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M1L1e.txt
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M1L1e.txt
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#
# File: content-mit-8-421-1x-subtitles/M1L1e.txt
#
# Captions for 8.421x module
#
# This file has 103 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------
So let me bring out the difference
between a two-level system and an harmonic oscillator
a little bit more by discussing the situation of cavity QED.
Let's assume we want 100% population in the first excited
state.
So an harmonic oscillator in the system
is prepared in the first excited state.
This is also called a Fock state,
with one quantum of excitation.
And it's a rather special state, where people have worked hard
to generate it, because you cannot realize it
in an harmonic oscillator.
And let me explain it in the following way.
If you have an harmonic oscillator,
you start and you would drive it.
And you try to put 100% in the n equals 1 state.
Before you have accumulated 100% percent
in the n equals 1 state, you drive it already
to higher states.
And of course, you know when you start
driving an harmonic oscillator classically or quantum
mechanically, you create a coherent state, which
is a superposition of excited states.
So we would say an n equals 1 state cannot be excited.
We usually get a coherent state, which
is a superposition of several-- of many or at least
several states.
Whereas in a two-level system, we can just do a pi pulse,
and to put all the atoms in the excited state
is nothing special.
Whereas to have a cavity filled with photons,
and selectively excite the n equals 1 state,
this is special because it's not easy.
It's not straightforward.
So in cavity QED, you can do it if you have anharmonicities
or nonlinearities.
So let me explain.
That means it needs either in-- well,
it's an anharmonicity or some form of-- so
if you have a situation where you
have your harmonic oscillator, but the energy levels
are not equidistant.
So the difference between this first and second excited state
are not the same, then you can drive the system.
You can prepare Fock state in n equals
1, like in a two-level system.
And you're out of resonance to drive it to higher states.
So here what you realize is a sort of two-level system,
and that allows you to create those special state which
are regarded as non-classical, very special states
of the harmonic oscillator.
And one way how you can create it-- well,
if you have an empty cavity, each photon
has the same energy.
Then you have an equidistant harmonic oscillator.
But if you put-- for instance, you add an atom to the cavity,
and the radiation is interacting with the atom,
then you get-- we'll talk about it later.
The atom and the photons interact with the Rabi
frequency, and then you get a splitting called
the normal mode splitting.
And this level splitting is proportional to the Rabi
frequency, and we discuss it later.
But many of you know that the Rabi frequency
scales with the square root of the photon number.
So therefore you have a splitting
which is proportional to square root one, square root
two, square root three.
And you have a spectrum which is no longer
an equidistant system, and then you
can create non-classical states of the photon
field, non-classical states on an harmonic oscillator.
So anyway, I thought I wanted to bring it up
at the beginning of the class, because a lot what
we are discussing in this class is
we re-discover in many situations in atoms,
in the light, in the way how light and atoms interact.
Harmonic oscillators and two-level systems,
often I say they are the same.
They behave in the same way.
But I hope this introduction remark tells you,
when can you think in one limit, and when do you
have to apply the other limit?
Another take-home message you may take from this discussion
is-- harmonic oscillators, yes, we
have quantum harmonic oscillators.
But even the quantum harmonic oscillator
follows a classical description.
So the real quantumness, what makes quantum optics quantum
optics, and Cavity QED a wonderful example of quantum
physics is the physics embedded in a two-level system.
That we can put one quantum excitation into something.
Exactly one is as much quantum as you can get.
This is realizing the two-level system,
and this is related to this phenomenon of saturation.
You can saturate a two-level system,