Collective modes of a strongly interacting Bose gas: probing the Mott transition

We analyze the collective modes of a harmonically trapped, strongly interacting Bose gas in an optical lattice in the vicinity of the Mott insulator transition. For that aim we employ the dynamical Gutzwiller equations, by performing real-time evolution and by solving the equations in linear response. We find a strong dependence on the spatial dimension of the system: while in one dimension the frequency of the dipole mode vanishes at the Mott transition, in higher dimensions the dominant dipole mode is featureless and we find a signature only in the breathing mode. We discuss implications for experiments with bosonic and fermionic atoms.Comment: 10 pages, 7 figures; updated figures, published versio

Microscopic Wave Functions of Spin Singlet and Nematic Mott States of Spin-One Bosons in High Dimensional Bipartite Lattices

We present microscopic wave functions of spin singlet Mott insulating states and nematic Mott insulating states. We also investigate quantum phase transitions between the spin singlet Mott phase and the nematic Mott phase in both large-N limit and small-N limit (N being the number of particles per site) in high dimensional bipartite lattices. In the mean field approximation employed in this article we find that phase transitions are generally weakly first order.Comment: 8 pages, 6 figures; final version, to appear in PR

Vortex-lattice melting in a one-dimensional optical lattice

We investigate quantum fluctuations of a vortex lattice in a one-dimensional optical lattice. Our method gives full access to all the modes of the vortex lattice and we discuss in particular the Bloch bands of the Tkachenko modes. Because of the small number of particles in the pancake Bose-Einstein condensates at every site of the optical lattice, finite-size effects become very important. Therefore, the fluctuations in the vortex positions are inhomogeneous and the melting of the lattice occurs from the outside inwards. Tunneling between neighbouring pancakes substantially reduces the inhomogeneity as well as the size of the fluctuations.Comment: 4 pages, 4 figure

Lattice-Ramp Induced Dynamics in an Interacting Bose-Bose Mixture

We investigate a bosonic quantum gas consisting of two interacting species in an optical lattice at zero and finite temperature. The equilibrium properties and dynamics of this system are obtained by means of the Gutzwiller mean-field method. In particular we model recent experiments where the ramp-up of the optical lattice occurs on a time scale comparable to the tunneling time of the bosons. We demonstrate the violation of adiabaticity of this process with respect to the many-body quantum states, and reproduce and explain the oscillations of the visibility as a function of ramp-up time, as seen in experiments.Comment: 11 pages, 12 figure

Hyperfine Spin-Two (F=2) Atoms in Three-Dimensional Optical Lattices: Phase Diagrams and Phase Transitions

We consider ultracold matter of spin-2 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.Comment: 10 pages, 10 figures, published versio

Two-Dimensional Dynamics of Ultracold Atoms in Optical Lattices

We analyze the dynamics of ultracold atoms in optical lattices induced by a sudden shift of the underlying harmonic trapping potential. In order to study the effect of strong interactions, dimensionality and lattice topology on transport properties, we consider bosonic atoms with arbitrarily strong repulsive interactions, on a two-dimensional square lattice and a hexagonal lattice. On the square lattice we find insulating behavior for weakly interacting atoms and slow relaxation for strong interactions, even when a Mott plateau is present, which in one dimension blocks the dynamics. On the hexagonal lattice the center of mass relaxes to the new equilibrium for any interaction strength.Comment: 4 pages, 6 figures; references added; improved figure

Effect of interactions on harmonically confined Bose-Fermi mixtures in optical lattices

We investigate a Bose-Fermi mixture in a three-dimensional optical lattice, trapped in a harmonic potential. Using Generalized Dynamical Mean-Field theory, which treats the Bose-Bose and Bose-Fermi interaction in a fully non-perturbative way, we show that for experimentally relevant parameters a peak in the condensate fraction close to the point of vanishing Bose-Fermi interaction is reproduced within a single band framework. We identify two physical mechanisms contributing to this effect: the spatial redistribution of particles when the interspecies interaction is changed and the reduced phase space for strong interactions, which results in a higher temperature at fixed entropy.Comment: 4 pages, 3 figures, published versio