Edge-Magnetoplasmon Wave-Packet Revivals in the Quantum Hall Effect

TL;DR

This paper explores the dynamics of edge-magnetoplasmon wave packets in the quantum Hall effect, demonstrating their potential for revealing edge properties through revival phenomena similar to atomic Rydberg states.

Contribution

It introduces the concept of wave packet revivals in edge magnetoplasmons and discusses their use for probing quantum Hall edge dynamics, a novel approach in this field.

Findings

Wave packets move with classical drift initially.

Periodic revivals of wave packets are possible.

Proposed methods for preparing and detecting wave packets.

Abstract

The quantum Hall effect is necessarily accompanied by low-energy excitations localized at the edge of a two-dimensional electron system. For the case of electrons interacting via the long-range Coulomb interaction, these excitations are edge magnetoplasmons. We address the time evolution of localized edge-magnetoplasmon wave packets. On short times the wave packets move along the edge with classical E cross B drift. We show that on longer times the wave packets can have properties similar to those of the Rydberg wave packets that are produced in atoms using short-pulsed lasers. In particular, we show that edge-magnetoplasmon wave packets can exhibit periodic revivals in which a dispersed wave packet reassembles into a localized one. We propose the study of edge-magnetoplasmon wave packets as a tool to investigate dynamical properties of integer and fractional quantum-Hall edges. Various scenarios are discussed for preparing the initial wave packet and for detecting it at a later time. We comment on the importance of magnetoplasmon-phonon coupling and on quantum and thermal fluctuations.