M5L22f.txt

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Any questions?
Yes, Colin.
Are there any requirements on these two atoms
being located, like, within an optical wavelength
of each other?
Yes and no.
In the simplest example of [? super ?] [? variance ?],
we want to put them to within one optical wavelength,
and then we do not have any phase factors.
But we will talk about it next week that we have also
[? super ?] [? variance ?] in extended samples.
And then we only get the [? super ?] [? variance ?],
a coherence between atoms, into a smaller solid angle where
the phase factors are-- well, where the different phases are
very well-defined.
If you would now average the spontaneous emission
over different directions, you would get propagation phases
and you would have-- and the atoms would only
be coherent in one solid angle, but not be
coherent in other solid angles.
Other questions?

So, that's to the best of my knowledge
at the most fundamental limit what spontaneous emission is,
how accurately a spontaneously-emitted photon
carries forward the phase of the laser beam
which excited the atom, and then eventually,
when we have completely lost the phase because we excited
the atom to an excited state.
All-- everything what we discussed will be actually
carried to the next level when we discuss [? super ?]
[? variance, ?] because then we have n atoms--
n can be a big number-- which we excite together.
And if they emit n photons, the phase of this n photon field
can be very precisely measured.
So some of the uncertainties we have here
simply comes from the fact that, if you have only one
photon or one atom, there are naturally quantum fluctuations
of any phase measurement.
But that part will go away when we go to ensembles of atoms
where we have many atoms, and [? super ?] [? variance ?] is
then the way how we can sort of revisit the subject,
how well can you retrieve the phase of the laser field from
the spontaneously-emitted photons.

Other questions?
Nancy.
For the [INAUDIBLE] [? single ?] [? atom ?],
[INAUDIBLE] [? emitting ?] [? the phase ?] [? out ?]
[INAUDIBLE], or we just don't [INAUDIBLE] that we're going
to use for many atoms later?
So what's the question?
We have [? the ?] [? pi over-- ?]
[INAUDIBLE] [? equals ?] what measurements
do we make if we have just one atom.
Do we make any measurements, or more phase information?
I think the measurement is, in a way, what I indicated here.
We excite the atom.
Then we switch off this path.
And then we take this short pulse of light.
It's a wave train which has a duration
on the order of the natural lifetime of the atom.
And this wave train is interfered
with a local oscillator.
And the interference term allows us to retrieve the phase.
And if you use a strong local oscillator,
then we pretty much retrieve the quantum limit
of the measurement.
And the quantum limit of the measurement
is what I showed you in this cartoon
drawings of the phase-space distribution.
So essentially, we can read a Fock state like this.
If there is a Fock state, we-- if you have a Fock state
and we'll repeat the measurement many times,
we will measure random phase.

So what happens here is-- let me put it this way.
The homodyne detection is a way how
we want to measure the phase.
And whenever you want to measure the phase,
you get a phase, because the number you get from a phase
measurement is a phase.
But if you have a Fock state which
has not a specific phase but an equal probability
for all phases between 0 and 2pi,
then if you repeat a phase measurement many, many times,
you will get a random result for the phase.
So I think that's what my question originally was,
what measurement would you perform for this [INAUDIBLE].
Like, would you still do a phase measurement?
Because it's--
It's your choice.
If you want to do a phase measurement,
that's a way to do it.
And then for a Fock state, you will get a random phase.
But maybe for the Fock state-- of course,
you can see in hindsight the Fock state
doesn't have a phase, so maybe you
shouldn't bother measuring the phase.
The special thing about the Fock state
is that it has exactly one photon.
And so maybe you want to have a measurement which
is measuring the special character of the Fock state,
namely that you have sub-Poissonian distribution
of the photons.
Of course, this aspect of just having one photon
gets completely lost when you have a beam splitter
and you have [? zillions ?] of photons in your laser beam
with all the Poissonian fluctuations
in a coherent state and you superimpose it.
But this is nothing else than complementarity.
You can either measure the phase,
or you can measure the photon number.
And the question is, what are you interested in.