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.
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.
This dissertation investigates properties of two-dimensional many-body systems. Studies are performed using the Spin-Density Functional Theory with the Local Spin-Density Approximation, and numerical exact diagonalization. The properties studied include symmetry-breaking states in few-electron quantum dots, gaps in confined few-body systems, magnetic properties of cold fermionic atoms in optical lattices, and vortex formation in few-body systems. The dissertation also studies the properties of the SDFT-LSDA method for many-body calculations itself. The dissertation comprises five original papers, which are presented following an introduction to the fields of research, and the methods used, and the systems studied. Paper I investigates symmetry-breaking states in quantum dots, and the reliability of SDFT-LSDA for such systems. It is found that SDFT-LSDA may introduce artificial energy splittings between the members of a degenerate spin multiplet in the ground state. Paper II investigates the reliability of SDFT-LSDA when used to calculate gaps, and addition and removal energies in few-body systems. It is found that, contrary to studies of atoms and bilk solids, Kohn-Sham eigenvalues can be used to calculate addition and removal energies in parabolically confined systems. Also, in Paper II, van der Waals blockade is predicted to occur in systems of cold atoms, in analogy to Coulomb blockade in electronic systems. In Papers III and IV, mean-field theory is used to study the magnetic properties of cold fermionic atoms in an optical lattice. The results are compared with a similar study for quantum-dot lattices. It is found that there is a rich magnetic phase diagram, with non-magnetic, ferromagnetic, and anti-ferromagnetic states. The phase diagram of the optical lattice is found to be very similar to the phase diagram of the quantum-dot lattice. Paper V uses exact diagonalization to study vortex formation in rotating few-body quantum systems. Systems consisting of Coulomb-interacting fermions (electrons), Coulomb-interacting bosons, and bosons with a short-range interaction are studied. It is found that vortex formation in these systems has universal properties.
We study many-body quantum coherence and interaction blockade in two Josephson-linked Bose-Einstein condensates. We introduce universal operators for characterizing many-body coherence without limitations on the system symmetry and total particle number N . We reproduce the results for both coherence fluctuations and number squeezing in symmetric systems of large N , and reveal several peculiar phenomena that may occur in asymmetric systems and systems of small N . For asymmetric systems, we show that, due to an interplay between asymmetry and inter-particle interaction, the coherence fluctuations are suppressed dramatically when | E C / E J |≪1, and both resonant tunneling and interaction blockade take place for large values of | E C / E J |, where E C and E J are the interaction and tunneling energies, respectively. We emphasize that the resonant tunneling and interaction blockade may allow creating single-atom devices with promising technology applications. We demonstrate that for the systems at finite temperatures the formation of self-trapped states causes an anomalous behavior.
We introduce a generic approach to study interaction effects in diffusive or chaotic quantum dots in the Coulomb blockade regime. The randomness of the single-particle wave functions induces randomness in the two-body interaction matrix elements. We classify the possible induced two-body ensembles, both in the presence and absence of spin degrees of freedom. The ensembles depend on the underlying space-time symmetries as well as on features of the two-body interaction. Confining ourselves to spinless electrons, we then use the Hartree-Fock (HF) approximation to calculate HF single-particle energies and HF wave functions for many realizations of the ensemble. We study the statistical properties of the resulting one-body HF ensemble for a fixed number of electrons. In particular, we determine the statistics of the interaction matrix elements in the HF basis, of the HF single-particle energies (including the HF gap between the last occupied and the first empty HF level), and of the HF single-particle wave functions. We also study the addition of electrons, and in particular the distribution of the distance between successive conductance peaks and of the conductance peak heights.
At the limit of an infinite confinement strength ω, the ground state of a system that comprises two fermions or bosons in harmonic confinement interacting through the Fermi-Huang pseudopotential remains strongly correlated. A detailed analysis of the one-particle description of this "contactium" reveals several peculiarities that are not encountered in conventional model systems (such as the two-electron harmonium atom, ballium, and spherium) involving Coulombic interparticle interactions. First of all, none of the natural orbitals (NOs) {ψn(ω;r)} of the contactium is unoccupied, which implies nonzero collective occupancies for all the angular momenta. Second, the NOs and their non-ascendingly ordered occupation numbers {νn} turn out to be related to the eigenfunctions and eigenvalues of a zero-energy Schrödinger equation with an attractive Gaussian potential. This observation enables the derivation of their properties, such as the n-4/3 asymptotic decay of νn at the n→∞ limit (which differs from that of n-8/3 in the Coulombic systems), the independence of the confinement energy vn=⟨ψn(ω;r)|12ω2r2|ψn(ω;r)⟩ of n, and the n-2/3 asymptotic decay of the respective contribution νntn to the kinetic energy. Upon suitable scaling, the weakly occupied NOs of the contactium turn out to be virtually identical to those of the two-electron harmonium atom at the ω → ∞ limit, despite the entirely different interparticle interactions in these systems.
This work is about the properties of several low dimensional, small systems of interacting particles. We demonstrate that interaction between particles in the low dimensional small systems can lead to many unexpected effects. We considered electrons in a Luttinger liquid, in a superconducting state, and atoms in a magneto-optical trap. Using bosonization techniques we calculated the thermopower of a Luttinger liquid wire with an impurity. We predicted the appearance of a phase dependent force and resonant phase dependent magnetization in the nanoscopic superconductor - normal metal superconductor (or superconductor - two dimensional electron gas - superconductor) junction. We also considered plasma oscillations inside thin superconducting tubes and rings and predicted that the velocities of the plasmons in these systems are periodic functions of the magnetic flux. By considering neutral atoms in a harmonic trap we discovered that strongly repelling atoms do not form Bose-Einstein condensate at zero temperature but tend to occupy different orbitals with small mutual overlap, forming crystallite structures similar to Wigner molecules of electrons inside a quantum dot.
We study the Rydberg blockade in a system of three atoms arranged in different two-dimensional geometries (linear and triangular configurations). In the strong blockade regime, we observe high-contrast, coherent collective oscillations of the single excitation probability and an almost perfect van der Waals blockade. Our data are consistent with a total population in doubly and triply excited states below 2%. In the partial blockade regime, we directly observe the anisotropy of the van der Waals interactions between |nD> Rydberg states in the triangular configuration. A simple model that only uses independently measured two-body van der Waals interactions fully reproduces the dynamics of the system without any adjustable parameter. These results are extremely promising for scalable quantum information processing and quantum simulation with neutral atoms.