A. F. Ho

Ultracold gases of ytterbium: ferromagnetism and Mott states in an SU(6) Fermi system

It is argued that an ultracold quantum degenerate gas of ytterbium 173Yb atoms having nuclear spin I=5/2 exhibits an enlarged SU(6) symmetry. Within the Landau Fermi liquid theory, stability criteria against Fermi liquid (Pomeranchuk) instabilities in the spin channel are considered. Focusing on the SU(n>2) generalizations of ferromagnetism, it is shown within mean-field theory that the transition from the paramagnet to the itinerant ferromagnet is generically first order. On symmetry grounds, general SU(n) itinerant ferromagnetic ground states and their topological excitations are also discussed. These SU(n>2) ferromagnets can become stable by increasing the scattering length using optical methods or in an optical lattice. However, in an optical lattice at current experimental temperatures, Mott states with different filling are expected to coexist in the same trap, as obtained from a calculation based on the SU(6) Hubbard model.

Instabilities in binary mixtures of one-dimensional quantum degenerate gases.

We show that one-dimensional binary mixtures of bosons or of a boson and a spin-polarized fermion are Luttinger liquids with the following instabilities: (i) For different particle densities, strong attraction between the mixture components leads to collapse, while strong repulsion leads to demixing, and (ii) For a low-density mixture of two gases of impenetrable bosons (or a spin-polarized fermion and an impenetrable boson) of equal densities, the system develops a gap and exhibits enhanced pairing fluctuations when there is attraction between the components. In the boson-fermion mixture, the pairing fluctuations occur at finite momentum. Our conclusions apply to mixtures both on the continuum and on optical lattices away from integer or fractional commensurability.

Quantum simulation of the Hubbard model: The attractive route

We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely, a Mott insulator in the paramagnetic and antiferromagnetic phases, and a putative d-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultracold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We argue that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are easier to observe in the attractive Hubbard mode as a band insulator of Cooper pairs and superfluid phase, respectively. The putative d-wave superfluid phase of the repulsive Hubbard model doped away from half filling is related to a d-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to “quantum simulate” the Hubbard model in an optical lattice over the simulation of the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.

Interacting Bose gases in quasi-one-dimensional optical lattices

We study a two-dimensional (2D) array of coupled 1D tubes of interacting bosons. Such systems can be produced by loading ultracold atoms in anisotropic optical lattices. We investigate the effects of coupling the tubes via hopping of the bosons (i.e. Josephson coupling). In the absence of a periodic potential along the tubes, or when such potential is incommensurate with the boson density, the system undergoes a transition from an array of incoherent Tomonaga–Luttinger liquids at high temperature to an anisotropic Bose–Einstein condensate (BEC), at low temperature. We determine the transition temperature and long wavelength excitations of the BEC. In addition to the usual gapless (Goldstone) mode found in standard superfluids, we also find a gapped mode associated with fluctuations of the amplitude of the order parameter. When a commensurate periodic potential is applied along the tubes, they can become 1D Mott insulators. Intertube hopping leads to a deconfinement quantum phase transition between the 1D Mott insulators and the anisotropic BEC. We also take into account the finite size of the gas tubes as realized in actual experiments. We map out the phase diagram of the quasi-1D lattice and compare our results with the existing experiments on such systems.

Nontrivial fixed point in a twofold orbitally degenerate Anderson impurity model.

We study a twofold orbitally degenerate Anderson impurity model which shows a nontrivial fixed point similar to that of the two-impurity Kondo model, but remarkably more robust, as it can only be destabilized by orbital- or gauge-symmetry breaking. The impurity model is interesting per se, but here our interest is rather in the possibility that it might be representative of a strongly correlated lattice model close to a Mott transition. We argue that this lattice model should unavoidably encounter the nontrivial fixed point just before the Mott transition and react to its instability by spontaneous generation of an orbital, spin-orbital or superconducting order parameter.

Energy absorption of a Bose gas in a periodically modulated optical lattice

We compute the energy absorbed by a one-dimensional system of cold bosonic atoms in an optical lattice subjected to lattice amplitude modulation periodic with time. We perform the calculation for the superfluid and the Mott insulator created by a weak lattice, and the Mott insulator in a strong lattice potential. For the latter case we show results for three-dimensional systems as well. Our calculations, based on bosonization techniques and strong-coupling methods, go beyond standard Bogoliubov theory. We show that the energy absorption rate exhibits distinctive features of low-dimensional systems and Luttinger liquid physics. We compare our results with experiments and find good agreement.

Deconfinement in a 2D Optical Lattice of Coupled 1D Boson Systems

We show that a two-dimensional (2D) array of 1D interacting boson tubes has a deconfinement transition between a 1D Mott insulator and a 3D superfluid for commensurate fillings and a dimensional crossover for the incommensurate case. We determine the phase diagram and excitations of this system and discuss the consequences for Bose condensates loaded in 2D optical lattices.

Dynamics of thermalization in small Hubbard-model systems.

We study numerically the thermalization and temporal evolution of a two-site subsystem of a fermionic Hubbard model prepared far from equilibrium at a definite energy. Even for very small systems near quantum degeneracy, the subsystem can reach a steady state resembling equilibrium. This occurs for a nonperturbative coupling between the subsystem and the rest of the lattice where relaxation to equilibrium is Gaussian in time, in sharp contrast to perturbative results. We find similar results for random couplings, suggesting such behavior is generic for small systems.

c-axis transport in highly anisotropic metals : Role of small polarons

We show in a simple model of interlayer hopping of single electrons, that transport along the weakly coupled c-axis of quasi-two-dimensional metals does not always probe only the in-plane electron properties. In our model where there is a strong coupling between electrons and a bosonic mode that propagates in the

Dynamics of thermalization and decoherence of a nanoscale system

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