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visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Welcome
to a new teaching, new lecturing of 8.421. 8.421 is an advanced course in
atomic physics-- graduate level course. 8.421 is part of a new semester
sequence in atomic physics. Actually, 8.421 is taken
first in this sequence because we start with more basic
things about light and atoms. But the cost is
designed in such a way that you can start
with 8.422 or 8.421. So just to get an idea, who
has already taken 8.422? Should be about half the class. OK, great. So yes, you're not
repeating anything. And maybe for those of you
it's a little bit anticlimactic because you had all the fun. You saw all the
great things which can be done with
two level systems. And now in this
course we sit down and I explain to you what
are those two levels. What happens to those two
levels in magnetic field and electric fields? How are what they modified by
the lens shift and all of that? But you see how the two
things are connected. I talk about some course
formalities in a few moments. But let me first point
out that you're interested or you're doing research in
atomic physics at a really exciting time. AMO science is booming
and is rapidly advancing. And a lot of it is really
do to, well, of course, new insight, new ideas,
new breakthrough, but also combined
with technology. We have seen over the
last couple of decades a major development
in light sources. If I remember what lasers
I have used in my PH.D. And what lasers you were using,
well, there's a big difference. Big difference in performance
but also big difference in reliability and convenience. But just a few systems which
didn't exist a few decades ago. The Ti:sapphire laser, which
has really become the workhorse of generating lots and lots of
power in the infrared domain. But then it can
also be frequency doubled to the visible. When I was a [INAUDIBLE]
in the early '90s, people just starting to use
diode lasers in atomic physics. Here you are 20 years later. We see you much more
solid state lasers. And I would say even in
the last 5 to 10 years there has been another,
well, revolution is too strong a word but
another major advance by having extremely high power fiber
lasers, which are covering more and more of
the spectral range. So those advanced lasers
empower in the spectral range. We have seen major advances
in shaping short pulses. I remember when I was a student
how femtosecond lasers were that the latest--
well, they're required. The [INAUDIBLE] and femtosecond
pulses could only be produced in a few laboratories in
the world with a discovery of the Ti:sapphire laser
in Kerr lens mode locking. This has now become standard and
is even commercially available. But researchers have pushed
on attosecond policies are now the frontier
of the field. Well, if you have very short
pulses that also opens up the possibility to go
to very high intensity, you don't need so
much energy per pulse. You just, if the
pulse is very short, you reach a very high intensity,
which is the range of terawatt. And it is now pretty standard
if you focus the short pulse laser. In the focus of the
short pulse laser, you create electric
field strengths, which are stronger than the
electric field in an atom. So therefore, the
dominant electric field is the one of the laser. And then you may add
[INAUDIBLE] on whatever scheme the field between the electons
or the electron and the proton. So this is the
generational flight. But light also
wants to be control. And this is done
by using cavities. A single photon
would just fly by. But If you want a photo to
really intimately interact with a atom-- maybe
get it absorbed, immediate absorbed, immediate. If you really want to have the
photon as a [INAUDIBLE] state and not just as
something which flies by, you need cavities,
resonators, and we have really seen peak advances in
superconducting cavities as super codings in
the optical regime. And cavity QED in the optical
and the microwave domain have led to major
advances in the series of spectacular
experiment performed now with single photons. So the single
photon is no longer an idealized concept for
the description of life atom interaction. It has been a reality. And single photon control
has advances quickly. Well you can make major
advances in terms of light. Find new lasers, shorter
policies, higher intensity policies, and things like this. But the other part of atomic
physics-- one is light, the other one are the atoms-- we
haven't invented new atoms yet. We still got stuck with
the same periodic table. But we have modified the way
how we can prepare and control atomic samples. A big revolution
in the '90s or '80s has been the cooling of
atoms that now microkelvin, nanokelvin, and with
evaporative cooling, even picokelvin regime
had become possible. In terms of atomic
samplers, this was an evolution which
took place during my time as a researcher. Atoms always mean you're the
sample of individual atoms. Sometimes you
started interaction when two atoms are colliding. But atomic physics
was really the physics of senior particles
or two particles interacting, colliding,
or forming a molecule. But the moment we reach for
cooling nanokelvin temperature, atoms move so slowly that
they feel out each other. And that means suddenly
we have a system to do many-body physics. So the event of quantum
degenerate gases and many developments after that
with optical lattices and lots of bells and
whistles really meant that-- and this dramatic--
that atomic physics has made the transition
from single and two particle physics to many body physics. And for several research
groups in this end of what are called
atoms, this is, of course, an
important point here. Well, somewhat related to
that but more generally, the precision and
preparation and manipulation which atomic physics has
reached with quantum systems puts now atomic physics
in a leading position at the forefront of exploring
new aspects of Hilbert space. One can say that
Hilbert space is vast. But what is realized,
this simple quantum system is only a tiny little
corner of Hilbert space. And atomic physics,
if I want to define it in the most abstract
way, the goal is to master Hilbert space. And that means we
want to harness parts of Hilbert space,
which are characterized by quantum entanglement. Maybe single forms
between two particles but also between many particles. And of course, this is it
to a whole new frontier in quantum computation and
quantum information processing. So this sort of should show
you how technology, new ideas, control, and manipulation
is suddenly opening up whole new scientific directions. And just to add something
more recent to the list, we have now a major
research direction in AMO physics dealing
with cold molecules. And they're even prospects
of rewritting chapters of chemistry. What happens when
you do chemistry but not in the ordinary way
but at nanokelvin temperature? Or what happens when
you do chemistry where you have coherent
control in such a way that maybe the molecules
before and after the reaction are in a cool and
superposition state. So in that sense, the
conclusion of that introduction is atomic physics
has been successful because it continues
to redefine itself. And to prove the case, I
can say when I predict, when I try to
predict-- I didn't even try because I know
it wouldn't work. But if I tried to
predict 10 years ago what would be the hot topics of
today, I would have failed. What happens is just
breakthroughs and discoveries. And usually they happen in areas
where they are not predicted. As another angle,
atomic physics has seen more than its usual
share of Nobel prizes in the last two decades. Maybe the price in
1989 for ion trapping in Ramsey spectroscopy. Ramsey spectroscopy is used for
the generation of atomic clock. Iron trapping is a
basic building block. This was sort of givenof
some of the technology. But this was the only prize in
the long list I'm writing down now which was given for
something which was maybe invented a few decades ago. A lot of Nobel prizes are given
decades after the discovery. But all the more recent
Nobel Prize and this speaks for the
vitality of the field, we awarded for
developments which had just happened in the decade
before the prize. Whether it was laser cooling
just invented in the '80s. Whether it was Bose
Einstein condensation observed for six years
before the 2005 prize on precision spectroscopy with
lasers and frequency comb. This was also a development that
happened just a few years ago. And the most recent recognition
for Serge Haroche and Dave Wineland is about
the manipulation of individual quantum system. And this is where the
highlights of this were accomplished just
a few years, lets say, over the last five or 10 years. OK. Just sort of to make
a general case here, I continue to be amazed
how interesting ad rich the physics of
simple systems are. I actually expect that there
maybe even two Nobel Prizes in the near future
for, pretty much, understanding the
Schrodinger equation. You would say this has been
done in the old days of quantum mechanics in the '20s and '30s. And of course, lots of
people have been recognized. But there are two aspects
of the Schrodinger equation, which hadn't been
understood or which have been understood
only recently. One is the aspect of
entanglement and error correction. Nobody until 10 or
20 years-- nobody until [INAUDIBLE]
and collaborators introduced error
correction would have thought that the quantum
system can [INAUDIBLE] here, but you can
reestablish coherence by what is called quantum
error corrections. [INAUDIBLE] properties of the
simplest wording or equation for just a few--
well, [INAUDIBLE] it's for a few particles--
which we are not known or even the expert in the
field would have fled and said, no, this is not possible. And another aspect of actually
single particle quantum physics, which has been fully
appreciated only recently is the question of [INAUDIBLE]
phase and topological phase. All the [INAUDIBLE] in
quantum metaphysics, which is also spilling over
to atomic physics of quantum [INAUDIBLE]
topologically insulate as an [INAUDIBLE] means that
there are non-trivial phases-- non-trivial symmetries in the
single particle Schrodinger equation. So it's just that
as a case in point that the single particle
Schrodinger equation a lot of people thought in
the '40s and '50s. That's it. There is nothing
else to do research. And now we when whole
new fields emerging exploiting new aspects of
the Schrodinger equation. Will there be something
else of the same caliber to be discovered? 20 years ago, people
would've said no. And I just gave you two examples
of major new insight, which is has really changed our
understanding of quantum physics. A few years ago, I served
on a National Academy of Science committee trying to
do the impossible to predict the future of the field. But sometimes the National
Academy of Science is asked to give advice and try
to provide the best [INAUDIBLE] impossible but is exciting. Of course, we didn't
predict the future. But at least to the
extent possible, we summarized what are
the frontier areas where we see rapid
development and where it would be worth
investing further. And you will actually see that
a number of those frontier areas are where your research happens. One is the traditional area
of precision measurements. As long as atomic
physics exists, one of the specialty
of atomic physics is we can emphasize
measurements, atomic locks, and precision measurements of
fundamental concepts and all that. And that continues
until the present day. It was just two weeks ago
that there was a new nature paper on the really major
advance in atomic locks. [INAUDIBLE] clock has reached
the precision of 6 times 10 to the minus 18. It's amazing. We'll talk more about it. You really have to carefully
understand and measure small changes in the black-body
radiation because just the black-body radiation
creates frequency shifts, which would interfere with
their precision. An amazing accomplishment
for the field. So precision
measurements continue to be an important frontier. Of course, is there's always
the aspect of metrology, determine time frequency,
and other things with higher and
higher [INAUDIBLE]. But there are also applications. Just one example is
making atomically. Atomic physics methods
can be now used if you open at home
in an environment you can measure the magnetic field. So people are now talking
by using atoms or artificial atoms in the form of
[INAUDIBLE] senders to measure the magnetic field,
biological sounds, and all that. So measurement is
fundamental aspects but is also applied aspects. Well, other frontiers
are, of course, you can use support ultra cold. We've talked about
high intensity lasers. Ultra intense. Ultra short. Atomic physics is
more and more getting involved with nano materials. Materials with blue properties. Maybe materials with negative
index of the refrection, metamaterials or, in general
or plus [INAUDIBLE] materials. Nano materials can help
to shed light and explore new aspects of how light
interacts with matter. And of course,
the major frontier is the frontier of
quantum information. So given all this
excitement, you have many reasons to want
to learn more about it. And this course is definitely
a good starting point. Let me maybe tell
you a little bit what is the philosophy behind
the cost and what you will get. That means, of course,
at the same time what you will not get. This course is meant as an
systematic, basic introduction into AMO physics. It should really lead
the basic foundation that when you talk about
atoms to talk about light you are really an expert and you
can talk about it at the most profound level. So it's important here, and
this is the goal of this course, to provide enough knowledge
and enough foundation for that. So it's not a cause
where I just try to sample highlights
of the field and provide you with a
semi understanding of all this wonderful phenomena. I rather try to focus on
selective basic things but then also exciting things
but rather explain them thoroughly and teach you by
example than teaching you the big overview. The course, if I
want to characterize, is I would say it is
a conservative course. It's also, r in this
sense, traditional. One reason for that is MIT. The tradition we have at MIT. At MIT we have this
several generations of atomic physicists who
have shaped the field. And I learned atomic
physics as a postdoc from Dave Pritchard, who was
a graduate student of Dan Kleppner. Dan Kleppner was a graduate
student from Norman Ramsey. And Norman Ramsay was
a postdoc with I Rabi. And Rabi resonance is this
is [? reciprocating ?] of atomic physics. The resonance is sort
of what we will also focus on today and
in the first week. This is, sort of, the
most important concept in atomic physics
to really understand the nature of resonances
and all its implication. So I should say late in
my life-- I was already passed 30-- when I took
the first atomic physics class in my life, I took
it from Dave Pritchard. And I was really,
sort of, amazed about the course, which
had the traditional topics but provided a lot of insight. You can teach
traditional physics from the perspective of somebody
who does research today. So I want to give
you all connections. But at the same
time, I like a lot about the traditional approach. And some of it can be traced
back to Norman Ramsey. So eventually, over
the last years, I was the main person who has
shaped that on atomic physics course when I expanded it from
one semester to two semesters. But when I created
a lot of new topics, I always looked through Dan's
and Dave's notes and made sure the best of what they
taught, the best ideas they put the course, they still
survive until the present day. So this course is a
development and continuation of a longstanding tradition. I should say I
have been immensely enjoyed to co-teach the
course on a couple of occasion with [INAUDIBLE]
and [INAUDIBLE]. And [INAUDIBLE] has
made major contribution to the second part of the
course and [INAUDIBLE], especially to what
we will be discussing in the next few weeks. So what I think is unusual-- you
won't find it in many textbooks is that we start
out by discussing the phenomenon of resonance of
the [? harmonic ?] oscillator. And we will emphasize for
a while the classical part but then also, of course,
go to the [? creating ?] the mechanical aspects
of [INAUDIBLE]. Now I have to say
this [INAUDIBLE] between classical
and quantum mechanics is something I will emphasize
again and again in the course. I can guarantee you in this
course I will sometimes ask you interesting question, which
challenge your intuition. And you will most
likely recognize that often when your intuition
goes completely wrong it happens because
you believe too much or you over-interpret one
aspect of quantum physics. If I then tell you, but wait a
moment, now think classically. Push the classical
concept further. [INAUDIBLE] the electron
and the [INAUDIBLE] as an [? harmonic ?] oscillator. Regard lights [? catering ?]
as [INAUDIBLE] not of a kind of mechanical [INAUDIBLE] but
of a driven [? harmonic ?] oscillator. Suddenly, a lot of things which
come out of quantum mechanics make much more sense. So I've often seen when I had
a conflict in my understanding. And it's a [INAUDIBLE]
classical and [INAUDIBLE] mechanical explanation,
I've learned to trust much more
the [? semi ?] classical explanation. So that's why I feel it's
important to understand the classical aspects. And usually I would
also say understand the means to really
understand it's limits. And often I feel you can
understand the phenomenon only when you have a quantum
aspect, a classical aspect, and we know exactly where they
overlap and where they differ. So to see even quantum
mechanical objects occasionally from the classical perspective
provide [INAUDIBLE] insight. So therefore, I would
emphasize classical aspects. And for instance,
it may come for , many of who as a surprise and
you will see that next week that some aspects like the
generalized [INAUDIBLE] frequency, which you all or
many of you have seen for a two level system. We find it in
classical resonance. Just the classic [INAUDIBLE] of
[? motion ?] of a [? childes ?] [? core ?] has a generalized
[INAUDIBLE] frequency. And I do feel that
it is absolutely important for the understanding
of concepts that you know where do the concepts emerge? Where are they? Are they already there
in classical physics and [? survive ?]
in quantum physics? Or is it something new, which
is genuinely [INAUDIBLE]. So yes, I will teach a little
bit more classical physics in [INAUDIBLE] course. But because I've seen
within my own research experience that it's
healthy to shape the intuition for the
fuller understanding of the systems [INAUDIBLE] for. So residence is an over
arching [INAUDIBLE]. But then we have to
introduce our main players. The atoms come to stage. And we want to understand
the electronic structure, the [? fine ?], structure,
the hyperfine structure, you're going to
understand what happens in magnetic, electric, and
electromagnetic light fields. We want to understand
in a deep [? way ?] how do atoms interact
with radiation. This also leads us. There's a big difference. You would say, well, what's the
difference when atoms interact with microwave and atoms
interact with light. Well light or at high
frequency spontaneous emission becomes important. And then you have
an [INAUDIBLE]. You have an [INAUDIBLE],
which couples automatically to many, many states. So that's why radiation
is different from just electric and magnetic fields
because of the presence of all the vacuum modes, and
we'll talk a lot about it. There's one special aspect
about the cost, which I don't think I've seen in
textbooks in the same way. We are singling out
in a rather long unit the aspect of line shape. OK, we talk a lot
about an [INAUDIBLE]. But when you measure
the resonance, there is a line shape. And I found it
extremely insightful when I first saw Dave
[INAUDIBLE] doing it in his atomic physics
course to just talk about all aspects which
modify a resonance from a data function from a stick
diagram into a real shape. It can be
[? doppled ?] up water. It can be finite
lifetime [INAUDIBLE]. It can be an [INAUDIBLE] field. But there are lots of
interesting effects. And By discussing
them all together you gain major insight. So we discuss how
[INAUDIBLE] recoil, how the velocity of atoms
effect the line shape. And if you think you've
understood everything, I will talk to you about in a
very [? counter intunitie ?] aspect of line shapes
named the [INAUDIBLE]. If you put atoms
in the environment, you would say they collide. This should lead to
collision [INAUDIBLE]. But there is one aspect where
clinicians need to [INAUDIBLE]. And that's sort of a highlight
of this chapter which really sort of shows you how actually
all of those [INAUDIBLE] mechanisms are
somehow connected. Finally, and this puts us more
towards the end of the course, we want to understand what
happens when atoms interact not just with one photon
but several photons. And then we talk about
multiple photon processes. I should actually
say that I'm also emphasizing the multi
photon process a lot. I mean, often we just
simply do a transition between two levels. And there is a
operator that can be [INAUDIBLE] on a
[? two folder ?] operator, yes. But to understand the multi
photon aspect is important. And maybe to just give
you one aspect of it, when you think you do
one photon physics, often, you do two
photon physics. A lot of people think atoms
can absorb the photon. I've never seen
in my life an atom which has absorbed a photon. The photon is
immediately readmitted. It's a scattering event. An atom cannot absorb the photon
for good because the lifetime of the [? excited ?]
state is shot. So when you think absorption
is a similar [INAUDIBLE] event, there is a limitation
where, yes, you're allowed to think about it. But if you get confused
and it will confuse you, then you need the fact that
every absorption process is actually a two
photon process. Photon in and photon out. And sometimes by remembering
that it's not single photons, there are always two
photons involved, it helps you to avoid some
pitfalls of the similar photon picture. So therefore, multi photon, yes. It's not just high intensity
to photo transitions and atomic and such. It's also about the
deeper understanding. How does the single photon
interact with atoms? And finally, there
is something which has fascinated many physicists. The question about coherence. And coherence is as
fascinating as it is diverse because coherence can
have as many aspects and has many implications. And I also like a lot in
this traditional MIT cause that coherence is sort of
singled out as a chapter. And now I'll tell you about
all the different phases of coherence in
this chapter and not scattered throughout
the whole course. We have coherence
in single atoms. The simplest one is the
coherent superposition of two level, which is so
simple that it's almost boring. But there is an
enormous [? richness ?] when we put in a third letter. About 20 years ago,
an understanding of [? three level ?]
physics has really created a new
frontier in the field. Let me just tell you
[INAUDIBLE] words. Lasing without inversion. Electromagnetically
induced resonance. Those concepts happen due to
coherence between three levels. And we'll talk about that
towards the end of the course. Well we have coherence within
an atom between two different or three different
energy levels. But we can have also
coherence between the atoms. And at that point, the atoms
interact not individually. They act collectively. And of course,
coherence between atoms can be the coherence of
many atoms in a [INAUDIBLE] where they form one
big [INAUDIBLE]. But it can also
be the coherence. The atoms are not
coherent because they've [? formed the ?] [INAUDIBLE]. But they interact in a
coherent way with light. So there's only one aspect
where the atoms act coherently. They may be in different
quantum states. But the interaction with the
light is absolutely identical. And when it then comes
to optical properties of the system, the
light doesn't care if the atoms are different. The light only cares if
whether the atoms interact with the light in an
absolute identical way. And then you have certain
[? symmetries ?] of the light [INAUDIBLE]. And these coherence
between many atoms in the interaction
with light needs to-- I just give you the passwords. It's responsible for the
[? poses ?] of phase matching. Renew the crystal and
frequency [INAUDIBLE] you want all the atoms
to interact coherently. And it is also important
for the [? phenomenon ?] of super radiance. I found this
subject of coherence particularly fascinating. I should say it was the
subject of coherence where some maybe 10 years ago, I was
in a long lasting controversy with some colleagues
in my field. You know, they're
people like Phillips. When I met him, he's
one of the smartest [? genoatomic ?] physicist
and one of the fastest ones. And ideas just fly
back and forth. And there was only
one example where we disagreed over a
long period of time where he had good,
intuitive arguments, I had good intuitive arguments,
and we couldn't agree. And this was related
to the question when it came to warm
atom amplification. You know, some coherent
process, whether it is really necessary to
[INAUDIBLE] our [INAUDIBLE] or whether you can get away
with less, which is more the simple radiant way
where the atoms are different on different states
but they have an identical way to interact with light. And in the end, I could prove
that certain aspect which all people thought
in the field were due to the coherent nature
of atoms where sort of they were due to the fact that
these atoms can [INAUDIBLE] as an atom laser. It was just some form of
super radiance in disguise. So anyway, you will notice
some of my own interest in the chapter of
coherence when I teach it. So it's something which is
this face [? matching ?] and super radiance is
the physics of the '50s. But a deeper
understanding of it really developed when we had Bose
Einstein [? comments ?] and could put some of
those ideas to the test. So lets what you expect. Let's an overview
over the topics. The course will
have 26 lectures. And these are the
topics we cover. Do you have any questions
about the [INAUDIBLE] the structure of the course. There is something I'm going
to say about home-work. This semester [? Ike Shaman ?]
has teamed up with me. And as many of you know,
[? Ike ?] is one of the real drivers of MIT x, ED x, and
[? teach ?] [INAUDIBLE] learn at MIT. So he is now teaming
up with me and trying to put some of the
pieces online that you can have conceptional questions
where you can work on. And you will et
immediate feedback whether you're on the
right track or not. So this is a new
element, which we ant to introduce to the course. I still think there
are certain problems you have to just sit down
with a white piece of paper not knowing what
to write and start scribbling some creations. So we'll have
conventional problems. But you also want to
experiment to what [INAUDIBLE] possible to use elements
of new technology of [INAUDIBLE] course like that. I actually have
to say I regard it as a really very interesting
and Paul promising experiment to have some aspects of
teaching and learning in a graduate course. When MIT does MIT
x and, you know, broadcasting education
to the whole world, it's much easier
to think about what to do when you have
a basic introduction to classical physics
and yo [INAUDIBLE]. There is, sort of, a
standard curriculum. A lot of questions are simple. It's pretty
straightforward how you can have simple questions as
multiple choice questions. But this is different. This is really a [INAUDIBLE]
course in atomic physics. It's about deep and
profound understanding of complicated and
complex physics. I'm not sure to what
extent those complexity can be broken into smaller
elements, which can be put up as multiple
choice questions. Probably not. But on the other hand,
since MIT will never reach millions of people
with a graduate course in atomic physics,
the whole interest of going to the whole world
and reaching the whole world is [? absent. ?] And for me, I just want to
introduce this technology to increase the residential
experience for you students. So for instance,
videotaping, I'm not sure if these
videotapes will ever be shown to a
[INAUDIBLE] audience before we make them available. But the primary audience
maybe people like you who have a conflict
in attending a class and you want to check what
was presenting in class. I also have the idea that
this would be in the future. Once we have the
videotapes, maybe I can tell you look at the
video recording of the class. And instead of having
a lecture, we'll just have a
classroom discussion. So these are aspects
I want to experiment. But it's sort of exciting to see
how can new technology be used for a course, which is very,
very different from all the other courses, which
have been put online at MIT. Well then, as expected,
we have some 20 minutes to start with our first
topic, which is resonance. And resonance is what
describes the [INAUDIBLE] for two level systems. And also, and we
will touch upon this, resonances are the way hope
precision measurements are made. So what is a resonance? Well, we can first look at
the classical resonance. Well a resonance is something
where we have some variable and it varies periodically. So in other words, yes,
there is a variable, which an be anything. It can be the population
of quantum state. It can be an electric field. It can be the
position of an atom. It can be anything
you can think about and anything you can measure. And if this variable
the varies periodically, you have a resonance. Of course, the periodic
variation usually requires that you
drive the system. So you first drive it. And then the system oscillates. And this means now that when
you drive the system-- so this maybe a free oscillation. But now you drive the system
with a variable frequency. And what you then observe
is you observe a peak. So the phenomenon
of resonance is that you have something
which can periodically vary. And when you drive it,
you see peaked response when driven with a
variable frequency. Yep, this is pretty basic. And I don't want to
[INAUDIBLE] much more about it. But I can tell you we are
interested in atomic physics in every single possible
aspect of this resonance. The shape of the curve. How we can modify it. What happens when
we tie it strongly? When we tie it weakly? I mean, resonance is really the
language we talk atoms with. So but here I just want to give
a lighthearted introduction. The first thing we want
to add to the phenomenon that there is a resonance
at [? a certain ?] frequency is finite damping
that would mean, after the system is
driven, the oscillation does not last for an
infinite amount of time. And that implies that when
we drive the system and look at the response as a
function of frequency, it's there is a finite
[INAUDIBLE] [? delta ?] [? f ?] for the driven system. And as we will see in many ways,
the damping time in delta f are related by
[INAUDIBLE] transform. And we usually
characterize oscillators by the sharpness
of the resonance. And the sharpness
of the resonance is a ratio of the
beats of the resonance and the frequency of
the [? inverse ?] of it. So if you have an oscillator,
the kilohertz and the resonance is one hertz wide. We see the resonance
has a [? que ?]-- a quality factor of 1,000--
and that means you can observe a thousand oscillations before
the oscillation decays away. So what is special about
atomic physics here? Why do I emphasize it in
the [? introduction ?] of an atomic physics course? Well, the system is
that in atomic physics we often have exquisitely
isolated system. An [? atomic ?] [INAUDIBLE]
vacuum chamber or systems, which are prepared with all of
the tools and the precision, which we have developed over
decades in atomic physics. And therefore, the result
is that in atomic physics our oscillators
are characterized by an extremely high
quality factor [? Que. ?] And let me give you an example. If we look at an
optical excitation, the-- maybe let me point out
[? it's ?] something you all should try when you take a
class in atomic physics and even [INAUDIBLE] in atomic
physics that you have a few numbers in your
mind which match. So you know, every single
person in this room should know what is
the frequency of light. How many [? hertz ?] is-- what
is the frequency of a laser? The number I usually use for
those estimates is 10 to 15 [? hertz ?]. Who knows what
wavelengths this laser-- 10 to the 15 [? hertz ?]-- is? Well I view some visible light. But the speed of light
is 3 times 10 to the 10. So therefore, if I just use
the power 10 to the 15 hertz, it has to be 300 [INAUDIBLE]. OK, so never forget that
for the rest of your life. 300 nanometer is
10 to the 15 hertz. That means that most
of us who are working with [INAUDIBLE], which is 600
nanometer or 800 nanometer, the frequency is more 5 times
10 to the [? 40 ?] or 3 times 10 to the [? 40 ?]. But just as a ballpark
number, 10 to the 15 hertz is 300 nanometer. OK, so if we have an
optical excitation and many atoms have
that, what is the Q? What is the quality
factor of this resonance? Well when you stabilize you
laser to a vapor cell and you look at the resonance, then you
observe in a vapor cell that you have room temperature
Doppler [INAUDIBLE]-- we'll talk about Doppler
[INAUDIBLE] later in this course-- that usually
corresponds to a frequency on the order of a gigahertz. And that means that your quality
factor is on the order of 10 to the 6 a [? million ?]. That's pretty good. A million oscillation. That's a very pure oscillator. But of course, you can do much
better if you do Doppler free spectroscopy. [? Either ?] by having
the atomic [INAUDIBLE], which is intersected
at the right angle. Or even better, put the atoms
in an optical [? lettuce. ?] And this is what people are
now doing with the optical [? lettuce ?] clocks that
they put an atom in optical [? lettuce ?] where the Doppler
[INAUDIBLE] is completely eliminated. If you take a metastable
level, the lifetime of the exciting state
is, maybe, one second. And [INAUDIBLE] and other atoms
have those metastable labels. Then you can actually
get [? aligned ?] with, which is one hertz. And the Q factor is on
the order of 10 to the 15. I will show you a graphic
example of such an experiment in one hertz line [INAUDIBLE]
of an optical transition for an optical clock experiment
in the next class on Monday when I want to discuss
other aspects of it. But this is one of the
worlds best oscillator you can imagine. 10 to the 15. It's a mind boggling number. Well it's clear why
clocks have gone atomic. Mechanical systems
are actually not bad but, of course,
not nearly as good. If you take quartz
oscillator, well you can build pretty good clocks
out of quartz oscillators. You have quality
factors which vary between a few thousands
and a million. The best values are
reached at low temperature. And actually, even in the
event of atomic clocks, quartz oscillators or sapphire
oscillators still play a roll because you need, sort of,
[? fly ?] [? wheels. ?] In atomic clock you may
[INAUDIBLE] only every [? Ramsey ?] spectroscopy. You know, every tens of
seconds you get a signal. And in between you
need a fly wheel. And then clocks, which
have a very high signal to an [INAUDIBLE] station
but not the [INAUDIBLE] have you to [? interpret ?]
the premeasurements. We see actually a [INAUDIBLE]
source of mechanical systems in the form of
micro-mechanical oscillators. It was only achieved in
the last 2 or 3 years that micro mechanical
oscillators could be cool to the
actual ground state. And there's a lot of
interest of coupling the emotion of the
mechanical oscillator to an atomic oscillator because
they have different properties and for parental computation
and other explorations of [? filbert ?] space you want
to have different oscillators. And, you know, combine the
best of the properties. So therefore, there
is a real [INAUDIBLE] in mechanical oscillators. And those micro-mechanical
mechanical oscillators have often quality
factors of 10 to the 5. Here, I want to show you
a picture of [INAUDIBLE]. A nice one. Yeah, this is a micro
fabricated device. It looks like a little mushroom. And what happens is this
mushroom type structure can confine light, which
travels around the parameter as a so-called
whispering gallery mode. It's similar to an
acoustic mode, which can travel in the dome of
a [? beak ?] cathedral. That's how it was discovered. It's an amazing effect. I wish somebody would
demonstrate it to me. But if you go to one of
the ancient cathedrals and you're in a dome, somebody
can talk in one direction, the sound can travel
around, and you can hear it. There's a guided
special mode, which can travel around the
parameter of the dome. And here in the
microscopic domain, it's light, which is confined
in such [? and resonator ?]. So this is resonator for
whispering gallery mode. And that can have a Q on
the order of a billion. So the idea here
is that you have either one of those
mushrooms or a glass sphere and the light can,
sort of, travel around. And this is the
characteristics of this mode. Well you can go from
a tiny glass sphere to astronomical dimensions. And you also find oscillators. And the Q of those
oscillators is not really bad. How good is the Q of the
rotation of the earth? It fulfills all of
our requirements for resonance and oscillator. It's a [? parodic ?] phenomenon. [INAUDIBLE] The Earth rotates around
the sun once a year. And the question is
how stable is it. Well the number is 10 to the 7. It has a Q of 10 to the 7. So the precision of the rotation
of the earth is better than [? one part ?]
[? in a million ?]. You can also look at the
rotation of [? neutron ?] star. If those [? neutron ?] star emit
flashes of X-rays [INAUDIBLE] [? pulses ?] and you can measure
the rotation [? of neutron ?] stars, those neutron stars
have a quality factor of 10 to the 10. And of course, if
[INAUDIBLE] says, if a resonance has a
high quality factor, it can be used for
quality research. Then everywhere the line
is the more sensitive you are to tiny little changes. And you probably know this
[INAUDIBLE] with a Q of 10 to the 10, well, has been
used for the first, also indirect, observation
of computation waves. The [INAUDIBLE] rotates with
a very precise frequency. And you can measure it with
one part of 10 to the 10. And people have seen
that, over the years, the frequency of
rotation became smaller. And you can figure out that
it becomes smaller by just one [INAUDIBLE] 10 to the 10
because you're at this position. And what happens is when
the [INAUDIBLE] rotates-- when a neutron star
rotates-- [? it admits ?] [? computational ?] waves. And the computational
wave is energy, which is taking away from the
kinetic energy of the rotation. And therefore, the
pulses slows down. So having an oscillator
with such a high Q has an allowed researchers
to find a small effect in the damping of this
oscillator, which in this case were [? computation ?] waves. Of course, the story
I will tell you is about very small changes
of atomic oscillators, which led to the discovery
of the Lamb shift and to quantum electrodynamics. But the story is the same. A high quality oscillator
is the tool for discovery. OK, so we've talked
about resonances. Of course, there are
resonances which are useful and others which
are less useful. By useful we mean
they're reproducible. We can really make a
measurement and [INAUDIBLE] and do it again. And that's not enough
[? for ?] being useful. You also want to learn
something about it. So usually, we got
resonances as useful when they are connected
by a theory to something we are interested in. It can either be
fundamentally constance or let [? me say ?] other
parameters of interest. If you want to measure the
magnetic field with very high precision and you look
at atomic resonance, it's only useful then
[? to the ?] theory, which tells you how chief
[? or the ?] [? broadening ?] of the resonance is
related to magnetic fields. And this is, again, a
specialty of AMO physics. We have plenty of
resonances, which are useful by those standards. And if you compare to
[? astrophysical ?] oscillators, or
quartz oscillators, or [? fabricated ?]
oscillators, in atomic physics, we have the great advantage
that atoms are identical. We know when you measure the
concision atomic hydrogen in Japan and Europe and
in the United States, the [? venue ?]
has to be the same. For other oscillators,
you often don't note It. [? So ?] [? the ?]
[? showcase ?] of atomic physics is the
[? root back ?] constant, which is the best known--
the most accurately known-- constant in all of physics. And the reason is because
it can be directly measured by performing
spectroscopy and hydrogen with highly
[? stipulised ?] lasers. OK, of course, the
question is who's interested in all
those [? teachings ?]? Why do you want to spend
all of your PH.D or half of your life measuring your
[INAUDIBLE] constant to, maybe, 10 times more precision? Well it depends. It's maybe not
something for everybody. But there are some
connoisseurs who think that every
[INAUDIBLE] has provided new inside into nature. And let me just give
you one example. If you measure the [INAUDIBLE]
constant very precisely, you can now-- and
this has become the frontier of our
field-- ask the question, is their change with time
a fundamental constance? So when you measure the
[INAUDIBLE] constant today with 10 to the
minus 15 precision and measure it
again in a year, who is guaranteeing to you that you
will measure the same value. So with the precision
which I've just given to you in this measurement
of the [INAUDIBLE] constant, people are now able to say
whether the [INAUDIBLE] constant has changed 10
to the minus 15 per year. Of course of know, the
age of the universe is 14 billion years. That's about 10 to the 10 years. So even the worst case is
that if you would go back to the beginning of the universe
and the [INAUDIBLE] constant would change to 10
the minus 15 per year, it would've changed
by 10 to the minus 5 over the age of the universe. But this would be climatic
because the connection shows that life would
not have developed. The whole organic chemistry
would have been different if some fundamental
constant of nature had been different by one
[INAUDIBLE] to the minus 6, 7, or 8. So [? there are very ?]
extremely stringent limits how much
fundamental constant could have changed through
the evolution of life because life would
not have been the same if fundamental
constant had changed. The question, of
course, is should those fundamental
constant change. Well the answer
is we don't know. But there is a whole research
area in [? string ?] theory where they say that
our universe is, sort of, just one of many
possible [? minima ?] in a multi-dimensional space. And it's actually dynamic
[? minimal ?] [INAUDIBLE] changes the function of time. So there are people who
wouldn't be surprised if the world is not
the same in the future as it is right now
because the universe or whatever defines fundamental
constants is changing as a function of time. So the question is will
it be during your lifetime or will it even
be during, maybe, your PH.D when one
researcher says you know have an [INAUDIBLE]. And we find out that, yes, we
measure fundamental constant using the most
accurate atomic clock. And a year later, you
have measured something that's just a tiny bit but
significantly different. The second aspect why you
should always measure things as accurately as
possible and this is, sort of the, tradition
[? of our ?] field. If you can measure
something very accurately, do it because, yes,
there maybe surprising. And for instance, when people
looked at the [INAUDIBLE] with higher precision, they
found [? what we ?] talk about when we talk about
atoms in the magnetic field when people looked at the
anomalies [INAUDIBLE] effect, the discovery of that
is what nobody expected. That particles
electron has a spin. Or when people saw a tiny
shift in the spectrum of atomic hydrogen, it was
1,000 megahertz splitting. It was [? the Lamb ?] shift. This was the discovery of
quantum electrodynamics. And we know that precision
always becomes a tool. A tool to control atomic systems
control quantum mechanics with more precision. For instance, if you
can completely, sort of, hyper [INAUDIBLE]
structure, you can prepare atoms in a certain
hyper [INAUDIBLE] state. If you don't have the
resolution, you can't do that. OK so we're now going to talk. Go back to the resonance. When we look at
typical resonance, we have a frequency omega. A resonance frequency
omega [? 0 ?]. And we measure line
with [? delta ?] omega. In many cases, we will
discuss in great detail the line shape is a [INAUDIBLE]. And the [INAUDIBLE] is the
imaginary part of the 1 over 6 function. Omega 0 minus omega. And then there is
this parameter gamma. Gamma, which appears
in the [INAUDIBLE], is identical to
the [? full bits ?] at half maximum. And the Q factor
of a [INAUDIBLE] is omega 0 over gamma. Let me finish a few more minutes
with a short note about-- we've talked about resonances. I've talked about now the
two important parameters. The resonance frequency
and the full [INAUDIBLE] set half maximum. How do we measure those? And there is actually
sometimes a confusion. The more systematic
approach is you should measure all those
frequency and line [INAUDIBLE] in angular frequency
units, which are technically
radian per second. 2 pi per second. But since radian
has more dimension, you sometimes say we measure
it in inverse seconds. So this is the measurement
angular frequencies. And this is different from
the unit of frequencies. When we have a frequency, which
is an angular frequency divided by 2 pi, frequencies are
usually measured in hertz. The problem is that a hertz is
always also 1 over a second. And this is where
the confusion comes. So then you just point out how
you can avoid the confusion. You may right an angular
frequency or maybe a 0. It is 2 pie times 1 megahertz. Then you exactly
know what it is. Of course, this is nothing
else than six times 6.28 times 10 to the 6 second
to the minus 1. But you should never
say that omega 0 is 6.8 times 10 to the 6
hertz because then people don't really know
and you get confused and you confuse other
people if you really mean that this has a
frequency of 6 times into the 6 hertz on
angular frequency. So just be clean in your
thinking and your homework and all that that
a frequency when you mean angular frequency
is 1 over second, when you mean it as a
frequency, it's hertz, and this is often the
clearest form to say, yes, I know where to put the two
pie and I put it in explicitly. So we often in our papers
report frequencies like that. Finally, there is the
question about gamma. So what are the units for gamma? Well if you look at the
exponential which decays, it has e to the minus i omega t. And then it has the
imaginary part, gamma t. So gamma is really
a temporal decay. And there is no question
about frequency and angular frequency. It's not a frequency. It's not an angular frequency. It's a decay of it. So for instance, if gamma
is 10 to the 4 per second, you should never say gamma
is 10 to the 4 hertz. Or you should also
never say gamma is 2 pi times 1.66 kilohertz. That just doesn't
make any sense. Gamma is really
at a damping rate. AUDIENCE: [INAUDIBLE]. PROFESSOR: Yes? I need one more minute. AUDIENCE: OK. PROFESSOR: And is there
for an inverse time. The damping time
associated with this camera is simply the inverse of it and
in the case chosen its hundred microsecond. So just keep that in mind. Time is over. Any questions? OK, great. We meet again same place,
same time, on Monday.
