250 research outputs found
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, . When a Mott insulator
sets in the middle of the trap, the center of mass barely moves after an
initial displacement, and 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
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
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
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
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
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