there's a different culture,
different tradition,
and still two
different communities.
And the overlap comes
about because there
are systems in
nature which you can
say-- they are natural
two or few level systems.
Of course, we've helped nature
a little bit by engineering.
Those systems are, for instance,
quantum dots or NV centers
in diamond.
Or another overlap with
condensed matter physics
is that AMO physics is now--
one frontier of AMO physics
is the optical control of
mechanical oscillators.
Micro cantilevers, membranes,
tiny mirrors in cavities,
they have mechanical motion.
And the mechanical
motion is strongly
coupled to the photon field.
Of course, for fundamental
AMO physicists,
a mechanical oscillator
is nothing else
than an harmonic oscillator.
So one can say-- and this
is sort of my third attempt
in defining for you
what AMO physics is--
AMO physics is almost defining
itself by low energy quantum
physics.
So all of the quantum mechanics
which doesn't take place
at giga and tera electron
volt, which takes place
at low energy, this
is AMO physics.
Of course, maybe not all of it.
Usually when it is in
[INAUDIBLE] solution,
it's biophysics,
and it's distinctly
different from AMO physics.
Or if the solid
state is involved,
then it's more condensed
matter physics.
But I would say there is one
part of solid state physics
which is already becoming
interdisciplinary
with AMO physics.
And this is when the
control of the system
is not done by wires
and carbon probes
but it is done by lasers.
So if you have a
solid state system
and you use all of the
methods you apply to atoms,
you use
electromagnetically-induced
transparency, coherence,
all those concepts,
then AMO physicists
feel at home and they
don't care if the two level
system or the harmonic
oscillator is an ion
oscillating in an ion trap
or whether it's a
small cantilever,
the methods and
concepts are the same.
So therefore, one
could say AMO physics
is sort of the playground
where we can work on extensions
of simple systems which
we understand and cherish.
And of course, our
exactly solvable problems
are the hydrogen atom--
my colleague, Dan Kepner,
would have said, maybe
the hydrogen atom,
if you understand
the hydrogen atom,
you understand all
of atomic physics.
I'm not so sure.
I would actually say, in
addition to the hydrogen atom,
you have to know the
two-level system.
And of course, you have
to understand the harmonic
oscillator.
So these are three
paradigmatic Hamiltonians,
and a lot of understanding of
much more complicated systems
really comes from taking the
best features of those three
systems and combining them.
If you have questions
or comments,
this is an interactive class.
Feel free to speak
out or interrupt me.
OK so, now we know, or we don't
know, what AMO physics is.
Let me now address-- how
has AMO physics developed?
And I mentioned to
you that AMO physics
has done breathtaking
evolution in my lifetime,
or even in the shorter
part of my life,
which is my research career.
Well, traditionally, almost
all fields in science
started with observing nature.
The pursuit of science was
born out of human curiosity
to understand the
world around us.
And atomic
physicists, well, they
started to observe atoms and
molecules, usually in the gas
phase, and what they were doing.
And already there
was some evolution,
because original observations
at low resolution
were taken to a
completely new level when
high-resolution methods were
developed, when lasers came
along, when people had light
sources which had fantastic
resolution and eventually
finer and finer details
of the structure of atoms and
interactions between atoms
were resolved.
But AMO physics is
a field which has
taken the pursuit of
science much further.
So there is not just
observation of nature--
and I want to write that
with capital letters--
there is CONTROL OF NATURE.
And you maybe take
it for granted,
but you should
really appreciate it,
that controlling nature, having
control over what you study,
modify it, advance it,
take it to the next level,
is really something wonderful.
It is completely absent
in certain fields,
like astrophysics.
In astrophysics, all you
can do is, you can observe.
In atomic physics, we create
the objects we can observe.
So the control of nature, the
control of our atomic physics
system, developed in stages.
The first kind of control was
exerted about internal states.
If you have an atom
at thermal energies,
it would only come in
hyperfine states which
are thermally
populated, or molecules
come in rotation states, and
well your limited control
was simply to raise and
lower the temperature.
But with the advent of optical
pumping-- this actually
happened already with
classical light sources
before the invention
of the laser-- so
with optical pumping, you can
pump the internal population
of molecules into, let's say,
a single rotational state.
So this is control over
the internal Hilbert space.
And this was actually
rewarded with a Nobel Prize
to Alfred Kastler in 1966.
Of course, the next
step after controlling
the internal degrees
of freedom is
have control over the
external degrees of freedom,
and this means control motion.
This was of course
pursued by understanding
the mechanical aspect of light.
How do photons mechanically
interact with atoms?
This eventually led
to laser cooling
and Bose-Einstein condensation.
And those developments were
recognized with major prizes.
Well there is more to
it than controlling
internal and external
degrees of freedom.
You can then also say,
well, how much can we
control the number
of building blocks?
And eventually AMO
physics advanced
to exert control
onto single quantum
systems-- single
photons, single atoms.
A single atom in a cavity
exchanging a photon
with a cavity
thousands of times.
So this control of
single quantum systems
was actually just recognized
with a Nobel Prize
a few months ago.
Well, at this point I
sometimes make the joke,
we have gone from big ensembles
in many, many quantum states
to single photons, single atoms,
in a single quantum state--
a single quantum state
for many particles
is Bose-Einstein condensation.
So we have really gone down to
single atoms, single photons,
single quantum states.
Well, what comes next?
To have no atoms and
no light in vacuum.
Well, the vacuum has some
very interesting properties.
And if you talk
to Frank Wilczek,
the nature of the
vacuum and dark energy
is one of the big mysteries
in physics and in science
in general.
But the study of
that is definitely
outside the scope
of AMO physics.
So what happens is, when we
have gone down and have now
control over the
building blocks,
now we can sort of go up
again in a controlled way,
create complexity by
assembling a few photons,
a few atoms into new
entangled states,
so we can now take our system
into very different regions
of Hilbert space.
So what is defining
now the control is,
we want to use this pristine
control over the building
blocks to now put in something
which hasn't existed naturally
before, or when it existed
it was completely obscured,
completely hidden by
thermal motion or by you
can say homogenous broadening
our lack of control.
And the best
buzzwords are here now
entanglement and
many-body physics.
It's hard to capture that as in
a diagram, but let me try that.
I don't know actually
what I'm drawing,
but I think you get
the message that this
is sort of Hilbert space.
And I have 2 x's.
One is sort of entropy,
high temperature,
and the other one is complexity.
And for quite awhile,
people studied hot gases.
So these are gases, there's
a lot of entropy in it.
The complexity is actually
not particularly high.
And everything is described
by a statistical operator--
the density matrix.
The pursuit of
cooling, and actually,
control-- gaining
information about a system
is also a way of cooling.
If you know in which
state the atom is,
the entropy of
the system is zero
even if you haven't changed
the state of the atom.
So control and cooling, control
measurement and cooling,
has now taken us
to the point where
we have systems which
have no entropy anymore.
They are very,
very well defined.
And our goal now is
to take these systems
to much more complexity where
wave functions become entangled
and we have strong correlations
in many-body systems.
But this is now,
maybe here, this
is now described
by wave functions.
But here is the wave function
of a single particle,
and here we have highly
correlated, highly entangled
many-body wave functions.
So at least for me--
but all predictions
are notoriously
incorrect when you
look at them in a
few years from now--
but for me, this is where
the future of our field
is moving, to get into
interesting regions of Hilbert
space where no person
has been before.
As an experimentalist, and with
a lot of experimental graduate
students in this room,
I want to emphasize
that a lot of those rapid
developments of the field
are driven by technology.
So it's driven by
technology advances.
In the '50s and
early '60s, people
thought AMO physics
is pretty much dead.
Only a few people with gray hair
continue what they have done
and the field will
eventually die.
But then technological
developments
made it possible to do
major conceptual advances.
I've mentioned the conceptual
advances-- let me now
say a few words about the
technology which has driven it.
There was one phase of
developing lasers which
I experienced when
I was a student.
But those lasers were fantastic.
They were very narrow
already, very stable,
but they were very expensive
and very complicated.
So if you had one laser,
this defined your laboratory
and then you studied
a lot of things
with the single laser
you could afford.
Well, you're probably
not used to one big dye
laser pumped with a
big argon ion laser.
It was a $250,000
investment for the lab.
And of course, you couldn't
afford a second laser.
It required 50 kilowatts
pf electrical power.
And all this power
had to be cooled away
by gushing water
through thick pipes.
So it was an
expensive undertaking
but you could really do
wonderful science with it.
So what I've seen
in the last 20 years
is the proliferation
of solid state lasers,
starting with diode
lasers and continuing
until the present year.
So now, in a lot of our
laboratories here at MIT,
we have 10 lasers.
And we've stopped counting
them, because adding a laser
to the system is
almost like adding
an amplifier to a circuit
or adding another circuit
to a data acquisition system.
But it's not just the
simplicity of the lasers
which we have now,
the robustness--
to have 10 lasers in
the lab, it's fine.
Previously, if you had
three lasers in the lab,
you spent 90% of your time just
keeping the lasers running.
Those lasers, not so much
continuous-wave lasers,
but pulse lasers have also
very, very different properties.
Laser pulses got very,
very short-- femtosecond
or even attosecond.
Shorter pulses means
that the energy is now
focused to a much
shorter temporal window.
Therefore, laser pulses of
very, very high intensity--
if you focus a short pulse
laser on an atomic system,
you can easily reach
an electric field
of the laser which is stronger
than the electric field
of the atom.
So in other words, if you have
protons and electrons-- well,
maybe the outer electrons, not
get down to the single protons.
But maybe an ionic core,
and you've electrons.
Now, you should first look at
the motion of free electrons
in the strong field of the laser
and add the atomic structure
as a perturbation.
It really takes the hierarchy
of effects upside down.
So the appearance of
high intensity lasers
has given rise to a whole
new field of atomic physics.
Lasers got more precise.
The invention of
the frequency combs,
recognized by the
Nobel Prize in 2005,
meant now that we can
control laser frequencies
at a level of 10
to the minus 17.
And this has completely
redefined precision metrology
and has advanced the control
over atoms and molecules
I've mentioned before.
Finally, another
technical development
which plays a major role in
research being pursued here
at MIT and elsewhere
are the development
of high finesse cavities.
High finesse cavities
in the microwave range--
then they're
superconducting-- or high
finesse optical cavities
by having super mirrors.
It is actually
those super cavities
which have enabled the study
of single photon physics.
Because after all, photons move
away with the speed of light.
And if you want to observe
a photon in your laboratory,
it has to bounce around
zillions of times
in order to have enough
time for the photon
to do something interesting.
So sometimes a field at
the frontier of science
is defined by paradigms.
If you want to explain
to somebody why
your field of interest
is cool and exciting,
you usually do it by picking a
few really exciting examples.
And I want to show you how,
over the years, it has advanced.
Definitely in the
'50s and '60s, you
would have mentioned that we
understand now atomic structure
of multi-electron atoms.
Optical pumping just started.
So these were flagship
developments of AMO science.
The cool thing to do
in the '60s and '80s
was, use the new tool, the
laser, applied to atoms
and do laser spectroscopy.
Sub-doppler spectroscopy,
sub-natural spectroscopy,
resolving hyperfine
structure-- wow.
I mean, this was really
exciting in those days.
And well, the older
people I have met,
my teachers, my
thesis adviser, these
were people who started
their research career
before the laser was
invented but then,
as a young researcher,
embraced this new tool
and helped to
redefine the field.
Definitely in the '80s and
'90s, the cool pictures
were those of
magneto-optical traps,
atoms standing still
and hovering around.
So the new aspect
where mechanical forces
of light which led to laser
cooling and trapped atoms.
In the late '90s, of
course, the excitement
was about Bose-Einstein
condensation.
And it was really
Bose-Einstein condensation
which drove AMO physics
from single atoms, maybe
two atoms colliding,
to many-body physics.
It's always easier to
analyze those things
by looking backward, so if I'm
now getting closer to the past,
I have to be a little bit vague.
But in the 2000s, I think hot
topics were ultracold fermions
and the study of entanglement
and correlations.
And what is the paradigm
now or in the near future?
Well, I think you have
to help to define it.
If you make an
interesting discovery,
this is what people will be
pointing to and would say,
this is what now
defines AMO physics.
Some candidates are,
of course, if there
is a major breakthrough
in quantum computation--
let me put question marks here.
In the field called
atom science,
we may actually do some progress
towards topological states
which have different symmetries
and different properties.
And another emerging frontier
is micro-mechanical oscillators.
The last couple
of years, we just
had the breakthrough
for the first time.
Mechanical objects were cooled
to the absolute ground state.
So at least for that community
it was, but for many of us,
Bose-Einstein condensation
was 15 years ago.
Any questions?
Well, eventually we have
to talk about this course.
So I've told you
about, at least,
a snapshot of where AMO physics
is, how it has developed,
and on what trajectory it is.
In this course I want to present
you the concepts behind many
of the major advances
in the field.
So over the years, quite often
a topic was added to the course,
because I felt, hey, that's
getting really exciting,
that's what people want
to do in research, that's
what graduate students
want to do here.
And then the subject was
added and other subjects
were dropped.
I know in the '90s, I was
teaching aspects of laser
cooling, sub recoil
laser cooling,
which was the latest excitement.
This year, I may mention
it for 30 seconds.
So the course has evolved.
It wants to stay connected to
what is exciting, what is hot,
and what prepares you for
research at the frontier.
8.422, the second part
of the two-course cycle
in the graduate
course in AMO physics,
is somewhat different,
not radically different,
but is somewhat different
from part one, from 8.421.
First of all, 8.421, 8.422
can be taken out of sequence.
We alternate between
AMO 1 and AMO 2.
And whenever you
enter MIT, you're
probably in your
second semester,
take whatever we offer.
So I expect-- let me ask you,
who of you has taken AMO 1?
Yes, statistically, it should
be about half of the class.
It can be taken out of
sequence because that's
the way how we've structured it.
But to give you one
example is, in 8.421
you really have to learn
about hyperfine structure.
You have to learn
about atoms, you
have to learn about
Lamb shift and all that.
So you have to learn what
all these atomic levels are.
And here in that course,
in 8.422, I will say,
here's a two-level system
and then I run with that.
And we do all sort
of entanglement,
manipulation of
two-level systems.
So it helps you if you know
where those two levels come
from, but you don't really
need the detailed knowledge
of atomic structure, for
instance, to understand that.
So this is why the different
parts of the course
are connected, but in terms of
learning the material, somewhat
decoupled.
I've spoken to many
students who said
there was no problem
in starting with 8.422.
The only sort of critical
comment I've heard
is that taking 8.422 first and
then 8.421 is anti-climactic.
You see all this excitement
in the modern physics,
and then, eventually, you have
to work on the foundation.
Prerequisites for this course--
the course announcement
said 8.05.
It is actually 8.05 and 8.06.
The main part of 8.06
which we really need here
is perturbation theory--
time independent, time
dependent perturbation
theory, and this is usually
covered in 8.06.
However, I've had students who
took the course without 8.06.
If you're really
determined and want
to acquire certain
things by self-study,
you can follow this course.
So the topics we will
cover include QED.
I really want to talk about
light-atom interactions
from first principles.
Sure, 95% of what
we're doing is just
done by saying we have
a matrix element, which
maybe the dipole matrix element.
But you really have to know what
are the approximations, what
are the conditions, which lead
to the dipole approximation.
And I want to do that
from first principles,
and we do that
starting on Monday.
So a discussion of light-atom
interaction has two parts.
One is the simple part--
excitation and stimulated
emission.
Because this can be simply
described by a unitary time
evolution, and you can do
a lot, if not everything,
by using Schroedinger's
equation.
Things get much more
complicated and richer
if you include spontaneous
emission or, more generally,
if you include dissipation.
Then we talk about open systems.
And for fundamental reasons,
we need a formulation
using the density matrix,
a statistical operator,
and a master equation.
One major part of the course
is discussion and [INAUDIBLE]
derivation of the
mechanical forces of light.
This will include
a discussion of
important experimental
techniques using
those mechanical forces.
So various simple and
sophisticated methods
of trapping and cooling.
We will spend some time in not
talking about atoms at all.
We're just going to talk about
photons, about single photons.
We want to understand where
the photon nature of light
makes light very,
very different from
a classical
electromagnetic wave.
Also, it's not
the focus, we will
come across basic building
blocks of quantum information
science.
Pretty much when atoms
and photons interact,
this is a fundamental
quantum gate.
And we'll talk about
the many-body physics
off quantum gases.
So maybe it becomes
clearer what we
are covering by saying
what we are not covering.
And this tells you
that there is at least
some selection of topics.
It's not that we talk
about everything.
We will not talk about the
physics above 10 electron
volts.
We will not talk
about collisions--
or maybe I should say,
high-energy collisions.
We will, of course, talk about
nanokelvin collisions, which
is the physics of
the scattering links
and some s-wave collisions
which are really
relevant to understand
quantum gases.
We're not talking about
any advanced topic
in atomic structure.
All we do about atomic
structure is done in 8.421.
And if you want to graduate
in atomic physics at MIT,
yes, you have to
understand atomic structure
at the level of
the hydrogen atom.
And maybe know a little
bit about a new phenomena--
when another electron enters,
when electrons interact
and that's a helium atom--
but we're not going beyond it.
Let me just mention here
that there is, of course,
more interesting things
in atomic structure.
For instance, if you go
to highly charged ions,
you have QED effects.
You can discuss very
interesting correlations
between two
electrons in an atom.
And you can have very
relativistic effects
if you have highly
ionized atoms.
If you have bare uranium,
then the electron
in the lowest orbits
becomes relativistic.
You can even see, if you scale
the fine structure constant--
which has an e squared in it--
with the charge of uranium 92,
well, 1 over 137 times
92 gives about 1,
so you really get
into a new regime
of coupling for atomic physics.
But we won't have
time to talk about it.
And this may be an
omission, because there
is really interesting
work going on.
We're not talking
about high intensity
lasers and short laser pulses.
This choice maybe
mainly determined
by that the experimental program
in the physics department
is not overlapping with that.
But of course, you know we
have world class researchers
and short pulse lasers in
the electrical engineering
department.
Any question about the syllabus?
Questions about what to expect
in the next 12, 13 weeks?
Well, then let's talk
about some technicalities.
I'll keep it short because
all this information is
available on the website.
We run the website
of the CUA server.
So it is cua.mit.edu/8.422.
When I say all the
information is available,
I have to say-- not yet.
I realized yesterday
night that [INAUDIBLE]
has re-modified the server.
I didn't have access
to the server.
I just got it an hour ago.
What you will find
under this URL
is the website from when the
class was taught two years ago.
And actually, more than 90
percent of the information
is the same.
I always try to
improve the course,
but I know it will be more
incremental changes and not
dramatic changes.
So if you look at the
website, you'll already
get a taste what the course is,
but within the next day or two,
we'll have updated information.
I know, at least
for most of you,
I have contact information
for MIT registration.
But if you are a Harvard student
or a listener just sitting
in and you haven't
registered for the class,
I would ask you to send an
email to our secretary, Joanna,
j_k@mit.edu, because I would
like to have an email list
for the class for corrections to
the homework assignment or last
minute announcements.
And then we'll add you
to the mailing list.
The schedule of the
class is, well, we
meet at this time on
Monday, Wednesday.
And let me know disclose, I
plan to occasionally teach
on Fridays at the same time.
Over many years, it
has been my experience,
if you have a class on Monday,
Wednesday at one o'clock,
you don't have another
class Friday at one o'clock.
Is that assumption correct?
So within the next few
days, I will tell you
on the website which Friday
I would like to teach.
The reason is rather simple.
Like every faculty member
who's active in research,
I have to go to funding agency
workshops and conferences.
I try to keep it to a
minimum, but on average I
will miss two or three classes.
And instead of
asking a [INAUDIBLE]
or a graduate student
to teach the class,
I would like to teach
the class myself.
So I will have makeup
classes on Fridays.
OK, that's the schedule.
Finally, talking
about requirements,
one requirement is homework.
We have 10 wonderful
problem sets
with a lot of problems
which I actually
designed from current research.
So you will actually recognize
that a lot of problems
are created based on some
research papers which came out
of my own group or other groups
at MIT in the last few years.
The good news is, there is no
mid-term, there is no final,
but there will be a term paper.
And the term paper is due
on the last day of classes.
The teaching team are
myself, Joanna Keseberg,
our secretary-- that's also
where you will be dropping off
your homework-- and
then we have assembled
a wonderful team of five TAs.
They are all advanced
graduate students.
And actually, I've picked TAs
from all of the active groups
here at MIT.
From Martin Zwierlein's
group, I. Chuang's
group, Vladan Vuletic's
group, and my group.
Are any of the TA's around?
Nick, Alexei, Jee Woo,
Lawrence, and Molu.
Each TA will be responsible
for two weeks in the course,
and the TA will indicate
availability and office hours
on the weekly
homework assignment.
Other details about
the term paper,
how long the term
paper should be,
the, kind of, what I
regard as an honesty code,
that you're not
trying to get access
to solutions from
previous courses,
all that is summarized
on the website.
And once I've
updated the website,
I'm sure you will read it.
Any questions?
OK, well, with that
we will actually
be ready to jump into
the middle of the course
and start with some heavy
duty equations of QED.
But no-- just joking.
I think this would maybe
spoil the introduction.
What I actually like to do
is, to make the transition
from the introduction
to the discussion
of atom-photon interactions
and quantum electrodynamics,
I always like to
start the course
by giving you an
appetizer by talking
to you in a lighthearted
but hopefully profound way
about the system,
which helps 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
during the semester.
But as I said, AMO
physics is moving along.
And what I now want to use
as an example which clearly
synthesizes many
aspects of this course
are atoms in an optical lattice.
So let me, in the last,
next 20 minutes or so,
make some connections to
different topics of this course
by using as a starting point a
concrete, 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 QED
Hamiltonian, which, after a lot
of manipulation and eliminating
complicated terms, will
be the dipole interaction.
But of course, each symbol
here is an operator,
and there's a long
story behind that.
In about two months, we will
describe light-atom interaction
with a formalism
which uses a Bloch
vector and the optical
Bloch equations.
There is a 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
defines a mechanical potential.
And if the electric
field is a standing wave,
then we generate, through
light-atom interaction,
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 find
it very interesting
to look at it from very
different point of view.
And maybe let me
use this example
to point out that I'm 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, and
the atom is just moving around.
We will use a photon picture
that every time the atom
feels a force,
photons are involved.
You don't see them in
the classical potential,
but photons are behind it,
and ultimately, the forces
of the classic 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 which
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 Lorenz force.
And I don't know if you
would know the answer,
but an atom is in
an optical lattice,
is the force just
the [INAUDIBLE]
the 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
Lorenz 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 add other
perspectives for you.
OK, so what I've
discussed so far
is that the standing
wave of light
creates now a periodic
potential for the atom.
And we will understand it
from many, many different
perspectives, from the
photon type, quantum optics
perspective, to the most
classical description.
So what immediately
comes to my mind
is that we now want to look at
this periodic potential in two
different situations.
We can ask, well,
whenever you have light,
spontaneous emission
is a possibility.
And we may ask, what happens
when spontaneous emission
is not negligible?
And we discuss
that approximately
in week nine of the course.
Then what happens is, an atom
has an excited and a ground
state.
And those in the excited
and the ground state,
do the atoms feel the
periodic potential?
Well, eventually, we
have to generalize
the notion of ground and excited
state into [INAUDIBLE] states,
and I will tell you all
about it in a few weeks.
But the situation can now be,
when an atom is in the ground
state, it has to move up
the standing wave potential.
Then it's getting
excited with a laser.
It has to move up again the
standing wave potential.
And then there may be
spontaneous emission.
So what I'm just describing
here is a situation
where the atom is mechanically
moving up the potential.
It's excited at the
top of the potential.
And it emits when it's
on top of the potential.
So the atom is doing
mechanical work,
and this is called
Sisyphus cooling.
This is the way, this is
one method, one mechanism,
of laser cooling which
leads to the lowest
temperatures in the laboratory
before evaporative cooling is
used.
So that's some cool
aspect we will come along
by discussing motion
in a standing wave,
but taking into account
that photons are emitted
and really understanding
when and where
are the photons emitted.
Well, the second
situation is, of course,
if spontaneous emission
is completely negligible.
Then we have a situation
where all what matters
is the potential,
and we can completely
forget that it's photons,
it's quantum optics
which has created
this potential.
We can simply use a
classical potential
in our description
in our Hamiltonian.
Now, again, we have
two limiting cases.
One case is when this
potential, or optical lattice,
is really deep.
Deep means that atoms are
sitting deep in the potential
and they can oscillate around,
but they cannot jump over
to the next potential.
So in this situation, you
would say, well, that's boring.
Nothing happens, the
atom just stays put.
But what is boring
for some of you
is exciting for some
others, because these atoms
are exquisitely controlled.
They cannot collide, they cannot
interact with other atoms.
So these are really the
most ideal situation
you can imagine for atoms.
Of course, if you have less
than one atom per site.
And this is the way how
you want to prepare atoms
for the most accurate
interrogations.
And you can build atomic
clocks, optical atomic clocks,
based on atoms insulated
in such a lattice, which
approach now 10 to
the minus 17 accuracy.
Well, if you drive
a clock transition,
if you take the atom from the
ground to the excited state,
you may face a situation
I mentioned earlier
that the periodic potential for
the ground and excited state
are different.
And that would actually
interfere with your clock,
because the clock
frequency depends now
on what the lattice is
doing to your atoms.
However, and we discuss
that in week four,
there are what people
call magic wavelengths,
where you pick a
certain wavelength
for your optical lattice where
the periodic potential is
absolutely the same for
ground and excited state.
So that means you have,
then, the perfect decoupling
between the ticking
of the clock,
the internal
structure of the atom
and the mechanical motion of
the atoms in the potential.
And in that situation,
you create a situation
which has been studied
since [INAUDIBLE], namely
with trapped ions.
If you have a single
ion in an ion trap--
and ion trapping is pursued here
at MIT in Ike Chuang's group--
you have just a single
object completely isolated.
And in the form of
the aluminum ion,
this has just been
demonstrated to be
the most accurate atomic
clock in the world with 10
to the minus 17 accuracy.
So anyway, with
optical lattices,
avoiding spontaneous emission
using magic wavelengths,
we can only engineer
with neutral atoms what
has been available
with trapped ions
but we can simultaneously
have 10,000 copies
and look at 10,000 atoms which
are all identical copies,
identical systems
with each other.
So you see already
from that example
that there will be intellectual
overlap and synergy
between talking about neutral
atoms in optical lattices
and talking about trapped
ions and how they are cooled
and how they are manipulated.
And we'll talk
about trapped ions
at the end of the
course, sideband cooling
of trapped ions,
which is week 12.
OK, so this is the simple
but pristine situation
that we have a deep lattice.
The other limit is
now that we have
a weak, or shallow lattice.
And the new physics
which now comes into play
is that atoms can
move around-- they
can tunnel from side to side.
So towards the
end of the course,
I think the last months,
approximately week 10,
I will give you a short
summary of what some of you
may have already learned in the
solid state course-- namely,
band structure of atoms in
optical lattices, Bloch states,
effective mass, et cetera.
This has now become
language of atomic physics,
because there is a very clean
and straightforward realization
of this physics
using cold atoms.
What we are mainly interested
in, in our research,
is when we have atoms which
tunnel in this optical lattice.
And for bosons, if the
interactions get strong enough,
the Bose-Einstein
condensate is destroyed
and what forms is
a Mott insulator.
This is a phase transition.
And for fermions,
we have a crossover
from a metal to a
fermionic Mott insulator.
And with that, we are already
overlapping conceptually
with condensed matter physics,
because the Mott insulator
is a paradigm-- one of these
paradigmatic examples where
you understand
some deep physics.
It's a paradigm of
condensed matter physics
where you have only a
partially-filled band.
Common sense, or
undergraduate textbooks,
would say,
partially-filled band, this
means you've a metal,
you've a conductor.
But because of the
interactions of the atoms,
the system is an insulator.
So this is where, really,
the many-body physics
profoundly changes the
character of your system.
Any questions?
Well then, let me
add one last aspect
to my introductory example
of optical lattices.
In a sort of
flyover, I described
to you what is the
physics we encounter when
we have an optical
lattice switched on
and the atoms move around
or they don't move around,
and both cases are interesting.
But if you think you've
explored everything, well,
then you think harder
and say, hey, there's
another angle we
can get out of it.
And this is, we can
take the optical lettuce
and simply pulse it on,
switch it on and off.
Well, what happens
is, and then it
becomes a
time-dependent problem.
It becomes something where
we can shape and control
the wave function of atoms
in time-dependent way.
Let me give you one example.
If we start with
very cold atoms-- can
be a Bose-Einstein condensate--
and then, for a short time,
we switch on the
lattice, afterwards, we
observe that we have still
some atoms at zero momentum.
But now we have atoms which
have a momentum transfer of plus
minus 2 h bar k.
You can understand
that-- and this again
exemplifies that we want
to look at the physics
from different
angles-- this can be
described that you have
an two-photon transition
from the ground state with
zero momentum to the ground
state with two-photon recoil.
So you can understand it
in the photon picture.
But you can also
understand it by saying
you have some matter
waves which are now
exposed to a periodic potential.
And you simply ask
what happens to waves
in a periodic potential?
Well, that's the same what
happens to optical waves
when they encounter
a grading, and that's
the physics of diffraction.
So in a nutshell,
this happens when
we use a pulse on an
optical potential.
And let me now finish
by telling you that,
again, in this situation,
we discover the ambiguity
or the two-sidedness of a lot of
things we do in atomic physics.
I've mentioned to you
that the same experiment,
the same experimental setup,
cold atoms in optical lattice--
you turn up the lattice and
you have the world's best
atomic clock, atoms just
isolated from each other.
You turn down the
lattice and you
have an interesting condensed
matter physics system.
Let me just show you that
the same two-sidedness
of atomic physics-- precision
and pristine control
and interesting
many-body physics--
happens when you pulse
on optical lattices.
So one application of
those optical lettuces
is atom optics.
You have atoms and when they
encounter an optical lattice,
some atoms will just continue,
will not be diffracted.
They have zero momentums.
Others are diffracted with
a transverse momentum.
You can then expose the
atoms to a second zone
where, eventually,
momentum is transferred,
and then the atoms
come back together.
So what we have here is an
atom interferometer where
atomic matter waves first
go through a beam splitter,
are reflected back towards each
other, all by photon transfer,
and then they're recombined.
So this pulsed optical lattice
acts as a beam splitter.
It is the way how, today,
the most precise atom
interferometers are built.
And this is used for
precision measurement,
for measurement of inertial
forces, gravity, rotation,
acceleration, and it is used
for navigation and accurate
observation of the changes
of the gravitational field
of the Earth.
Since we just had a talk by
Holger Mueller from Berkeley
day before yesterday
over at Harvard,
he talked about the combination
of atom interferometer
and frequency combs,
another development--
let me just mention that.
If you derive those
laser frequencies
from an optical frequency comb,
and with an optical frequency
comb you can pretty much
count the frequencies.
So this laser is mode,
I don't know-- 100,000
or whatever you are in the comb.
By doing that, by combining
it, you can actually
build an atomic clock
where-- let me just say,
plus combs-- can
give an atomic clock
which is called the Compton
clock because the frequency is
now given by the rest
mass of the atom,
but divided by a
big integer number.
So using completely unrelated
developments in AMO science
which I've mentioned, the
optical frequency comb,
combining it with the physics
of a pulse standing wave,
you now have an atomic clock
which is directly related
to the energy of the rest mass.
But finally, if you pulse
on an optical standing wave
and your object are
not individual atoms,
non-interacting
atoms, your object
is the Bose-Einstein condensate
or atoms which strongly
interact, then you're
not transferring
recoil to individual
atoms, you're
transferring momentum to a
complicated many-body system.
And this means what
we are measuring
is the dynamic structure factor.
If you have atoms, you
want to do spectroscopy,
you want to know what
energy levels are there,
and then you know your atom.
If you have a
strongly-interacting system,
you also want to know what
energy levels are there.
But each energy level
in a homogeneous system
or in a periodic
potential is associated
with momentum and
quasi-momentum.
So in other words, if you have
a more complicated system,
you want to figure out what are
the possible states in terms
of momentum and energy.
And the optical standing wave,
the pulsed optical standing
wave is the way how we
impart momentum and energy
to a system.
What I actually just
told you is a story
in my own research career.
I was a post-doc
with Dave Pritchard.
He had trained at
MIT in the '90s
by a pioneer in laser cooling.
And when we had
Bose-Einstein condensates
in the late '90s, Professor
Pritchard and myself,
we teamed up.
I was the expert on
Bose-Einstein condensation
and he was the expert
on atom interferometry.
So just by sort of
exploring things,
we took Bose-Einstein
condensates
and we pulsed on
a standing wave.
What was on our mind was, hey,
let's build an interferometer.
But I'm more of a
many-body physics person.
I suddenly said,
yes, but if we now
change the momentum and the
frequency of this standing
wave, what happens?
And I suddenly
realized that this
is a way to measure properties
of a Bose-Einstein condensate
in a way which hadn't
been done before.
So I realized--
and this is maybe
the last thing I want
to tell you today--
I realized in my own
research and my collaboration
with Dave Pritchard, that
we'd built an experiment,
and we just turned one
knob at our experiment,
and the following day
we were no longer doing
atomic interferometry, we
were doing many-body physics.
So this is, I think, what
makes our field exciting.
We are using the tools, the
precision, and the control
of atomic physics,
which leads to the most
accurate atomic
clocks in the world--
atomic clocks, which are the
most accurate in the world.
And we are using those tools to
do entanglement and many-body
physics.
And I think it's just a
compelling combination.
Anyway, that's an
appetizer, that's
an outlook over the semester.
Do you have any questions about
the last examples I gave you
or the course in itself?
OK.
No homework assignment today.
And we'll meet Monday
at the same time
here in this lecture hall.
