  A periodic perturbation such as a laser field cannot induce transitions
between two decoupled states for which the transition matrix element vanishes.
We show, however, that if in addition some system parameters are varied
adiabatically, such transitions become possible via adiabatic-change-induced
excitations to other states. We demonstrate that full amplitude transfer
between the two decoupled states can be achieved, and more significantly, the
evolution of the system only depends on its path in parameter space. Our
technique then provides a valuable means of studying nontrivial geometrical
dynamics via auxiliary states with large energy splittings.
