M1L7o.txt

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This section is called Quantum Metrology.
It is a section where we want to apply
the concepts we have learned to precision measurements.
It's actually a chapter which I find nice.
We're not really introducing new concepts.
We're using concepts previously introduced.
And now you see how powerful those concepts
are What can be used for.
So we want to discuss the precision we can
obtain in quantum measurement.
We apply it here to an interferometer,
to an optical interferometer.
You could also discuss the precisional spectroscopic
measurements.
A lot of precision measurements have many things in common.
So what we discuss here is a generic example
for precision measurement, that we send light
through Mach-Zehnder interferometer.
Here is a phase shift.
And the question is, how accurately
can be measured the phase shift when
we use n photons as a resource?
And of course, you are familiar with the fundamental limit
of standard measurements, which is the shot noise.
And as a warm up, I showed you that when
we use coherent states of light at the input
of the interferometer, you obtained the shot noise.
Well that may not be surprising, because coherent light is
as close as possible, it is similar to classic light.
But then we discussed single photon input.
And by using the formalism of the Mach-Zehnder
interferometer, we found that the phase uncertainty
is, again, 1 over the square root n.
So then the question , is how can we go to the Heisenberg
limit, where we have an uncertainty in the phase of one
over n?
And, just as a reminder, I find it very helpful,
I told you that you can always envision, if you have n photons
and you multiply, put the n photons together
by multiplying the frequency by n,
then you have one photon with n times the frequency.
And it's clear, if you do a measurement,
that n times the frequency, your precision in phase
is n times beta.
So what we have to do is, we have
to put the n photons together, and then
we can get n precision of the measurement, which
is not square root n, but n times beta.
So this is what we want to continue today.
This is the outline I gave you in the last class.
If you have this optical interferometer,
this Mach-Zehnder interferometer,
and if you use coherent states or singular
photons as the input state, you obtain the shot noise.
Now we have to change something.
And we can change the input state,
we can change the beam splitter, or we can change the readout.
So we have to change something where
we entangle the n photons.
Make sure, in some sense, they act as one giant photons,
with either n time the frequency,
but definitely with n times the sensitivity to phase shift.