Dynamical Signatures of Floquet Topology in Wave Packet Dynamics

TL;DR

This paper develops a theoretical framework linking wave packet center-of-mass dynamics to Floquet topological invariants, enabling experimental detection of topological phase transitions in driven quantum systems.

Contribution

It introduces a Floquet perturbation theory that connects CoM oscillations to Floquet band structures and topological transitions in periodically driven systems.

Findings

CoM exhibits multi-frequency Zitterbewegung oscillations linked to Floquet bands.

Band inversions at topological transitions produce distinct CoM signatures.

The method applies to both high-frequency and strongly driven regimes.

Abstract

Periodically driven quantum systems, known as Floquet systems, provide a versatile platform for engineering novel topological phases absent in static settings. However, dynamically characterizing these non-equilibrium topological invariants remains a challenge. Here, we develop a Floquet perturbation theory in the extended Hilbert space to analytically describe the center-of-mass (CoM) dynamics of a wave packet. When applied to the driven Su-Schrieffer-Heeger model, our theory reveals that the CoM exhibits multi-frequency Zitterbewegung oscillations, whose spectral composition and phase are directly tied to the system's Floquet band structure. Crucially, we find that band inversions at topological phase transitions imprint distinct signatures in the CoM dynamics, including the emergence of low-frequency modes and phase shifts of the oscillatory trajectory. These dynamical signatures offer a practical protocol for detecting Floquet topological invariants, which we demonstrate for both high-frequency and strongly driven regimes. Our work establishes CoM dynamics as a simple and experimentally accessible probe for exploring topological phase transitions in Floquet systems.