16 research outputs found
Supersolids in confined fermions on one-dimensional optical lattices
Using quantum Monte Carlo simulations, we show that density-density and
pairing correlation functions of the one-dimensional attractive fermionic
Hubbard model in a harmonic confinement potential are characterized by the
anomalous dimension of a corresponding periodic system, and hence
display quantum critical behavior. The corresponding fluctuations render the
SU(2) symmetry breaking by the confining potential irrelevant, leading to
structure form factors for both correlation functions that scale with the same
exponent upon increasing the system size, thus giving rise to a
(quasi)supersolid.Comment: 4 pages, 5 figures, published versio
Quantum Monte Carlo study of confined fermions in one-dimensional optical lattices
Using quantum Monte Carlo (QMC) simulations we study the ground-state
properties of the one-dimensional fermionic Hubbard model in traps with an
underlying lattice. Since due to the confining potential the density is space
dependent, Mott-insulating domains always coexist with metallic regions, such
that global quantities are not appropriate to describe the system. We define a
local compressibility that characterizes the Mott-insulating regions and
analyze other local quantities. It is shown that the momentum distribution
function, a quantity that is commonly considered in experiments, fails in
giving a clear signal of the Mott-insulator transition. Furthermore, we analyze
a mean-field approach to these systems and compare it with the numerically
exact QMC results. Finally, we determine a generic form for the phase diagram
that allows us to predict the phases to be observed in the experiments.Comment: RevTex file, 13 pages, 19 figures, published versio
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
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
Coherent matter waves emerging from Mott-insulators
We study the formation of (quasi-)coherent matter waves emerging from a Mott
insulator for strongly interacting bosons on a one-dimensional lattice. It has
been shown previously that a quasi-condensate emerges at momentum k=\pi/2a,
where a is the lattice constant, in the limit of infinitely strong repulsion
(hard-core bosons). Here we show that this phenomenon persists for all values
of the repulsive interaction that lead to a Mott insulator at a commensurate
filling. The non-equilibrium dynamics of hard-core bosons is treated exactly by
means of a Jordan-Wigner transformation, and the generic case is studied using
a time-dependent density matrix renormalization group technique. Different
methods for controlling the emerging matter wave are discussed.Comment: 20 pages, 11 figures. Published versio
Quantum distillation: dynamical generation of low-entropy states of strongly correlated fermions in an optical lattice
Correlations between particles can lead to subtle and sometimes
counterintuitive phenomena. We analyze one such case, occurring during the
sudden expansion of fermions in a lattice when the initial state has a strong
admixture of double occupancies. We promote the notion of quantum distillation:
during the expansion, and in the presence of strongly repulsive interactions,
doublons group together, forming a nearly ideal band insulator, which is
metastable with a low entropy. We propose that this effect could be used for
cooling purposes in experiments with two-component Fermi gases.Comment: Final version as published, minor revisions, more discussion on the
cooling proposal, includes auxiliary material (EPAPS), 7 pages Revtex 4, 12
eps figure
From the superfluid to the Mott regime and back: triggering a non-trivial dynamics in an array of coupled condensates
We consider a system formed by an array of Bose-Einstein condensates trapped
in a harmonic potential with a superimposed periodic optical potential.
Starting from the boson field Hamiltonian, appropriate to describe dilute gas
of bosonic atoms, we reformulate the system dynamics within the Bose-Hubbard
model picture. Then we analyse the effective dynamics of the system when the
optical potential depth is suddenly varied according to a procedure applied in
many of the recent experiments on superfluid-Mott transition in Bose-Einstein
condensates.
Initially the condensates' array generated in a weak optical potential is
assumed to be in the superfluid ground-state which is well described in terms
of coherent states. At a given time, the optical potential depth is suddenly
increased and, after a waiting time, it is quickly decreased so that the
initial depth is restored. We compute the system-state evolution and show that
the potential jump brings on an excitation of the system, incorporated in the
final condensate wave functions, whose effects are analysed in terms of
two-site correlation functions and of on-site population oscillations. Also we
show how a too long waiting time can destroy completely the coherence of the
final state making it unobservable.Comment: 10 pages, 4 figures, to appear on Journal of Physics B (Special
Issue: Levico BEC workshop). Publication status update
Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices
We present an extensive numerical study of ground-state properties of
confined repulsively interacting fermions on one-dimensional optical lattices.
Detailed predictions for the atom-density profiles are obtained from parallel
Kohn-Sham density-functional calculations and quantum Monte Carlo simulations.
The density-functional calculations employ a Bethe-Ansatz-based local-density
approximation for the correlation energy, which accounts for Luttinger-liquid
and Mott-insulator physics. Semi-analytical and fully numerical formulations of
this approximation are compared with each other and with a cruder
Thomas-Fermi-like local-density approximation for the total energy. Precise
quantum Monte Carlo simulations are used to assess the reliability of the
various local-density approximations, and in conjunction with these allow to
obtain a detailed microscopic picture of the consequences of the interplay
between particle-particle interactions and confinement in one-dimensional
systems of strongly correlated fermions.Comment: 14 pages, 11 figures, 1 table, submitte