172 research outputs found
Analytical mean-field approach to the phase-diagram of ultracold bosons in optical superlattices
We report a multiple-site mean-field analysis of the zero-temperature phase
diagram for ultracold bosons in realistic optical superlattices. The system of
interacting bosons is described by a Bose-Hubbard model whose site-dependent
parameters reflect the nontrivial periodicity of the optical superlattice. An
analytic approach is formulated based on the analysis of the stability of a
fixed-point of the map defined by the self-consistency condition inherent in
the mean-field approximation. The experimentally relevant case of the period-2
one-dimensional superlattice is briefly discussed. In particular, it is shown
that, for a special choice of the superlattice parameters, the half-filling
insulator domain features an unusual loophole shape that the single-site
mean-field approach fails to capture.Comment: 7 pages, 1 figur
Strong-coupling expansions for the topologically inhomogeneous Bose-Hubbard model
We consider a Bose-Hubbard model with an arbitrary hopping term and provide
the boundary of the insulating phase thereof in terms of third-order strong
coupling perturbative expansions for the ground state energy. In the general
case two previously unreported terms occur, arising from triangular loops and
hopping inhomogeneities, respectively. Quite interestingly the latter involves
the entire spectrum of the hopping matrix rather than its maximal eigenpair,
like the remaining perturbative terms. We also show that hopping
inhomogeneities produce a first order correction in the local density of
bosons. Our results apply to ultracold bosons trapped in confining potentials
with arbitrary topology, including the realistic case of optical superlattices
with uneven hopping amplitudes. Significant examples are provided. Furthermore,
our results can be extented to magnetically tuned transitions in Josephson
junction arrays.Comment: 5 pages, 2 figures,final versio
Persistence of mean-field features in the energy spectrum of small arrays of Bose-Einstein condensates
The Bose-Hubbard Hamiltonian capturing the essential physics of the arrays of
interacting Bose-Einstein condensates is addressed, focusing on arrays
consisting of two (dimer) and three (trimer) sites. In the former case, some
results concerning the persistence of mean-field features in the energy
spectrum of the symmetric dimer are extended to the asymmetric version of the
system, where the two sites are characterized by different on-site energies.
Based on a previous systematic study of the mean-field limit of the trimer,
where the dynamics is exhaustively described in terms of its fixed points for
every choice of the significant parameters, an interesting mapping between the
dimer and the trimer is emphasized and used as a guide in investigating the
persistence of mean-field features in the rather complex energy spectrum of the
trimer. These results form the basis for the systematic investigation of the
purely quantum trimer extending and completing the existing mean-field
analysis. In this respect we recall that, similar to larger arrays, the trimer
is characterized by a non-integrable mean-field dynamics featuring chaotic
trajectories. Hence, the correspondence between mean-field fixed points and
quantum energy levels emphasized in the present work may provide a key to
investigate the quantum counterpart of classical instability.Comment: 12 pages, 6 figures, to appear on Journal of Physics B (Special
Issue: Levico BEC workshop). Publication status update
Glassy features of a Bose Glass
We study a two-dimensional Bose-Hubbard model at a zero temperature with
random local potentials in the presence of either uniform or binary disorder.
Many low-energy metastable configurations are found with virtually the same
energy as the ground state. These are characterized by the same blotchy pattern
of the, in principle, complex nonzero local order parameter as the ground
state. Yet, unlike the ground state, each island exhibits an overall random
independent phase. The different phases in different coherent islands could
provide a further explanation for the lack of coherence observed in experiments
on Bose glasses.Comment: 14 pages, 4 figures
Fractional-filling Mott domains in two dimensional optical superlattices
Ultracold bosons in optical superlattices are expected to exhibit
fractional-filling insulating phases for sufficiently large repulsive
interactions. On strictly 1D systems, the exact mapping between hard-core
bosons and free spinless fermions shows that any periodic modulation in the
lattice parameters causes the presence of fractional-filling insulator domains.
Here, we focus on two recently proposed realistic 2D structures where such
mapping does not hold, i.e. the two-leg ladder and the trimerized kagome'
lattice. Based on a cell strong-coupling perturbation technique, we provide
quantitatively satisfactory phase diagrams for these structures, and give
estimates for the occurrence of the fractional-filling insulator domains in
terms of the inter-cell/intra-cell hopping amplitude ratio.Comment: 4 pages, 3 figure
Topological Reduction of Tight-Binding Models on Complex Networks
Complex molecules and mesoscopic structures are naturally described by
general networks of elementary building blocks and tight-binding is one of the
simplest quantum model suitable for studying the physical properties arising
from the network topology. Despite the simplicity of the model, topological
complexity can make the evaluation of the spectrum of the tight-binding
Hamiltonian a rather hard task, since the lack of translation invariance rules
out such a powerful tool as Fourier transform. In this paper we introduce a
rigorous analytical technique, based on topological methods, for the exact
solution of this problem on branched structures. Besides its analytic power,
this technique is also a promising engineering tool, helpful in the design of
netwoks displaying the desired spectral features.Comment: 19 pages, 14 figure
Control of unstable macroscopic oscillations in the dynamics of three coupled Bose condensates
We study the dynamical stability of the macroscopic quantum oscillations
characterizing a system of three coupled Bose-Einstein condensates arranged
into an open-chain geometry. The boson interaction, the hopping amplitude and
the central-well relative depth are regarded as adjustable parameters. After
deriving the stability diagrams of the system, we identify three mechanisms to
realize the transition from an unstable to stable behavior and analyze specific
configurations that, by suitably tuning the model parameters, give rise to
macroscopic effects which are expected to be accessible to experimental
observation. Also, we pinpoint a system regime that realizes a
Josephson-junction-like effect. In this regime the system configuration do not
depend on the model interaction parameters, and the population oscillation
amplitude is related to the condensate-phase difference. This fact makes
possible estimating the latter quantity, since the measure of the oscillating
amplitudes is experimentally accessible.Comment: 25 pages, 12 figure
Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
We analyze the quantum phase transition in the Bose-Hubbard model borrowing
two tools from quantum-information theory, i.e. the ground-state fidelity and
entanglement measures. We consider systems at unitary filling comprising up to
50 sites and show for the first time that a finite-size scaling analysis of
these quantities provides excellent estimates for the quantum critical point.We
conclude that fidelity is particularly suited for revealing a quantum phase
transition and pinning down the critical point thereof, while the success of
entanglement measures depends on the mechanisms governing the transition.Comment: 7 pages, 5 figures (endfloats used due to problems with figures and
latex. Sorry about that); final version, similar to the published on
On the dispute between Boltzmann and Gibbs entropy
Very recently, the validity of the concept of negative temperature has been
challenged by several authors since they consider Boltzmann's entropy (that
allows negative temperatures) inconsistent from a mathematical and statistical
point of view, whereas they consider Gibbs' entropy (that does not admit
negative temperatures) the correct definition for microcanonical entropy.
In the present paper we prove that for systems with equivalence of the
statistical ensembles Boltzmann entropy is the correct microcanonical entropy.
Analytical results on two systems supporting negative temperatures, confirm the
scenario we propose. In addition, we corroborate our proof by numeric
simulations on an explicit lattice system showing that negative temperature
equilibrium states are accessible and obey standard statistical mechanics
prevision.Comment: To appear in Annals of Physic
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