Synthetic Landau levels and spinor vortex matter on Haldane spherical surface with magnetic monopole

TL;DR

This paper proposes a method to create exact Landau levels and synthetic monopole fields on a spherical surface using cold atoms, enabling exploration of quantum Hall physics and vortex matter in curved geometries.

Contribution

It introduces a Floquet engineering scheme to realize flat Landau levels and synthetic monopoles on a sphere with cold atoms, mapping to Haldane's fractional quantum Hall model.

Findings

Successfully maps cold atom system to electron-monopole model on sphere

Analyzes vortex patterns in atomic condensates with interactions

Demonstrates stability of vortex patterns with dipolar interactions

Abstract

We present a flexible scheme to realize exact flat Landau levels on curved spherical geometry in a system of spinful cold atoms. This is achieved by Floquet engineering of a magnetic quadrupole field. We show that a synthetic monopole field in real space can be created. We prove that the system can be exactly mapped to the electron-monopole system on sphere, thus realizing Haldane's spherical geometry for fractional quantum Hall physics. The scheme works for either bosons or fermions. We investigate the ground state vortex pattern for an $s$-wave interacting atomic condensate by mapping this system to the classical Thompson's problem. We further study the distortion and stability of the vortex pattern when dipolar interaction is present. Our scheme is compatible with current experimental setup, and may serve as a promising route of investigating quantum Hall physics and exotic spinor vortex matter on curved space.