Dynamics of fractional quantum Hall Liquids with a pulse at the edge

TL;DR

This paper models the edge dynamics of fractional quantum Hall liquids following a localized perturbation, revealing how excitations propagate along and into the bulk, consistent with recent experimental observations.

Contribution

It introduces a detailed pump-probe model for edge dynamics in fractional quantum Hall systems, highlighting the influence of tip potential parameters on excitation propagation.

Findings

Edge excitations spread along the boundary and into the bulk.

Magnetoroton excitations dominate bulk responses.

Tip parameters significantly affect the dynamical evolution.

Abstract

Motivated by recent experimental advancements in scanning optical stroboscopic confocal microscopy and spectroscopy measurements, which have facilitated exceptional energy-space-time resolution for investigating edge and bulk dynamics in fractional quantum Hall systems, we formulated a model for the pump-probe process on the edge. Starting with a ground state, we applied a tip potential near the fractional quantum Hall liquid edge, which was subsequently turned off after a defined time duration. By examining how the specific nature of the tip potential influences the evolution of the wave function and its distribution in energy spectrum, we identify that quench dynamics of the edge pulse leads to excitations that spread both along the edge and perpendicularly into the bulk. Moreover, magnetoroton excitations are predominant among the bulk excitations. These results align well with the experimental observations. Furthermore, we analyzed the effects of the tip's position, intensity, and duration on the dynamics.