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M5L23k.txt
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M5L23k.txt
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#
# File: content-mit-8-421-5x-subtitles/M5L23k.txt
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# Captions for 8.421x module
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# This file has 151 caption lines.
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# Do not add or delete any lines.
#
#----------------------------------------
So we want to go from state g to state
f with two-photon Raman transition.
Let's assume we have a detuning delta.
So now do you have any expectations whether this-- we
can do a pi pulse.
Two-photon Raman transition has a two-photon Rabi frequency.
I'll remind you in a second of it.
And if we do a pi pulse in that, we
have half a Rabi oscillation, which takes us from state g
to f, and we 100% transfer.
So do you have an expectation if this Raman
process-- how will it turn out to be in our figure of merit,
how many photons are emitted from the excited
state during the transfer?
Will it be the same at STIRAP?
Will it be the same as population transfer?
Will it be something else?
[INAUDIBLE]
It will scale with a detuning, but-- OK,
what I will do is actually I will in a moment say OK,
we have a certain laser-- what I'm going to say?
We have to compare apples with apples.
And here we have the detuning as a parameter.
And what I want to replace is what
will replace the detuning by the time it
takes to do the pi pulse.
So the detuning is determined by the condition
that we want to do the transfer in the same time as the STIRAP.
So this will eliminate the detuning.
So we want to use the same resources.
Our resources are time and laser power.
And we want to use our resources of time and laser power
in the same way for the two-photon transition.
So the question is, what happens to-- what
is the answer to the question how much
excited state is involved in the two-photon Raman process as
compared to STIRAP.
Do you have an expectation?
Who of you is doing STIRAP in the laboratory?
A few people, yeah?
Actually I know that 99-- or let me--
my observation is that 99% of the people
see STIRAP is special because it's a dark state transfer.
And when I started to confront famous people in the field
and say the two-photon Raman process does exactly the same,
they were completely surprised.
Anyway, I want to show you in one equation
that the two-photon Raman process has
exactly the same integrated population in the excited
state.
And therefore, it is as good-- the two-photon Raman process
performs exactly as well as the so-called dark state
transfer, where you never go through the excited state.
And this for me completely demystifies it,
because the two-photon Raman process
has in common with the STIRAP that everything is coherent.
And if everything is coherent, it
means we are not building our population,
we are only building up amplitude in the excited state.
So let me just show you in one equation
that indeed it works out in that way.
It's also a nice way to quickly recapitulate
what we learned in the previous chapter
about two-photon transitions.
So the two-photon Rabi frequency is nothing else
than the product of the two Rabi frequencies divided
by the detuning.
And of course, if you see larger and larger detuning,
as you said, everything will slow down.
But we know that the transfer time
will be the inverse of the two-photon Rabi frequency.
And this is delta over omega squared.
So therefore, we will eliminate delta from our equations
by replacing it by the time it will
take to perform a pi pulse between the two ground states.
OK, so what is the probability to be in the excited state?
Well, we've done the theory of the [INAUDIBLE] stock effect.
We have beaten perturbation theory to death.
You know the first order admixture
is omega Rabi over delta, and the probability
is omega Rabi squared over delta squared.
So therefore, the probability to spontaneously emit a photon
is omega Rabi squared over delta squared times gamma times t
transfer.
And this is nothing else than gamma divided by omega Rabi
squared times t transfer.
So if you use a Raman pulse to transfer the population
coherently, the integrated population
of the excited state, which is a measure for heating
and a measure for winding up in the wrong state
through emission through a false state
is inversely proportional to your laser power,
and inversely proportional to the time
you can afford to do the transfer.
Exactly the same as for STIRAP.
And the limit to the transfer time in both cases
is set by the coherence time.
Try to tell people who do STIRAP that a two-photon Raman
pulse will do exactly the same as STIRAP,
at least in populating the excited state.
They will be surprised.
Because here you explicitly go through the excited state.
We don't have a counter-intuitive sequence.
We switch on both lasers simultaneously.
But I think this for me illustrates, or completely
demystifies, what people have said about the dark state
transfer in the STIRAP process.
Any question?
Cody.
[INAUDIBLE]
What's the advantage?
Why are you using [INAUDIBLE] sweeps
when you go from one hyperfine state to the next,
and why don't you use a pi pulse with your rf generator?
Because it's more robust.
[INAUDIBLE]
As you said--
No.
What if you do STIRAP [INAUDIBLE]
But similar if you detune-- if you detune your--
the condition is the same.
If you have your two Raman lasers and you detune them,
you no longer have resonant Rabi oscillations,
you have off-resonant Rabi oscillations.
And you will find, if you want to do the transfer in half
a period, you have to make sure that you
don't get one cycle of the beat node
or one cycle of the detuning in your transfer time.
So the condition for the frequency stability
for the two-photon Raman and the STIRAP I think
are pretty exactly identical.
So I think it's pretty much the robustness,
and you have to decide what you need and what you want.
For instance, if you have a laser beam and the laser beam
has an inhomogeneous profile, you cannot meet the pi pulse
condition for the atoms in the middle and at the edge
of your laser beam.
But in STIRAP, you just provide plenty of extra power,
and then everything is robust against the laser beam profile.
So there are clearly advantages like that.
But all what I point out is the advantage
is not the population of the excited state.
It's the same.
Questions?