Nonlinearity-Inhomogeneity Competition in Discrete-Time Quantum Walks

TL;DR

This paper explores how nonlinearity and inhomogeneities interact in discrete-time quantum walks, revealing their effects on localization, delocalization, and the emergence of partially localized regimes through a comprehensive parameter analysis.

Contribution

It introduces a detailed analysis of the competition between nonlinearity and inhomogeneities in quantum walks, highlighting their impact on quantum transport and localization phenomena.

Findings

Spatial inhomogeneities weaken localization and induce partial localization regimes.

Temporal inhomogeneities disrupt phase coherence, promoting delocalization.

The phase diagrams illustrate the interplay and stability of different dynamical regimes.

Abstract

We investigate the interplay between nonlinearity and inhomogeneities in discrete-time quantum walks on one-dimensional lattices. Nonlinear effects are introduced through a Kerr-like, intensity-dependent local phase, while spatial and temporal inhomogeneities are implemented via random variations of the quantum gate operations. By analyzing typical quantities, such as the return probability and the participation function, we identify distinct quantum walking regimes as the nonlinear parameter $\chi$ and the quantum gate parameter $\theta$ are varied. Spatial inhomogeneities weaken nonlinear self-trapping and constrict the region of robust localization. In this process, partially localized regimes emerge, characterized by the coexistence of a confined core and dispersive wave-packet components. In contrast, temporal inhomogeneities act as time-dependent perturbations that continuously disrupt the phase coherence required for self-trapped excitation, thereby enhancing dispersive emission and promoting delocalization. By using $\chi$ versus $\theta$ diagrams, we display a comprehensive characterization of how inhomogeneities modify the stability and extent of prevailing dynamical regimes, elucidating the competition between nonlinearity and inhomogeneities in discrete-time quantum walks.