M1L6g.txt

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# Captions for 8.422x module
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As I was preparing for today's class,
I actually saw a paper which just came out in science.
And they discussed the whole [INAUDIBLE] interference
experiment with fermions.
So let me just explain what happens.
So if you have two identical photons,
if you have two particles which impinge on the beam splitter,
they are the two input beams for the beam splitter,
you would see you have four different outcomes.
One is both come out here, both come out here.
Or they are both reflected.
Or they are both transmitted through.
And what happens is bosons, as I just pointed out,
bosons characterized by photons can only do that.
Identical photons want to bunch up.
They appear in pairs, 50% left output, 50% right output.
Well, for fermions they just do the opposite.
For fermions, you will always get one particle each.
You may immediately, of course, explain it
with the Pauli exclusion principle, which does not
allow two particles to be in the same state
after the beam splitter.
And you should contrast it with classical particle.
When you have two classical particles,
you will actually find that all those four possibilities, each
of them has a 25% probability.
So it was a major experiment, which
was featured in science when people realized
that with electrons they created electrons in a semiconductor
structure and showed, through some statistical measurement,
that this was the physics which happened.
The measurement they did is I forgot now details.
If you have bosons and you get either two here or two there,
you have more fluctuations in your system than for fermions.
And they conclusively showed that they
had realized the Hong-Ou-Mandel interference for fermions.
So this Hong-Ou-Mandel interference
is at the heart how we perform the measurement, which
is ultimately entangling the atoms.
But we need one more element.
We need sort of to scramble the photons in one more way.
And this is by adding circular polarizers at the input.
So we assume for now that we start out
with linear polarization in those states.
And here's our beam splitter.
Here is mode A and mode B which we detect.
And before we measure this home interference,
we put in quarter wave plates, which
provide circular polarization.
So if you start with linearly polarized light,
but we put in a polarizer, we-- after the circular polarizer,
we have a linear superposition of horizontal and vertical
at mode one.
And we have a linear polarization
and a superposition of linear polarization in mode two.
So this is a situation at the input of the beam splitter.
And if we expand it, we have probabilities
where the polarization is different
and where the polarization is the same.
So we have two detectors here.
And if both detectors click, then we
know that the input to the interferometer
was not HH or VV, because in that case
the whole Ou-Mandel interference would have directed
both photons to one output, and we would not
have obtained clicks for both.
So therefore, when both detectors click,
we know that the quantum state before the interferometer,
before the beam splitter, was HV or VH.
Or, of course, in another basis, one of those.
And this is sort of the ingredient,
is I will show you on Wednesday, which
can lead to probabilistic entanglement of atoms.