Vortices in quantum droplets: Analogies between boson and fermion systems

TL;DR

This review explores the similarities in vortex behavior in small quantum droplets of bosons and fermions, highlighting universal features, computational methods, and experimental challenges in understanding these complex many-body systems.

Contribution

It provides a comprehensive comparison of vortex phenomena in bosonic and fermionic quantum droplets, emphasizing analogies and computational approaches.

Findings

Vortex formation shows remarkable universality across systems.

Finite rotating quantum droplets exhibit localized vortices.

Particle-vortex composites emerge in quantum Hall regimes.

Abstract

The main theme of this review is the many-body physics of vortices in quantum droplets of bosons or fermions, in the limit of small particle numbers. Systems of interest include cold atoms in traps as well as electrons confined in quantum dots. When set to rotate, these in principle very different quantum systems show remarkable analogies. The topics reviewed include the structure of the finite rotating many-body state, universality of vortex formation and localization of vortices in both bosonic and fermionic systems, and the emergence of particle-vortex composites in the quantum Hall regime. An overview of the computational many-body techniques sets focus on the configuration interaction and density-functional methods. Studies of quantum droplets with one or several particle components, where vortices as well as coreless vortices may occur, are reviewed, and theoretical as well as experimental challenges are discussed.