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M1L3h.txt
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M1L3h.txt
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#
# File: content-mit-8422-1x-captions/M1L3h.txt
#
# Captions for 8.422x module
#
# This file has 126 caption lines.
#
# Do not add or delete any lines. If there is text missing at the end, please add it to the last line.
#
#----------------------------------------
So this is now drawing our attention to the single photon.
And this is our next subsection.
I mean, this shouldn't come unexpected.
If we want to emphasize-- if you want
to emphasize the difference between quantum
light and classical light, where does it comes from?
Well, it comes from the quantization of light.
It comes from the photon character.
It comes from the fact that light is not
a continuous stream of energy.
It becomes quantized in photons.
So the granularity of light due to the photon character
is, of course, most pronounced for a single photon.
For instance, when we defined the G2 function
as the correlation of detecting a photon
and detecting another photon, well,
if you've only one photon, you find one photon.
And the next photon-- there is no photon to be detected.
So the probability of detecting two photons
is zero, and that only happens when
you go down to single photons.
So this is when certain fluctuations
are most pronounced, because the energy sort of is
dependent on a single photon.
Let me first address one misconception.
You can say, well, let's just use a coherent state.
And we talk about the attenuator--
the quantum attenuator, with all its operator beauty-- probably
not today, but in the next lecture.
But let me already sort of prepare you for that.
When you have a coherent state-- when you have a laser beam--
you can put in attenuator, and your laser beam
gets weaker and weaker and weaker.
But it stays a coherent state, and I will prove that to you
very soon.
So you can now say that you take your coherent state,
and you attenuate it down that there is only one photon left.
Is that a single photon state?
The answer is no, it is an attenuated coherent state.
Coherent states, as I've just shown you, are very classical.
They've always Poisson distribution.
They've always a G2 function of 1,
and attenuation is not changing it.
Attenuation is preserving that.
So now, I want to show you explicitly
why an attenuated coherent state may have an average photon
number of 1, but it shares nothing else
with a quantum state of one photon of any [INAUDIBLE]
in Fock state.
So a coherent state with an expectation value of one photon
is not a single photon.
And this can be, for instance, expressed
by looking-- what is, actually, the probability
if you have such a cohesion state, to find one, two,
or three photons?
Well the probability to find zero photons-- no photon
at all-- is actually 1/3.
So the probability to find one photon,
or to find zero photons, is the same.
The probability to find two photons is 0.18.
So here, you have a probability of finding a photon
and correlating it with the photon click.
And you have even, on first sight,
a surprisingly large probability to find three and four photons.
So in 2% of the cases, you will find four photons.
Whereas, in contrast, the Fock state with quantum number n=1
is an eigenstate of the number operator,
with eigenvalue m equals 1.
So that tells you that, if you want to get an n equals 1,
if you want to get a single photon state,
you cannot just use a strong laser beam,
or a strong light source, and attenuate it.
You have to work with something which genuinely creates
only one photon, without any ambiguity,
without any fluctuations, without any possibility
of creating two photons.
And I would actually say, over the last 10 or 15 years,
the creation of single photons has
been sort of a small cottage industry,
because single photons are often needed for protocols in quantum
computations, for experiments which really require accurate
quantum state preparation of light
and, in particular, non-classical light.
But of course, there are ways how you can get single photons,
and this is where you start with single atoms.
If you have a single atom in the excited state,
it can emit only one photon.
So, in other words, we cannot-- we often don't, or usually we
don't have the tools to prepare a single photon,
to take a single photon out of many,
many photons and store it separately.
But what we can control is single atoms.
We can prepare single atoms, and then we
can make sure that single atoms create single photons.
It's a little bit a way that-- we cannot control the bullets
which are fired, but we can control the guns.
And we make sure that each gun can emit exactly one bullet.
So that's a way how we can create
non-classical states of light.
Yes, so let's now look for those single photons
at the quasi-probability distribution.
So we obtain the quasi-probability distribution
by taking the single photon state,
and projecting it on a coherent state.
You'll remember-- it's higher up in the notes-- what
the coherent state alpha is in the Fock state basis,
in a number basis.
And so we are just picking out n=1.
And this was nothing else than alpha
squared times e to the minus alpha squared.
So therefore, in these diagrams, with real part
and imaginary part-- imaginary part,
if I plot the quasi-probability distribution, we get a ring.
The ring immediately tells us that there is no phase defined.
All phases are equally probable.
And that also means, if you don't have a phrase,
the average value of the electric field is 0.