Vortex and fractional quantum Hall phases in a rotating anisotropic Bose gas

TL;DR

This paper presents a theoretical study of a rapidly rotating anisotropic Bose gas, revealing a phase diagram with topological and symmetry-broken phases, advancing understanding of fractional quantum Hall states in ultracold atomic systems.

Contribution

It introduces a two-parameter model capturing interaction, rotation, and anisotropy effects, and uses numerical methods to map out the phase diagram of the system.

Findings

Identification of topologically ordered quantum Hall states

Discovery of broken-symmetry phases due to anisotropy

Edge physics effects in the phase diagram

Abstract

Realizing fractional quantum Hall (FQH) states in ultracold atomic systems remains a major goal despite numerous experimental advances in the last few decades. Recent progress in trap anisotropy control under rapid rotation has renewed interest in ultracold atomic FQH physics, enabling experiments that impart much larger angular momentum per particle and offer in-situ imaging with resolution finer than the cyclotron orbit size. In this paper, we present a theoretical investigation of a rapidly rotating anisotropic Bose gas. By projecting the full Hamiltonian, including both kinetic and interaction terms, onto the lowest Landau level, we derive a compact two-parameter model that captures the effects of interaction strength, rotation rate, and anisotropy. Using exact diagonalization and density matrix renormalization group, we obtain a phase diagram that features broken-symmetry phases and topologically ordered quantum Hall states, while also highlighting the distinctive physics arising from the system's edges. Our results demonstrate the potential for future theoretical and experimental exploration of anisotropic quantum fluids, offering a unified framework for weakly interacting Bose condensates, vortex matter, and strongly correlated topological phases.