Controlled Quantized Adiabatic Transport in a superlattice Wannier-Stark ladder

TL;DR

This paper demonstrates how adiabatic control in a superlattice Wannier-Stark ladder enables perfectly quantized single-particle transport across multiple lattice sites, advancing quantum control techniques.

Contribution

It introduces a method for controlling eigenstates in a superlattice to achieve quantized adiabatic transport, a novel application in quantum lattice systems.

Findings

Achieved perfect quantized transport in a superlattice model.

Controlled eigenstate order to direct adiabatic transfer.

Demonstrated robustness of quantized transport against certain perturbations.

Abstract

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.