M1L3j_CQ1.txt

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The first question which I will ask you,
should we calculate the transition probability
by using perturbation theory for an incoherent transition,
or for coherent transition?
Let me just explain to you what I mean, and then I'll
ask you for your opinion.
Coherently, we simply say in perturbation theory
we start with our population in state one.
We have, due to the coupling Hamiltonian, the time
dependence of the population in state two,
and that means if we integrate this equation for a short time,
we find an amplitude a2, and the probability
to be in the state two, which is the amplitude squared
is proportional to the Rabi frequency
squared times the effective time squared, the effective time
of driving the system.
Coherent processes are always quadratic in time.
OK.
If we do it incoherently, well, the way
how we describe incoherent processes
are Fermi's Golden Rule, which we have all seen.
And the probability in Fermi's Golden Rule is very different.
Well, it is proportional to the Rabi frequency squared,
to the matrix element squared.
But Fermi's Golden Rule gives us a constant rate,
and for constant rate, the probability is rate times time.
So now it is linear in time, and then
because of the delta function, Fermi's Golden Rule--
I'm missing a symbol, so I use gamma here.
It has nothing to do with the Landau-Zener probability,
this is just the density of states.
So I hope you know now what is the difference
between coherent and incoherent.
The most important part is that things
are linear in time for an incoherent process, rate
equation, and at least for small times
quadratic in time for coherent process.

OK, so now we come to this process
where we take atoms from spin up to spin down.
We evaporate with a weak cross-- almost 80.
With a weaker F drive, so we are closer to the diabatic limit.
So if you think about this problem,
I want you to tell me if this process, the transition,
the perturbative transition close to the diabatic case
is that should we use when we apply the perturbation
theory, the coherent picture.

Or the incoherent picture.
In other words, it's the dynamics of the quantum system.
When we go relatively quickly through the Landau-Zener,
crossing -- is that a coherent or an incoherent process?

I could add, see, it doesn't matter, but it does matter.