Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices

TL;DR

This paper studies wave packet dynamics in a one-dimensional incommensurate optical lattice with a mobility edge, revealing unique mixed features and phase distinctions using Loschmidt echo analysis.

Contribution

It introduces a model with an analytically defined mobility edge and analyzes its dynamical properties, distinguishing it from other regimes.

Findings

Mobility edge regime exhibits mixed extended and localized features.

Wave packet dynamics differ significantly from multifractal phase.

Loschmidt echo effectively distinguishes different phases.

Abstract

We investigate the wave packet dynamics for a one-dimensional incommensurate optical lattice with a special on-site potential which exhibits the mobility edge in a compactly analytic form. We calculate the density propagation, long-time survival probability and mean square displacement of the wave packet in the regime with the mobility edge and compare with the cases in extended, localized and multifractal regimes. Our numerical results indicate that the dynamics in the mobility-edge regime mix both extended and localized features which is quite different from that in the mulitfractal phase. We utilize the Loschmidt echo dynamics by choosing different eigenstates as initial states and sudden changing the parameters of the system to distinguish the phases in the presence of such system.