M1L3j.txt

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The last thing in this major section
is the famous Hanbury Brown-Twiss experiment.
This was a landmark experiment done in the 1950s
and it was the first experiment which really looked
at G2 functions, correlations, which one could see
was the beginning of quantum optics
and modern experiments with light.
Probably until then, light was just an electromagnetic wave
people regarded as boring.
But by measuring now correlations,
people realized that it's an interesting object to study.
I want to just go over the basic scheme.
You'll look at it a little bit more
closely in your homework assignment.
So the idea behind the Hanbury Brown-Twiss experiment
is that you have a light source and you
want to characterize it.
So the light source emits light.
And now this is important.
Whenever you want to detect two photons,
you want to figure out, is one photon
followed by another photon?
Technically, you cannot do it with a photon multiplier
because when a photon multiplier clicks, it needs many,
many nanoseconds for the photon multiplier to read out
the signal and recover to recharge up its electrodes
and be ready to take the next photon.
So therefore, when you want to find click click, double clicks
in the stream of light, you have to involve a beam splitter
and involve two photodetectors.
Sure, you now need an adequate description.
But in principle, you can now find two photons
which are only a few picoseconds apart because the first photon
is observed by the first detector
and the second photon is detected
by the second detector.
Sure, you would see what happens if in the beam splitter,
both photons go detector one.
Well, that's tough luck.
That's one-- you take one chance in two
that the photons, the two photons
go to two different detectors.
But the beam splitter has to be part of your experiment,
has to become part of your description.
And this is what you do in homework number one.
So, what we are asking here when we measure the G2 function--
let's assume that tau equals 0.
We are reading out a signal and what we are using
is a coincidence detector.
We are looking there in a very small temporal window,
two photons are detected simultaneously.
Well, this is the quantum version.
The classical version is that the G2 function
is the product of the intensity at times
t times the product of the intensity at time t plus tau.
So what you would do here in this circuit,
you would take the signal from this detector,
the signal from that, and multiply the two.
This is how you determine i of t times i of t plus tau.
So whether you do it in the classical domain
or whether you do it in the quantum domain,
this is the way how you experimentally
measure the second order correlation function.
In the classical limit, you don't have to worry about it.
The classical limit is always the limit of high intensity.
So at any given time, you have a ton of photons.
And then at beam splitter, half of the photons go left,
half of the photons go right.
You have an equal splitting.
You have exactly half the intensity
in the left arm and the height arm after the beam splitter.
So there is no problem at all with the quantization
because this is the classical limit.
So classically, you can say-- actually,
I shouldn't say photon.
I should actually say intensity.
The intensity splits equally.

And if you do the measurement with a coincidence detector,
you find the difference between the G2 function, which
I discussed earlier-- the G2 function is
one for coherent light or laser light and the G2 function
is two for thermal light.
That's actually the only way how you can distinguish
a light bulb from a laser beam.
If you put a light bulb into a cavity or couple the light
from a light bulb into a fiber, the light
becomes spatially a single mode.
If you put a very narrow spectral filter
or [INAUDIBLE] cavity, the light becomes single mode
in frequency domain.
So when you take a light bulb and spatially and spectrally
filter you that it is single mode, in terms of the mode,
it is single mode as a single mode laser.
But it is a correlation experiment which shows you
that you started with a thermal source,
it has a G2 functional of two, and you can never
get rid of it, whereas the laser beam has a G2 function of one.
OK, so this is a classical version.
In the quantum version, especially when
we have a single photon, the photon
can go to only one detector.
And that means for this extreme case of a single photon,
the G2 function is 0.
Anyway, you will look at the whole situations in more detail
in your homework assignment.
Yes.
So, if you looked at different [INAUDIBLE]
in the single mode [INAUDIBLE] final G2 [INAUDIBLE].
Because [? they're ?] [INAUDIBLE]

A single-- we have to be now a little bit careful.
If you have a single mode [? flux ?] state,
there's only one photon.
And once this photon is detected, we have vacuum.
We have no photon left.
So, what may be confusing here on first sight
is that the way the experiment is done and has
been historically done, it's not done with [? flux ?] states.
It's done with a light source and a continuous stream
of photons.
So [INAUDIBLE] experiment, he looked at a light bulb
or he looked at starlight and such
and determined the intensity correlation.
He couldn't do the experiment with lasers.
But now, we do it with a laser beam
and we find the G2 with one.
But in those situations, we actually
do not have the way-- actually, we
have a beam, which is a stream of photons,
and this requires a little bit different description.
In other words, when I have a coherent state,
a laser beam is always replenishing
the coherent state.
The laser beam preserves the electric field
whereas, strictly speaking, the way how I described it
for pedagogical reasons is you have a cavity which is filled
with coherent state alpha.
And then you start analyzing that.
But in other words, what we have focused
in the simple description is that we have a quantum
state, which is prepared.
It's a closed system.
And now we do our detection.
The experiment, how it is done, is often
done as an open system where you couple the system
to a light source which is always
replenished in your experiment.
So have to be careful, especially
with a single photon.
I think in essence, the experiment
would be done with a single photon light source,
but the single photon light source
has a high repetition rate.
It's sort of-- I showed you how to generate single photons.
You have sort of an [? heralded ?] single photon.
You know the single photon comes now.
You do the experiment and then you repeat it again.
And then what you have is you only
look at one single photon punch at a time.
And then you find indeed that doing that temporal window,
you will never find a second photon.
So this may happen in a few nanoseconds.
Then, you wait a microsecond and the next photon arrives.
And it doesn't-- of course, if you would now describe
your light source, what is the G2 of tau and tau is
a microsecond and the microsecond is the time between
the first single photon bursts and the next single photon
burst, now you will find that your G2 function is not zero.
But this is unrelated to the repetition rate of a signal
photon and not to the single photon itself.
I think you got that taste.
Your homework is really simple.
You just deal with a closed system.
You look at a quantum state at a time.
But if you map it onto a beam experiment,
you have to think about it what does it
mean to have a replenishment of the quantum state?
Any other question?
I know I have to stop, but--
We just [INAUDIBLE] in the beam splitter [INAUDIBLE]
beam splitter should do some [? stuff, ?] right?

Yes.
Actually, this will keep us busy for a while,
[? that ?] even if we do not put in any light,
we put in the vacuum state.
And you will find that the description of the beam
splitter in the quantum picture is incomplete
unless you specify that your beam
splitter is coupling in from a different mode-- the vacuum
state.
Yes, this will be very important and we'll cover it
in its full glory. [? Timo? ?]
I just had a quick question. [INAUDIBLE] the way you can
distinguish from a thermal state [? and a coherent ?] state is
[? from ?] the G2 .
So, from an experimental perspective,
we do most of our experiments if we just
had, like, thermal sources that were very single node,
so to speak?
Oh, yes.
[INAUDIBLE]
All the laser cooling, all the molasses,
all the absorption imaging-- all of that
would work if you had a single mode thermal source.
Lets face it.
We say we use lasers for everything we are doing,
but the only property which distinguishes
a laser from a tehrma.
Light source, we're not taking advantage of it.
[INAUDIBLE]
Of course, practically, if you take a thermal source
and filter it down to a single mode,
you will be left with only a few photons.
You cannot create an intense enough single light source
unless you use stimulated emission into a single mode,
and that's a laser.
[? Colin. ?]
The correlation function for [INAUDIBLE] LED light,
that's not really a thermal source as [INAUDIBLE] describe
[INAUDIBLE] distribution [INAUDIBLE]
be closer to [INAUDIBLE] like a laser even
though there is no [INAUDIBLE].

Well, LEDs in some limit are quantum objects.
So actually, do you know what the G2 function of LED is?
Does it become laser-like or does
it become even anti-bunched?
Because if [? this is ?] a relaxation mechanism-- so
anyway, what Colin says is there are actually
more different light sources than just the laser
and the thermal light source.
There are LEDs or semiconductor devices
which provide photons with interesting statistical
properties.
I don't know exactly what-- I've heard about it that LED light
sources have some special properties,
but I don't remember which is the one.