  Adiabatic passage employs a slowly varying time-dependent Hamiltonian to
control the evolution of a quantum system along the Hamiltonian eigenstates.
For processes of finite duration, the exact time evolving state may deviate
from the adiabatic eigenstate at intermediate times, but in numerous
applications it is observed that this deviation reaches a maximum and then
decreases significantly towards the end of the process. We provide a
straightforward theoretical explanation for this welcome but often
unappreciated fact. Our analysis emphasizes a separate adiabaticity criterion
for high fidelity state-to-state transfer and it points to new effective
shortcut strategies for near adiabatic dynamics.
