Rotating spin-1 bosons in the lowest Landau level

TL;DR

This paper investigates the ground states of spin-1 bosons in a rotating trap within the lowest Landau level, exploring phase diagrams, exact solutions, mean field states, and quantum Hall liquids across different geometries and interaction regimes.

Contribution

It provides the first comprehensive analysis of spin-1 bosons in the LLL, including exact ground states, mean field configurations, and quantum Hall states, across various geometries and interaction parameters.

Findings

Exact ground states for spin-independent interactions at L ≤ N.

Mean field states for general interactions and slow rotation.

Identification of vortex, skyrmion lattices, and quantum Hall liquids.

Abstract

We present results for the ground states of a system of spin-1 bosons in a rotating trap. We focus on the dilute, weakly interacting regime, and restrict the bosons to the quantum states in the lowest Landau level (LLL) in the plane (disc), sphere or torus geometries. We map out parts of the zero temperature phase diagram, using both exact quantum ground states and LLL mean field configurations. For the case of a spin-independent interaction we present exact quantum ground states at angular momentum $L\leq N$. For general values of the interaction parameters, we present mean field studies of general ground states at slow rotation and of lattices of vortices and skyrmions at higher rotation rates. Finally, we discuss quantum Hall liquid states at ultra-high rotation.