TOPOLOGICAL CHARACTERIZATION OF NONLINEAR QUANTUM SYSTEMS

Abstract

In this dissertation, we aim to study the effects of nonlinearity on the topological characteristics of topological phases of matter. The main content of this dissertation consists of three projects. In each project, we study a nonlinear topological phase characterized by the Gross-Pitaevskii equation. Notable results include the derivation of general expressions for topological invariants such as the nonlinear Zak phase or the displacement of a particle in nonlinear Thouless pumping, obtained by taking into account additional contributions to the geometric phase due to nonlinear dynamics. Additionally, we indentify a critical nonlinearity strength at which quantized pumping of solitons breaks down regardless of the protocol time scale. Such an obstruction to pumping quantization is attributed to the presence of self-crossing in nonlinear topological bands. These results are then used to design a probe for the observation of the nodal structures of a nonlinear Weyl semimetal.