M1L4a.txt

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The last topic we discussed, it was a situation
of the Landau-Zener transition that you sweep for resonance.
You've all seen the Landau-Zener formula,
you all know that in crossing turns into an avoided crossing.
But I try to at least provide you
additional insight by emphasizing
that the whole process is absolutely coherent.
There is full face coherence throughout.
And what happens is there is a coherent transfer of amplitude
from the state one to the state two.
This is nothing else than Schrodinger's equation.
But I want to point out that for the short times
you sweep through, there is no detuning dependence here.
In other words, when I discuss what
is the effective time during which
the transfer of population takes place,
the time here is so short that the detuning doesn't matter.
Actually, the criterion which leads
to this effective time during which the transfer takes place
is actually exactly the time window
where the detuning is small enough that to say it loosely,
it doesn't make a difference whether you're
on resonance or slightly away.
The atom experience is the same drive field.
So based on this criterion we discussed,
that we can understand the Landau-Zener probability
in the perturbative limit as a coherent process
where we transfer population, we transfer amplitude with a Rabi
frequency during this effective time delta
T. It's not the only way how we can look at it,