Controlled quantized adiabatic transport in a superlattice Wannier-Stark ladder

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, labeled by a conserved integer quantum number. Thus, controlling the eigenstates of the Hamiltonian and their energetic order in asymptotic limits allows one 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 labeling the order of eigenstates. We show here, 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.

Automated summary

The Born-Fock theorem is a fundamental theorem in quantum mechanics that provides the basis for reliable and efficient navigation in the Hilbert space of a quantum system with a time-dependent Hamiltonian through adiabatic evolution. By controlling the eigenstates and their energetic order, perfect adiabatic transfer between initial and target states can be achieved. The fidelity of the state transfer is limited by adiabaticity, and the selection of target states is controlled by the integer invariant labeling the order of eigenstates. In this study, we demonstrate the adiabatic control of eigenstates in a finite superlattice Wannier-Stark ladder, resulting in perfectly quantized single-particle transport across a predetermined 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 greatly influenced our understanding in this field.