  The Born-Fock theorem is one of the most fundamental theorems of quantum
mechanics and forms the basis for reliable and efficient navigation in the
Hilbert space of a quantum system with a time-dependent Hamiltonian by
adiabatic evolution. In the absence of level crossings, i.e. without
degeneracies, and under adiabatic time evolution all eigenstates of the
Hamiltonian keep their energetic order, labelled by a conserved integer quantum
number. Thus controlling the eigenstates of the Hamiltonian and their energetic
order in asymptotic limits allows to engineer a perfect adiabatic transfer
between a large number of initial and target states. The fidelity of the state
transfer is only limited by adiabaticity and the selection of target states is
controlled by the integer invariant labelling the order of eigenstates. We here
show for the example of a finite superlattice Wannier-Stark ladder, i.e. a
one-dimensional lattice with alternating hopping amplitudes and constant
potential gradient, that such an adiabatic control of eigenstates can be used
to induce perfectly quantized single-particle transport across a pre-determined
number of lattice sites. We dedicate this paper to the memory of our late
friend and colleague Bruce Shore, who was an expert in adiabatic processes and
taught us much about this field.
