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Many-body effects in confined quantum systems pose a challenging problem due to the simultaneous presence of particle-particle interactions and spatial inhomogeneity. Here we investigate universal properties of strongly confined particles that turn out to be dramatically different from what is observed for electrons in atoms and molecules. We show that for a large class of harmonically confined systems, including small quantum dots and optically trapped atoms, many-body particle addition and removal energies, and energy gaps, can accurately be obtained from single-particle eigenvalues. Transport blockade phenomena are related to the derivative discontinuity of the exchange-correlation functional. This implies that they occur very generally, with Coulomb blockade being a particular realization of a more general phenomenon. In particul...
We examine the spin asymmetry of ground states for two-dimensional, harmonically trapped two-component gases of fermionic atoms at zero temperature with weakly repulsive short range interactions. Our main result is that, in contrast to the three-dimensional case, in two dimensions a non-trivial spin-asymmetric phase can only be caused by shell structure. A simple, qualitative description is given in terms of an approximate single particle model, comparing well to the standard results of Hartree-Fock or direct diagonalization methods.
We compare magnetism in two artificial lattice structures, a quantum dot array formed in a two-dimensional electron gas and an optical lattice loaded with repulsive, contact-interacting fermionic atoms. When the tunneling between the lattice sites is strong, both lattices are non-magnetic. With reduced tunneling in the tight-binding limit, the shell-filling of the single-site quantum wells combined with Hund's rule determines the magnetism. This leads to a systematic magnetic phase diagram with non-magnetic, ferromagnetic and antiferromagnetic phases.
We demonstrate that a two-dimensional (2D) optical lattice loaded with repulsive, contact-interacting fermions shows a rich and systematic magnetic phase diagram. Trapping a few (N ≤ 12) fermions in each of the single-site minima of the optical lattice, we find that the shell structure in these quantum wells determines the magnetism. In a shallow lattice, the tunnelling between the single wells is strong, and the lattice is non-magnetic (NM). For deeper lattices, however, the shell filling of the single wells with fermionic atoms determines the magnetism. As a consequence of Hund's first rule, the interaction energy is lowered by maximizing the number of atoms of the same species. This leads to a systematic sequence of NM, ferromagnetic (F) and antiferromagnetic (AF) phases.
We investigate universal properties of strongly confined particles that turn out to be dramatically different from what is observed for electrons in atoms and molecules. For a large class of harmonically confined systems, such as small quantum dots and optically trapped atoms, many-body particle addition and removal energies, and energy gaps, are accurately obtained from single-particle eigenvalues. Transport blockade phenomena are related to the derivative discontinuity of the exchange-correlation functional. This implies that they occur very generally, with Coulomb blockade being a particular realization of a more general phenomenon. In particular, we predict a van der Waals blockade in cold atom gases in traps.
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