M1L5k_CQ12.txt

#
# File:   content-mit-8422-1x-captions/M1L5k_CQ12.txt
#
# Captions for 8.422x module
#
# This file has 50 caption lines.
#
# Do not add or delete any lines.  If there is text missing at the end, please add it to the last line.
#
#----------------------------------------

Any questions?
And finally-- I think this is one of the coolest things--
now we want to talk about the displaced squeezed vacuum.
Now we put everything together.
Remember, we have learned by applying the squeezing operator
how we can squeeze the vacuum.
And then with the displacement operator,
I can move the displaced vacuum that there is an expectation
value alpha for the field.
So it now looks like a squeezed coherent state.
So this is now the state we have generated.
And I explained to you that such a state
can be generated by using a beam splitter in the limit where
the transmission coefficient goes to 1.
So the squeezed vacuum is pretty much transmitted without loss.
But now we have a very strong local oscillator.
Also, the reflection coefficient goes to 0.
We can just crank up the power in alpha in such a way
that r alpha squared-- the number of photons which get
reflected-- is n.
So the limit we are looking at-- it is small n and large alpha.
But what we keep constant, for actually all those equations,
is that we have n photons in that beam.
And I explained to you in class, and I showed it to you
with operators, that this set up is really creating
the displaced squeezed vacuum.
OK, now we have one laser beam which
has an average value of the field, alpha.
It has certain properties.
And now I want to ask you what is the variance of this beam?
We measure the photo current of this beam.
We measure, of course, the photo current is n photons.
But what is this variance?

So the choices are we have n photons is the variance n.
We learned before, with the 50-50 beam splitter,
that we were able, by squeezing the vacuum,
to eliminate half of the shot noise.
Maybe what I've done is wrong, and we get 2n.
We increase the noise.
Or does the noise really go to 0,
which means it's on the order of epsilon, whatever I defined
for the squeezing, for the short axis of the squeezed vacuum?
So now we are not subtracting currents-- no i1 minus i2.
We have one beam hitting straight the photodiode.
There are n photons per unit time.
And the question is, what are the fluctuations of this beam?
What is the variance?