Vortices in quantum droplets: Analogies between boson and fermion systems

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.Comment: Review article, 53 pages, 53 figure

Density Functional Theory of Multicomponent Quantum Dots

Quantum dots with conduction electrons or holes originating from several bands are considered. We assume the particles are confined in a harmonic potential and assume the electrons (or holes) belonging to different bands to be different types of fermions with isotropic effective masses. The density functional method with the local density approximation is used. The increased number of internal (Kohn-Sham) states leads to a generalisation of Hund's first rule at high densities. At low densitites the formation of Wigner molecules is favored by the increased internal freedom.Comment: 11 pages, 5 figure

Vortices in fermion droplets with repulsive dipole-dipole interactions

Vortices are found in a fermion system with repulsive dipole-dipole interactions, trapped by a rotating quasi-two-dimensional harmonic oscillator potential. Such systems have much in common with electrons in quantum dots, where rotation is induced via an external magnetic field. In contrast to the Coulomb interactions between electrons, the (externally tunable) anisotropy of the dipole-dipole interaction breaks the rotational symmetry of the Hamiltonian. This may cause the otherwise rotationally symmetric exact wavefunction to reveal its internal structure more directly.Comment: 5 pages, 5 figure

Universal vortex formation in rotating traps with bosons and fermions

When a system consisting of many interacting particles is set rotating, it may form vortices. This is familiar to us from every-day life: you can observe vortices while stirring your coffee or watching a hurricane. In the world of quantum mechanics, famous examples of vortices are superconducting films and rotating bosonic $^4$He or fermionic $^3$He liquids. Vortices are also observed in rotating Bose-Einstein condensates in atomic traps and are predicted to exist for paired fermionic atoms. Here we show that the rotation of trapped particles with a repulsive interaction leads to a similar vortex formation, regardless of whether the particles are bosons or (unpaired) fermions. The exact, quantum mechanical many-particle wave function provides evidence that in fact, the mechanism of this vortex formation is the same for boson and fermion systems.Comment: 4 pages, 4 figure