7 research outputs found
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 He or fermionic 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
Spectral properties of rotating electrons in quantum dots and their relation to quantum Hall liquids
The exact diagonalization technique is used to study many-particle properties
of interacting electrons with spin, confined in a two-dimensional harmonic
potential. The single-particle basis is limited to the lowest Landau level. The
results are analyzed as a function of the total angular momentum of the system.
Only at angular momenta corresponding to the filling factors 1, 1/3, 1/5 etc.
the system is fully polarized. The lowest energy states exhibit spin-waves,
domains, and localization, depending on the angular momentum. Vortices exist
only at excited polarized states. The high angular momentum limit shows
localization of electrons and separation of the charge and spin excitations.Comment: 14 pages 18 figure
Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
Investigations of emergent symmetry breaking phenomena occurring in small
finite-size systems are reviewed, with a focus on the strongly correlated
regime of electrons in two-dimensional semicoductor quantum dots and trapped
ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize
universal aspects and similarities of symmetry breaking found in these systems,
as well as in more traditional fields like nuclear physics and quantum
chemistry, which are characterized by very different interparticle forces. A
unified description of strongly correlated phenomena in finite systems of
repelling particles (whether fermions or bosons) is presented through the
development of a two-step method of symmetry breaking at the unrestricted
Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock
projection techniques. Quantitative and qualitative aspects of the two-step
method are treated and validated by exact diagonalization calculations.
Strongly-correlated phenomena emerging from symmetry breaking include: (I)
Chemical bonding, dissociation, and entanglement (at zero and finite magnetic
fields) in quantum dot molecules and in pinned electron molecular dimers formed
within a single anisotropic quantum dot. (II) Electron crystallization, with
particle localization on the vertices of concentric polygonal rings, and
formation of rotating electron molecules (REMs) in circular quantum dots. (III)
At high magnetic fields, the REMs are described by parameter-free analytic wave
functions, which are an alternative to the Laughlin and composite-fermion
approaches. (IV) Crystalline phases of strongly repelling bosons. In rotating
traps and in analogy with the REMs, such repelling bosons form rotating boson
molecules (RBMs).Comment: Review article published in Reports on Progress in Physics. REVTEX4.
95 pages with 37 color figures. To download a copy with high-quality figures,
go to publication #82 in http://www.prism.gatech.edu/~ph274cy
Finite boson and fermion systems under extreme rotation: edge reconstruction and vortex formation
Vortices can form when finite quantal systems are set rotating. In the limit of small particle numbers, the vortex formation in a harmonically trapped fermion system, with repulsively interacting particles, shows similarities to the corresponding boson system, with vortices entering the rotating cloud for increasing rotation. For a larger number of fermions, N greater than or similar to 15, the fermion vortices compete and co-exist with (Chamon-Wen) edge-reconstructed ground states, forcing some ground states, as for example the central single vortex, into the spectrum of excited states. Experimentally, the fermion system could, for instance, be electrons in a semiconductor heterostructure, a quantum dot, and the corresponding boson system, a Bose-Einstein condensate in a magneto optical trap
Correlation and spin polarization in quantum dots: local spin density functional theory revisited
Using quantum dot artificial atoms as a simple toy model, we reflect on the question of whether spin density functional theory (SDFT) can accurately describe correlation effects in low-dimensional fermion systems. Different expressions for the local density approximation of the exchange-correlation energy for the two-dimensional electron gas, such as the much-used functional of Tanatar and Ceperley, and the recent suggestion by Attaccalite et al., are compared with the results of a numerical diagonalization of the many-body Hamiltonian matrix in the limit of small electron numbers. For systems with degeneracies, as shown in the present work for the example of a spin triplet with S = 1, the direct comparison with configuration interaction (CI) methods demonstrates that the spin representation of SDFT may, under certain circumstances, produce artificial energy splittings between states that belong to the same spin multiplet. For a singlet ground state with S = Sz = 0, however, the correlation functions of the CI solutions confirm the spin-density wave states found earlier within the SDFT method
Quantum dots and quantum dot lattices:Correlations in small quantal systems
Recently, Attaccalite et al. proposed a new expression for the exchange-correlation energy of the two-dimensional electron gas, based on quantum Monte Carlo calculations. We compare this functional with the established expression given by Tanatar and Ceperley for use in density functional calculations. As model systems serve a circular few-electron quantum dot and a square lattice of dots. For single dots, electronic structure calculations are performed using both energy functionals for the self-consistent solution of the Kohn-Sham equations. The results are compared with those of a numerical diagonalization of the many-body Hamiltonian