Controlled quantized adiabatic transport in a superlattice Wannier-Stark ladder

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