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arXiv:2403.10598 · Physical Review Letters

Quantum Nonlinear Optics on the Edge of a Few-Particle Fractional Quantum Hall Fluid in a Small Lattice

Alberto Nardin, Daniele De Bernardis, R. O. Umucalılar, Leonardo Mazza, Matteo Rizzi, Iacopo Carusotto

Published Oct 29, 2024• 6 citations
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Abstract

We study the quantum dynamics in response to time-dependent external potentials of the edge modes of a small fractional quantum Hall fluid composed of few particles on a lattice in a bosonic Laughlin-like state at filling ν=1/2. We show that the nonlinear chiral Luttinger liquid theory provides a quantitatively accurate description even for the small lattices that are available in state-of-the-art experiments, away from the continuum limit. Experimentally accessible data related to the quantized value of the bulk transverse Hall conductivity are identified both in the linear and the non-linear response to an external excitation. The strong nonlinearity induced by the open boundaries is responsible for sizable quantum blockade effects, leading to the generation of nonclassical states of the edge modes.

DOI
10.1103/physrevlett.133.183401

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We study the quantum dynamics in response to time-dependent external potentials of the edge modes of a small fractional quantum Hall fluid composed of few particles on a lattice in a bosonic Laughlin-like state at filling ν=1/2. We show that the nonlinear chiral Luttinger liquid theory provides a quantitatively accurate description even for the small lattices that are available in state-of-the-art experiments, away from the continuum limit. Experimentally accessible data related to the quantized value of the bulk transverse Hall conductivity are identified both in the linear and the non-linear response to an external excitation. The strong nonlinearity induced by the open boundaries is responsible for sizable quantum blockade effects, leading to the generation of nonclassical states of the edge modes.
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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.
This paper investigates the bulk and boundary dynamics of Laughlin states, which are modeled using composite boson theory within a fluid dynamics framework. In this work, we adopt an alternative starting point based on a hydrodynamic action with topological terms, which fleshes out the fluid aspects of the Laughlin state manifestly. For a particular choice of the velocity field, the fluid equation for this action is akin to first-order hydrodynamic equations, supplemented with an additional constitutive equation known as the Hall constraint. When a hard wall boundary is present, one of the topological terms in the fluid action triggers anomaly inflow, indicating the presence of gauge anomaly at the edge. The first-order hydrodynamic equations require a second boundary condition, which, in the absence of dissipation, can be either a no-slip or a no-stress condition. We find that the no-slip condition, where the fluid adheres to the wall, is incompatible with the chiral edge dynamics. On the other hand, the no-stress condition, which allows the fluid to move along the wall without friction, is consistent with the expected chiral edge dynamics of the Laughlin state. Furthermore, our work derives this modified no-stress boundary condition within a variational principle. This is accomplished by incorporating a chiral boson action within the boundary action that is nonlinearly coupled to the edge density, thus systematically extending the edge chiral Luttinger liquid theory.
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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.