M1L7j.txt

#
# File:   content-mit-8422-1x-captions/M1L7j.txt
#
# Captions for 8.422x module
#
# This file has 35 caption lines.
#
# Do not add or delete any lines.  If there is text missing at the end, please add it to the last line.
#
#----------------------------------------

Before we can improve over the fundamental shot noise limit,
I have to show you how the fundamental short noise
limit naturally emerges.
So I want to introduce to you beam splitter interferometers.
Interferometers are there to measure phase shifts.
You split a beam, we combine it, and if there's a phase shift,
you notice it.
You get interference fringes.
And I want to show you that, very naturally,
the standard quantum limit, the short noise emerges.
But then we are ready to look at our description
of the interferometer and say, where can we now change
the rules to put in more quantumness, more entanglement,
and eventually get higher precision.
Since the standard quantum limit is well known,
I want to rather quickly go over that.
So the goal is that we want to measure a phase shift.
And my first simple derivation of the phase shift
is that in this picture of the quasi probabilities,
the coherent state is a circle like that.
The width of the circle in natural units
is 1, but the radius of that is alpha of the coherent state,
which is square root n.
So now, if you ask how well with this uncertainty can
I observe the phase of the photon which circulates
in this quasi probability plane, you
find that the phase is 1 over square root n.
Or, based on your homework assignment number one,
you can see we have some Heisenberg
uncertainty between photon number and the phase.
And in a coherent state, the standard deviation
in the photon number is square root n,
and you again get the standard quantum limit.