Degenerate Fermi gas in a combined harmonic-lattice potential

In this paper we derive an analytic approximation to the density of states for atoms in a combined optical lattice and harmonic trap potential as used in current experiments with quantum degenerate gases. We compare this analytic density of states to numerical solutions and demonstrate its validity regime. Our work explicitly considers the role of higher bands and when they are important in quantitative analysis of this system. Applying our density of states to a degenerate Fermi gas we consider how adiabatic loading from a harmonic trap into the combined harmonic-lattice potential affects the degeneracy temperature. Our results suggest that occupation of excited bands during loading should lead to more favourable conditions for realizing degenerate Fermi gases in optical lattices.Comment: 11 pages, 9 figure

Collective Oscillations of Strongly Correlated One-Dimensional Bosons on a Lattice

We study the dipole oscillations of strongly correlated 1D bosons, in the hard-core limit, on a lattice, by an exact numerical approach. We show that far from the regime where a Mott insulator appears in the system, damping is always present and increases for larger initial displacements of the trap, causing dramatic changes in the momentum distribution, $n_k$. When a Mott insulator sets in the middle of the trap, the center of mass barely moves after an initial displacement, and $n_k$ remains very similar to the one in the ground state. We also study changes introduced by the damping in the natural orbital occupations, and the revival of the center of mass oscillations after long times.Comment: 4 pages, 5 figures, published versio

Phase coherence, visibility, and the superfluid--Mott-insulator transition on one-dimensional optical lattices

We study the phase coherence and visibility of trapped atomic condensates on one-dimensional optical lattices, by means of quantum Monte-Carlo simulations. We obtain structures in the visibility similar to the kinks recently observed experimentally by Gerbier et.al.[Phy. Rev. Lett. 95, 050404 (2005); Phys. Rev. A 72, 053606 (2005)]. We examine these features in detail and offer a connection to the evolution of the density profiles as the depth of the lattice is increased. Our simulations reveal that as the interaction strength, U, is increased, the evolution of superfluid and Mott-insulating domains stall for finite intervals of U. The density profiles do not change with increasing U. We show here that in one dimension the visibility provides unequivocal signatures of the melting of Mott domains with densities larger than one.Comment: 4 pages, 5 figure

Free expansion of impenetrable bosons on one-dimensional optical lattices

We review recent exact results for the free expansion of impenetrable bosons on one-dimensional lattices, after switching off a confining potential. When the system is initially in a superfluid state, far from the regime in which the Mott-insulator appears in the middle of the trap, the momentum distribution of the expanding bosons rapidly approaches the momentum distribution of noninteracting fermions. Remarkably, no loss in coherence is observed in the system as reflected by a large occupation of the lowest eigenstate of the one-particle density matrix. In the opposite limit, when the initial system is a pure Mott insulator with one particle per lattice site, the expansion leads to the emergence of quasicondensates at finite momentum. In this case, one-particle correlations like the ones shown to be universal in the equilibrium case develop in the system. We show that the out-of-equilibrium behavior of the Shannon information entropy in momentum space, and its contrast with the one of noninteracting fermions, allows to differentiate the two different regimes of interest. It also helps in understanding the crossover between them.Comment: 21 pages, 14 figures, invited brief revie

Time of flight observables and the formation of Mott domains of fermions and bosons on optical lattices

We study, using quantum Monte Carlo simulations, the energetics of the formation of Mott domains of fermions and bosons trapped on one-dimensional lattices. We show that, in both cases, the sum of kinetic and interaction energies exhibits minima when Mott domains appear in the trap. In addition, we examine the derivatives of the kinetic and interaction energies, and of their sum, which display clear signatures of the Mott transition. We discuss the relevance of these findings to time-of-flight experiments that could allow the detection of the metal--Mott-insulator transition in confined fermions on optical lattices, and support established results on the superfluid--Mott-insulator transition in confined bosons on optical lattices.Comment: 5 pages, 6 figures, published versio

Correlations and diagonal entropy after quantum quenches in XXZ chains

We study quantum quenches in the XXZ spin-1/2 Heisenberg chain from families of ferromagnetic and antiferromagnetic initial states. Using Bethe ansatz techniques, we compute short-range correlators in the complete generalized Gibbs ensemble (GGE), which takes into account all local and quasi-local conservation laws. We compare our results to exact diagonalization and numerical linked cluster expansion calculations for the diagonal ensemble finding excellent agreement and thus providing a very accurate test for the validity of the complete GGE. Furthermore, we compute the diagonal entropy in the post-quench steady state. By careful finite-size scaling analyses of the exact diagonalization results, we show that the diagonal entropy is equal to one half the Yang-Yang entropy corresponding to the complete GGE. Finally, the complete GGE is quantitatively contrasted with the GGE built using only the local conserved charges (local GGE). The predictions of the two ensembles are found to differ significantly in the case of ferromagnetic initial states. Such initial states are better suited than others considered in the literature to experimentally test the validity of the complete GGE and contrast it to the failure of the local GGE

Comment on "Novel Superfluidity in a Trapped Gas of Fermi Atoms with Repulsive Interaction Loaded on an Optical Lattice"

In a recent letter Machida et al. [Phys. Rev. Lett. 93, 200402 (2004)] concluded that in a trapped gas of fermions with repulsive interactions a superfluid phase appears around the Mott-insulator at the center of the trap. They base their conclusion on a negative binding energy, and a large weight for a singlet formed by particles located at opposite sides of the Mott-insulator. We show here that the observed effects are not related to superfluidity.Comment: Revtex file, 1 page, 1 figure, published versio

Exact Study of the 1D Boson Hubbard Model with a Superlattice Potential

We use Quantum Monte Carlo simulations and exact diagonalization to explore the phase diagram of the Bose-Hubbard model with an additional superlattice potential. We first analyze the properties of superfluid and insulating phases present in the hard-core limit where an exact analytic treatment is possible via the Jordan-Wigner transformation. The extension to finite on-site interaction is achieved by means of quantum Monte Carlo simulations. We determine insulator/superfluid phase diagrams as functions of the on-site repulsive interaction, superlattice potential strength, and filling, finding that insulators with fractional occupation numbers, which are present in the hard-core case, extend deep into the soft-core region. Furthermore, at integer fillings, we find that the competition between the on-site repulsion and the superlattice potential can produce a phase transition between a Mott insulator and a charge density wave insulator, with an intermediate superfluid phase. Our results are relevant to the behavior of ultracold atoms in optical superlattices which are beginning to be studied experimentally.Comment: 13 pages, 23 figure

Superfluid and Mott Insulator phases of one-dimensional Bose-Fermi mixtures

We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the Canonical Worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and inter-species interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.Comment: 8 pages, 12 figure

Mott Domains of Bosons Confined on Optical Lattices

In the absence of a confining potential, the boson Hubbard model in its ground state is known to exhibit a superfluid to Mott insulator quantum phase transition at commensurate fillings and strong on-site repulsion. In this paper, we use quantum Monte Carlo simulations to study the ground state of the one dimensional bosonic Hubbard model in a trap. We show that some, but not all, aspects of the Mott insulating phase persist when a confining potential is present. The Mott behavior is present for a continuous range of incommensurate fillings, a very different situation from the unconfined case. Furthermore the establishment of the Mott phase does not proceed via a quantum phase transition in the traditional sense. These observations have important implications for the interpretation of experimental results for atoms trapped on optical lattices. Initial results show that, qualitatively, the same results persist in higher dimensions.Comment: Revtex file, five figures, include