Bilayer fractional quantum Hall states with ultracold dysprosium

TL;DR

This paper proposes a method to realize fractional quantum Hall states using dipolar interactions of ultracold dysprosium atoms in an optical lattice, enabling exploration of topological quantum phases.

Contribution

It introduces a scheme to engineer topological flat bands and fractional quantum Hall states with ultracold dysprosium atoms via optical and microwave dressing.

Findings

Realization of /2 Laughlin state from spin-1/2 atoms.

Formation of bilayer Halperin (2,2,1) state from spin-1 atoms.

Phase diagram showing competition between topological states and superfluidity.

Abstract

We show how dipolar interactions between dysprosium atoms in an optical lattice can be used to obtain fractional quantum Hall states. In our approach, dysprosium atoms are trapped one atom per site in a deep optical lattice with negligible tunneling. Microwave and spatially dependent optical dressing fields are used to define an effective spin-1/2 or spin-1 degree of freedom in each atom. Thinking of spin-1/2 particles as hardcore bosons, dipole-dipole interactions give rise to boson hopping, topological flat bands with Chern number 1, and the \nu = 1/2 Laughlin state. Thinking of spin-1 particles as two-component hardcore bosons, dipole-dipole interactions again give rise to boson hopping, topological flat bands with Chern number 2, and the bilayer Halperin (2,2,1) state. By adjusting the optical fields, we find a phase diagram, in which the (2,2,1) state competes with superfluidity. Generalizations to solid-state magnetic dipoles are discussed.