2,119 research outputs found
Exploring the grand-canonical phase diagram of interacting bosons in optical lattices by trap squeezing
In this paper we theoretically discuss how quantum simulators based on
trapped cold bosons in optical lattices can explore the grand-canonical phase
diagram of homogeneous lattice boson models, via control of the trapping
potential independently of all other experimental parameters (trap squeezing).
Based on quantum Monte Carlo, we establish the general scaling relation linking
the global chemical potential to the Hamiltonian parameters of the Bose-Hubbard
model in a parabolic trap, describing cold bosons in optical lattices; we find
that this scaling relation is well captured by a modified Thomas-Fermi scaling
behavior - corrected for quantum fluctuations - in the case of high enough
density and/or weak enough interactions, and by a mean-field Gutzwiller Ansatz
over a much larger parameter range. The above scaling relation allows to
control experimentally the chemical potential, independently of all other
Hamiltonian parameters, via trap squeezing; given that the global chemical
potential coincides with the local chemical potential in the trap center,
measurements of the central density as a function of the chemical potential
gives access to the information on the bulk compressibility of the Bose-Hubbard
model. Supplemented with time-of-flight measurements of the coherence
properties, the measurement of compressibility enables one to discern among the
various possible phases realized by bosons in an optical lattice with or
without external (periodic or random) potentials -- e.g. superfluid, Mott
insulator, band insulator, and Bose glass. We theoretically demonstrate the
trap-squeezing investigation of the above phases in the case of bosons in a
one-dimensional optical lattice, and in a one-dimensional incommensurate
superlattice.Comment: 27 pages, 26 figures. v2: added references and further discussion of
the local-density approximation
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results
The problem of finding the exact energies and configurations for the
Frenkel-Kontorova model consisting of particles in one dimension connected to
their nearest-neighbors by springs and placed in a periodic potential
consisting of segments from parabolas of identical (positive) curvature but
arbitrary height and spacing, is reduced to that of minimizing a certain convex
function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6
Postscript figures, accepted by Phys. Rev.
Order in extremal trajectories
Given a chaotic dynamical system and a time interval in which some quantity
takes an unusually large average value, what can we say of the trajectory that
yields this deviation? As an example, we study the trajectories of the
archetypical chaotic system, the baker's map. We show that, out of all
irregular trajectories, a large-deviation requirement selects (isolated) orbits
that are periodic or quasiperiodic. We discuss what the relevance of this
calculation may be for dynamical systems and for glasses
Finite-size effects in Anderson localization of one-dimensional Bose-Einstein condensates
We investigate the disorder-induced localization transition in Bose-Einstein
condensates for the Anderson and Aubry-Andre models in the non-interacting
limit using exact diagonalization. We show that, in addition to the standard
superfluid fraction, other tools such as the entanglement and fidelity can
provide clear signatures of the transition. Interestingly, the fidelity
exhibits good sensitivity even for small lattices. Effects of the system size
on these quantities are analyzed in detail, including the determination of a
finite-size-scaling law for the critical disorder strength in the case of the
Anderson model.Comment: 15 pages, 7 figure
Surface spin-flop phases and bulk discommensurations in antiferromagnets
Phase diagrams as a function of anisotropy D and magnetic field H are
obtained for discommensurations and surface states for a model antiferromagnet
in which is parallel to the easy axis. The surface spin-flop phase exists
for all . We show that there is a region where the penetration length of the
surface spin-flop phase diverges. Introducing a discommensuration of even
length then becomes preferable to reconstructing the surface. The results are
used to clarify and correct previous studies in which discommensurations have
been confused with genuine surface spin-flop states.Comment: 4 pages, RevTeX, 2 Postscript figure
Enhanced soliton transport in quasi-periodic lattices with short-range aperiodicity
We study linear transmission and nonlinear soliton transport through
quasi-periodic structures, which profiles are described by multiple modulation
frequencies. We show that resonant scattering at mixed-frequency resonances
limits transmission efficiency of localized wave packets, leading to radiation
and possible trapping of solitons. We obtain an explicit analytical expression
for optimal quasi-periodic lattice profiles, where additional aperiodic
modulations suppress mixed-frequency resonances, resulting in dramatic
enhancement of soliton mobility. Our results can be applied to the design of
photonic waveguide structures, and arrays of magnetic micro-traps for atomic
Bose-Einstein condensates.Comment: 4 pages, 4 figure
Localization of a Bose-Einstein condensate vortex in a bichromatic optical lattice
By numerical simulation of the time-dependent Gross-Pitaevskii equation we
show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC)
vortex can be localized in a three-dimensional bichromatic quasi-periodic
optical-lattice (OL) potential generated by the superposition of two
standing-wave polarized laser beams with incommensurate wavelengths. This is a
generalization of the localization of a BEC in a one-dimensional bichromatic OL
as studied in a recent experiment [Roati et al., Nature 453, 895 (2008)]. We
demonstrate the stability of the localized state by considering its time
evolution in the form of a stable breathing oscillation in a slightly altered
potential for a large period of time. {Finally, we consider the localization of
a BEC in a random 1D potential in the form of several identical repulsive
spikes arbitrarily distributed in space
Localization of a Bose-Einstein condensate in a bichromatic optical lattice
By direct numerical simulation of the time-dependent Gross-Pitaevskii
equation we study different aspects of the localization of a non-interacting
ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic
quasi-periodic optical-lattice potential. Such a quasi-periodic potential, used
in a recent experiment on the localization of a BEC [Roati et al., Nature 453,
895 (2008)], can be formed by the superposition of two standing-wave polarized
laser beams with different wavelengths. We investigate the effect of the
variation of optical amplitudes and wavelengths on the localization of a
non-interacting BEC. We also simulate the non-linear dynamics when a
harmonically trapped BEC is suddenly released into a quasi-periodic potential,
{as done experimentally in a laser speckle potential [Billy et al., Nature 453,
891 (2008)]$ We finally study the destruction of the localization in an
interacting BEC due to the repulsion generated by a positive scattering length
between the bosonic atoms.Comment: 8 page
Energy transmission in the forbidden bandgap of a nonlinear chain
A nonlinear chain driven by one end may propagate energy in the forbidden
band gap by means of nonlinear modes. For harmonic driving at a given
frequency, the process ocurs at a threshold amplitude by sudden large energy
flow, that we call nonlinear supratransmission. The bifurcation of energy
transmission is demonstrated numerically and experimentally on the chain of
coupled pendula (sine-Gordon and nonlinear Klein-Gordon equations) and
sustained by an extremely simple theory.Comment: LaTex file, 6 figures, published in Phys Rev Lett 89 (2002) 13410
Fractal Spin Glass Properties of Low Energy Configurations in the Frenkel-Kontorova chain
We study numerically and analytically the classical one-dimensional
Frenkel-Kontorova chain in the regime of pinned phase characterized by phonon
gap. Our results show the existence of exponentially many static equilibrium
configurations which are exponentially close to the energy of the ground state.
The energies of these configurations form a fractal quasi-degenerate band
structure which is described on the basis of elementary excitations. Contrary
to the ground state, the configurations inside these bands are disordered.Comment: revtex, 9 pages, 9 figure
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