M1L3k_CQ2.txt

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OK.
So, if we assume now-- I hope you all
agree-- that the amplitude is obtained in this coherent way.
Then, of course, the question is: but, what
is the effective time?
When we sweep the resonance, we are far away.
Nothing happens.
Nothing happens.
Nothing happens.
Nothing happens.
We go through the resonance, everything happens.
Nothing happens.
Nothing happens.
Nothing happens.
So, this is the effective time.
When the wave function really changes,
and we create the coherent admixture in the second state.
And, it is this effective times squared,
which determines what happens.
What our transition amplitude is.
So, therefore, the question is: what is the effective time
in the Landau-Zener crossing?
I can give you three choices.
One is, the effective time is-- well we changed omega,
and the effective time is what is
the time until we have a detuning,
which is equal to the Rabi frequency.
Another possibility is that the effective time that
will coherently drive the system,
is one over the Rabi frequency-- just the Rabi, period.
Or, another choice how I can construct time out of-- the two
frequencies we have is omega Rabi omega dot--
these are our two elements.
So, another possibility how I can get time
is omega is frequency, omega dot is frequency squared,
and the square root of one over omega
dot-- at least fulfills the dimensional
criterion that this time.
So, my question for you is: what do you think
is the effective time during which we drive the system
coherently?
I have to tell you, before I made up the problem,
I did not know the answer.
But, I can also tell you that there is one-- only
one-- answer which is correct.