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arXiv:2507.10366 · Physical review. B./Physical review. B

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

Jie Li, Chenxin Jiang, Zi-Xiang Hu

Published Apr 21, 2026• 0 citations
arXivHTMLPDF

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.

DOI
10.1103/1h9l-mrdv

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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.
The rapid development of artificial gauge fields in ultracold gases suggests that atomic realization of fractional quantum Hall physics will become experimentally practical in the near future. While it is known that bosons on lattices can support quantum Hall states, the universal edge excitations that provide the most likely experimental probe of the topological order have not been obtained. We find that the edge excitations of an interacting boson lattice model are surprisingly sensitive to interedge hybridization and edge-bulk mixing for some confining potentials. With properly chosen potentials and fluxes, the edge spectrum is surprisingly clear even for small systems with strong lattice effects such as bandwidth. Various fractional quantum Hall phases for bosons can be obtained, and the phases $\ensuremath{\nu}=1/2$ and $\ensuremath{\nu}=2/3$ have the edge spectra predicted by the chiral Luttinger liquid theory.
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The exploration of atomic fractional quantum Hall (FQH) states is now within reach in optical-lattice experiments. While ground-state signatures have been observed in a system realizing the Hofstadter-Bose-Hubbard model in a box [Leonard et al., Nature 2023], how to access hallmark low-energy collective modes remains a central open question in this context. We introduce a spectroscopic scheme based on two interfering Laguerre-Gaussian beams, which transfer a controlled angular momentum and energy to the system. The edge and bulk responses to the probe are detected through local density measurements, by tracking the transfer of atoms between the bulk and the edge of the FQH droplet. This detection scheme is shown to simultaneously reveal two specific signatures of FQH states: their chiral edge branch and their bulk magneto-roton mode. We numerically benchmark our method by considering few bosons in the ν=1/2ν=1/2ν=1/2 Laughlin ground state of the Hofstadter-Bose-Hubbard model, and demonstrate that these signatures are already detectable in realistic systems of two bosons, provided that the box potential is larger than the droplet. Our work paves the way for the detection of fractional statistics in cold atoms through edge signatures.
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The edge of the electronic fractional quantum Hall (FQH) system obeys the law of the chiral Luttinger liquid theory due to its intrinsic topological properties and the relation of bulk-edge correspondence. However, in a realistic experimental system, such as the usual Hall bar setup, the softening of the background confinement potential can induce the reconstruction of the edge spectrum, which breaks the chirality and universality of the FQH edge. The entanglement spectrum (ES) of the FQH ground state has the same counting structure as that of the energy spectrum indicating the topological characters of the quantum state. In this work, we report that the ES can also have an edge reconstruction while sweeping the area of the subsystem in real space cut. Moreover, we found that the critical area of the subsystem matches accurately with the intrinsic building block of the FQH liquids, namely the correlation hole of the FQH liquids. The above results seem to be universal after our study of a series of typical FQH states, such as two Laughlin states at $\ensuremath{\nu}=1/3$ and 1/51/51/5, and the Moore-Read state for $\ensuremath{\nu}=5/2$.
The authors consider here the behavior of quantum Hall edges away from the Luttinger liquid fixed point that describes the low energy, large system limit. Using the links between quantum Hall wave functions and conformal field theories, they construct effective Hamiltonians and constrain their forms by considering bulk symmetries. In examining the effect of bulk interactions on this edge, they find remarkable simplifications to these effective theories that allow a very accurate description of the low-energy physics of quantum Hall edges relatively far away from the Luttinger liquid fixed point, and that apply to small systems and higher energies.