20 research outputs found
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
Dynamical Instability in a Trimeric Chain of Interacting Bose-Einstein Condensates
We analyze thoroughly the mean-field dynamics of a linear chain of three
coupled Bose-Einstein condensates, where both the tunneling and the
central-well relative depth are adjustable parameters. Owing to its
nonintegrability, entailing a complex dynamics with chaos occurrence, this
system is a paradigm for longer arrays whose simplicity still allows a thorough
analytical study.We identify the set of dynamics fixed points, along with the
associated proper modes, and establish their stability character depending on
the significant parameters. As an example of the remarkable operational value
of our analysis, we point out some macroscopic effects that seem viable to
experiments.Comment: 5 pages, 3 figure
Ground-state Properties of Small-Size Nonlinear Dynamical Lattices
We investigate the ground state of a system of interacting particles in small
nonlinear lattices with M > 2 sites, using as a prototypical example the
discrete nonlinear Schroedinger equation that has been recently used
extensively in the contexts of nonlinear optics of waveguide arrays, and
Bose-Einstein condensates in optical lattices. We find that, in the presence of
attractive interactions, the dynamical scenario relevant to the ground state
and the lowest-energy modes of such few-site nonlinear lattices reveals a
variety of nontrivial features that are absent in the large/infinite lattice
limits: the single-pulse solution and the uniform solution are found to coexist
in a finite range of the lattice intersite coupling where, depending on the
latter, one of them represents the ground state; in addition, the single-pulse
mode does not even exist beyond a critical parametric threshold. Finally, the
onset of the ground state (modulational) instability appears to be intimately
connected with a non-standard (``double transcritical'') type of bifurcation
that, to the best of our knowledge, has not been reported previously in other
physical systems.Comment: 7 pages, 4 figures; submitted to PR
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
Some remarks on the coherent-state variational approach to nonlinear boson models
The mean-field pictures based on the standard time-dependent variational
approach have widely been used in the study of nonlinear many-boson systems
such as the Bose-Hubbard model. The mean-field schemes relevant to
Gutzwiller-like trial states , number-preserving states and
Glauber-like trial states are compared to evidence the specific
properties of such schemes. After deriving the Hamiltonian picture relevant to
from that based on , the latter is shown to exhibit a Poisson
algebra equipped with a Weyl-Heisenberg subalgebra which preludes to the
-based picture. Then states are shown to be a superposition of -boson states and the similarities/differences of the -based and
-based pictures are discussed. Finally, after proving that the simple,
symmetric state indeed corresponds to a SU(M) coherent state, a dual
version of states and in terms of momentum-mode operators is
discussed together with some applications.Comment: 16 page
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
Hamiltonian Hopf bifurcations in the discrete nonlinear Schr\"odinger trimer: oscillatory instabilities, quasiperiodic solutions and a 'new' type of self-trapping transition
Oscillatory instabilities in Hamiltonian anharmonic lattices are known to
appear through Hamiltonian Hopf bifurcations of certain time-periodic solutions
of multibreather type. Here, we analyze the basic mechanisms for this scenario
by considering the simplest possible model system of this kind where they
appear: the three-site discrete nonlinear Schr\"odinger model with periodic
boundary conditions. The stationary solution having equal amplitude and
opposite phases on two sites and zero amplitude on the third is known to be
unstable for an interval of intermediate amplitudes. We numerically analyze the
nature of the two bifurcations leading to this instability and find them to be
of two different types. Close to the lower-amplitude threshold stable
two-frequency quasiperiodic solutions exist surrounding the unstable stationary
solution, and the dynamics remains trapped around the latter so that in
particular the amplitude of the originally unexcited site remains small. By
contrast, close to the higher-amplitude threshold all two-frequency
quasiperiodic solutions are detached from the unstable stationary solution, and
the resulting dynamics is of 'population-inversion' type involving also the
originally unexcited site.Comment: 25 pages, 11 figures, to be published in J. Phys. A: Math. Gen.
Revised and shortened version with few clarifying remarks adde
Spectral properties and self-trapping effect in coupled Bose-Einstein condensates
We study the energy spectrum structure of a system of two interacting bosonic wells (dimer model) occupied by N bosons and compare it with the phase-space topology of the same model within the mean-field approach. To this end, we characterize the structure of energy eigenstates by using the symmetry properties of the Hamiltonian, and show that the energy levels are nondegenerate. The presence of doublets leads to recover in the classical limit the self-trapping effect exhibited by the mean-field dimer model. Finally, we do some comments on trimer dynamics to show how the interaction with a third well can cause both dimer-like regimes and strongly chaotic behaviors