From Rotating Atomic Rings to Quantum Hall States

TL;DR

This paper proposes a dynamic method to realize quantum Hall states in ultracold atoms by starting from a rotating ring trap and adiabatically transforming it, easing experimental challenges compared to thermodynamic approaches.

Contribution

It introduces a novel dynamic pathway from a rotating ring to quantum Hall states, reducing the need for extreme rotational control in experiments.

Findings

Giant vortex states are adiabatically connected to Laughlin states.

Numerical evidence supports the feasibility of the proposed method.

The approach scales favorably with particle number.

Abstract

Considerable efforts are currently devoted to the preparation of ultracold neutral atoms in the emblematic strongly correlated quantum Hall regime. The routes followed so far essentially rely on thermodynamics, i.e. imposing the proper Hamiltonian and cooling the system towards its ground state. In rapidly rotating 2D harmonic traps the role of the transverse magnetic field is played by the angular velocity. For particle numbers significantly larger than unity, the required angular momentum is very large and it can be obtained only for spinning frequencies extremely near to the deconfinement limit; consequently, the required control on experimental parameters turns out to be far too stringent. Here we propose to follow instead a dynamic path starting from the gas confined in a rotating ring. The large moment of inertia of the fluid facilitates the access to states with a large angular momentum, corresponding to a giant vortex. The initial ring-shaped trapping potential is then adiabatically transformed into a harmonic confinement, which brings the interacting atomic gas in the desired quantum Hall regime. We provide clear numerical evidence that for a relatively broad range of initial angular frequencies, the giant vortex state is adiabatically connected to the bosonic $\nu=1/2$ Laughlin state, and we discuss the scaling to many particles.