ADIABATIC PUMPING IN FLOQUET AND OPEN QUANTUM SYSTEMS: AN INTERPLAY AMONG GEOMETRY, TOPOLOGY AND QUANTUM COHERENCE

Abstract

Adiabatic quantum pumping refers to particle transport induced by adiabatic sweeping of system parameters. In this thesis, adiabatic quantum pumping is studied with the aim of facilitating our understanding of topological phases in nonequilibrium and open system settings. The thesis is organized into seven chapters. In chapter 1, topological phenomena in condensed matter physics is briefly reviewed. Basic theoretical tools underlying the study of this thesis are developed in chapter 2, and demonstrated in several model systems in chapter 3. In chapter 4, we explore a periodically driven superlattice model, which could support colorful topological nontrivial phases absent in static systems. Their features are demonstrated in terms of quantized adiabatic pumping of Wannier states. In chapter 5, we further show that the inter-band coherence in the initial state could induce a significant correction to the adiabatic pumping, which would be useful to the detection of topological phase transitions and the coherent control of quantum dynamics. In chapter 6, an adiabatic perturbation theory for Lindblad evolutions is developed and applied to a dephasing Chern insulator model. There the pumping current is non-quantized and formed by a geometric component and a dynamical one originates from the inter-band coherence. We summarize our discoveries and point to some future directions in chapter 7.