Bosonic quantum Hall droplets in rapidly rotating two-dimensional Bose-Einstein condensates

TL;DR

This paper explores the formation, stability, and dynamics of quantum Hall droplets and arrays in rapidly rotating Bose-Einstein condensates, providing theoretical constructions and demonstrating their stability and formation.

Contribution

It introduces a rigorous method to construct stationary quantum Hall droplet states and demonstrates their stability and formation in rotating BECs, advancing understanding of quantum Hall phenomena in cold atoms.

Findings

Single quantum Hall droplet is dynamically stable.

Quantum Hall droplet arrays can be formed from engineered initial states.

The study offers a new approach to generate and manipulate quantum Hall droplets.

Abstract

Recent experiments demonstrate that rapidly rotating Bose-Einstein condensates (BECs) near the lowest Landau level can self-organize into interaction-driven persistent quantum Hall droplet arrays. Inspired by this discovery, we investigate the formation and dynamics of single quantum Hall droplet and droplet arrays in rapidly rotating BECs. Guided by a rigorous theorem on localized many-body states for two-dimensional interacting systems in a magnetic field, we construct single quantum Hall droplet and droplet array states which are shown to be stationary solutions to the Gross-Pitaevskii equation in the rotating frame. The single quantum Hall droplet is shown to be dynamically stable, which underpins its role as the basic unit in a droplet array. The stability of the quantum Hall droplet arrays is demonstrated by their dynamic formation from a phase engineered initial condensate. Our study sheds light onto the nature of the quantum Hall droplet state in a rapidly rotating BEC and offers a new approach for generating and manipulating quantum Hall droplet arrays through designing the initial condensate phase.