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arXiv:0908.3484 · Physical Review A

Hyperfine spin-two (F=2) atoms in three-dimensional optical lattices: Phase diagrams and phase transitions

Michiel Snoek, Jun Liang Song, Fei Zhou

Published Nov 19, 2009• 7 citations
arXivHTMLPDF

Abstract

We consider ultracold matter of spin-two atoms in optical lattices. We derive an effective Hamiltonian for the studies of spin ordering in Mott states and investigate hyperfine spin correlations. Particularly, we diagonalize the Hamiltonian in an on-site Hilbert space taking into account spin-dependent interactions and exchange between different sites. We obtain phase diagrams and quantum phase transitions between various magnetic phases.

DOI
10.1103/physreva.80.053618

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We consider ultracold matter of spin-two atoms in optical lattices. We derive an effective Hamiltonian for the studies of spin ordering in Mott states and investigate hyperfine spin correlations. Particularly, we diagonalize the Hamiltonian in an on-site Hilbert space taking into account spin-dependent interactions and exchange between different sites. We obtain phase diagrams and quantum phase transitions between various magnetic phases.
We investigate magnetic properties of Mott-insulating phases of ultracold Bose and Fermi spinor gases in optical lattices. We consider in particular the F = 2 Bose gas, and the F = 3/2 and 5/2 Fermi gases. We derive effective spin Hamiltonians for one and two atoms per site and discuss the possibilities of manipulating the magnetic properties of the system using optical Feshbach resonances. We discuss low temperature quantum phases of a Rb-87 gas in the F = 2 hyperfine state, as well as possible realizations of high spin Fermi gases with either Li-6 or Cs-132 atoms in the F = 3/2 state, and with Yb-173 atoms in the F = 5/2 state.
We investigate magnetic properties of Mott-insulating phases of ultracold Bose and Fermi spinor gases in optical lattices. We consider in particular the F = 2 Bose gas, and the F = 3/2 and 5/2 Fermi gases. We derive effective spin Hamiltonians for one and two atoms per site and discuss the possibilities of manipulating the magnetic properties of the system using optical Feshbach resonances. We discuss low temperature quantum phases of a 87 Rb gas in the F = 2 hyperfine state, as well as possible realizations of high spin Fermi gases with either 6 Li or 132 Cs atoms in the F = 3/2 state, and with 173 Yb atoms in the F = 5/2 state.
Abstract We investigate the ground-state phase diagram of interacting binary Bose gases trapped in two-dimensional optical lattices by means of quantum Monte Carlo simulations. Our simulations reveal a magnetic phase transition from a ferromagnetic-order to a spin insulator inside the Mott insulating phase with two particles per site for quasi-balanced on-site inter- and intra-particle interactions, i.e. , . This 3D-XY transition is characterized by the establishment of a finite local magnetic moment along the z -axis, ferromagnetic correlations in the plane and by counterflow superfluidity inside the Mott phase. When decreasing , this transition merges with the Mott-superfluid transition and becomes first order. The merging of the two transitions is investigated with respect to the parameter.
We study the quantum phase transition of ultracold atoms in the honeycomb optical lattice. The Hamiltonian of ultracold bosonic atoms in the honeycomb optical lattice is derived. We take the mean-field approximation and further solve the Hamiltonian with the numerical diagonalization method. We obtain the phase diagram and find that the Mott-insulator (MI), density wave (DW) and modulated superfluid (MS) phases appear. Furthermore, the phase diagram is analyzed according to the order parameter and the average number of particles.
We first introduce the ultracold atoms and the optical lattices. Then, we analyze various Mott insulating phases of interacting spin-3=2 fermionic ultracold atoms in two-dimensional square optical lattices. Using a generalized Hubbard model, we identify two distinct symmetry breaking phases: the spin-quadrupole ordering phase and the spin-dipole-spin-octupole ordering phase. Near the SU(4) symmetric point, we find that an algebraic spin liquid phase may emerge due to strong quantum fluctuations. Finally, the possible quantum phase transitions between these exotic phases are also discussed.
Ultracold atomic gases in optical lattices provide an unique framework to study quantum phenomena in strongly correlated systems. In addition to the precise control over all relevant parameters in the experiment, these experiments can be mapped to a fundamental model from solid-state physics. For the bosonic version of this model, the so-called Bose-Hubbard model, a phase transition from a superfluid to a Mott insulator was theoretically predicted and later experimentally observed in an ultracold gas of Rb-87 atoms in three-dimensional as well as in one-dimensional optical lattices. Apart from homogeneous optical lattices one can introduce more complex lattice topologies such as two-color superlattices which give rise to a rich phase diagram including more exotic phases like the Bose-glass. We employ various powerful many-body techniques like exact diagonalization in complete and truncated Hilbert spaces and the Density-Matrix Renormalization Group (DMRG) algorithm to study the phase diagrams of the one-dimensional Bose-Hubbard and the one-dimensional Bose-Fermi-Hubbard Hamiltonian. Most theoretical studies of these systems discuss the phase diagrams with respect to the generic parameters of the Hubbard model. These Hubbard parameters, however, depend non-trivially on the control parameters used in experiments. The focus of this work is on the ab-initio calculation of the phase diagram of ultracold Rb-87 in one-dimensional optical superlattices starting directly from the experimental setup. To this end, we first employ band-structure calculations to extract the Hubbard parameters from the experimental parameters. Then, we use state-of-the-art DMRG techniques to solve the many-body problem for realistic particle numbers and lattice sizes that occur in experiments. Our results show that by using the intensities of the two laser fields forming the two-color superlattice as control parameters while keeping all other experimental parameters fixed, it is possible to access all relevant quantum phases of the system. Furthermore, we found out that the critical values of the laser intensities for the different phase transitions depend strongly on a third parameter that has to be included for a realistic description of the experiment. This third parameter is the strength of a harmonic trapping potential which accounts for the Gaussian shape of the laser fields and an additional magnetic potential used to confine the atoms in the center of the trap.