- #1

Malamala

- 299

- 27

\begin{pmatrix}

0 & A \\

A & Bcos(\omega t)

\end{pmatrix}

If I populate only one of the states initially, at ##t=0## the 2 states are B apart, while after half a period they are -B apart. Basically the system went from one side of the avoided crossing to the other. If I am in the regime where ##A<<B<\omega##, based on some numerical calculations I made, the population transfer between the states is well described by ##sin^2(At)##. I thought that if you move very fast through the avoided crossing, you get full population transfer with a period of ##~1/\omega##. Why does it take so much longer ##~1/A## to get full population transfer. Also why is the population transfer even happening? Given that I go back and forth around the crossing I would have expected to populate and depopulate the states with a rate of ##~1/\omega##. Can someone help me understand this behaviour? Thank you!