317 research outputs found
Matter-wave localization in a random potential
By numerical and variational solution of the Gross-Pitaevskii equation, we
studied the localization of a noninteracting and weakly-interacting
Bose-Einstein condensate (BEC) in a disordered cold atom lattice and a speckle
potential. In the case of a single BEC fragment, the variational analysis
produced good results. For a weakly disordered potential, the localized BECs
are found to have an exponential tail as in weak Anderson localization. We also
investigated the expansion of a noninteracting BEC in these potential. We find
that the BEC will be locked in an appropriate localized state after an initial
expansion and will execute breathing oscillation around a mean shape when a BEC
at equilibrium in a harmonic trap is suddenly released into a disorder
potential
Localization in momentum space of ultracold atoms in incommensurate lattices
We characterize the disorder induced localization in momentum space for
ultracold atoms in one-dimensional incommensurate lattices, according to the
dual Aubry-Andr\'e model. For low disorder the system is localized in momentum
space, and the momentum distribution exhibits time-periodic oscillations of the
relative intensity of its components. The behavior of these oscillations is
explained by means of a simple three-mode approximation. We predict their
frequency and visibility by using typical parameters of feasible experiments.
Above the transition the system diffuses in momentum space, and the
oscillations vanish when averaged over different realizations, offering a clear
signature of the transition
Superradiant light scattering from a moving Bose-Einstein condensate
We investigate the interaction of a moving BEC with a far detuned laser beam.
Superradiant Rayleigh scattering arises from the spontaneous formation of a
matter-wave grating due to the interference of two wavepackets with different
momenta. The system is described by the CARL-BEC model which is a
generalization of the Gross-Pitaevskii model to include the self-consistent
evolution of the scattered field. The experiment gives evidence of a damping of
the matter-wave grating which depends on the initial velocity of the
condensate. We describe this damping in terms of a phase-diffusion decoherence
process, in good agreement with the experimental results
A Bose-Einstein condensate in a random potential
An optical speckle potential is used to investigate the static and dynamic
properties of a Bose-Einstein condensate in the presence of disorder. For
strong disorder the condensate is localized in the deep wells of the potential.
With smaller levels of disorder, stripes are observed in the expanded density
profile and strong damping of dipole and quadrupole oscillations is seen.
Uncorrelated frequency shifts of the two modes are measured for a weak disorder
and are explained using a sum-rules approach and by the numerical solution of
the Gross-Pitaevskii equation
Integrating EEG and MEG signals to improve motor imagery classification in brain-computer interfaces
We propose a fusion approach that combines features from simultaneously
recorded electroencephalographic (EEG) and magnetoencephalographic (MEG)
signals to improve classification performances in motor imagery-based
brain-computer interfaces (BCIs). We applied our approach to a group of 15
healthy subjects and found a significant classification performance enhancement
as compared to standard single-modality approaches in the alpha and beta bands.
Taken together, our findings demonstrate the advantage of considering
multimodal approaches as complementary tools for improving the impact of
non-invasive BCIs
Collective excitations of a trapped Bose-Einstein condensate in the presence of a 1D optical lattice
We study low-lying collective modes of a horizontally elongated 87Rb
condensate produced in a 3D magnetic harmonic trap with the addition of a 1D
periodic potential which is provided by a laser standing-wave along the
horizontal axis. While the transverse breathing mode results unperturbed,
quadrupole and dipole oscillations along the optical lattice are strongly
modified. Precise measurements of the collective mode frequencies at different
height of the optical barriers provide a stringent test of the theoretical
model recently introduced [M.Kraemer et al. Phys. Rev. Lett. 88 180404 (2002)].Comment: 4 pages, 4 figure
Optically-induced lensing effect on a Bose-Einstein condensate expanding in a moving lattice
We report the experimental observation of a lensing effect on a Bose-Einstein
condensate expanding in a moving 1D optical lattice. The effect of the periodic
potential can be described by an effective mass dependent on the condensate
quasi-momentum. By changing the velocity of the atoms in the frame of the
optical lattice we induce a focusing of the condensate along the lattice
direction. The experimental results are compared with the numerical predictions
of an effective 1D theoretical model. Besides, a precise band spectroscopy of
the system is carried out by looking at the real-space propagation of the
atomic wavepacket in the optical lattice.Comment: 5 pages, 4 figures; minor changes applied and typos corrected; a new
paragraph added; some references updated; journal reference adde
The inverse problem for the Gross - Pitaevskii equation
Two different methods are proposed for the generation of wide classes of
exact solutions to the stationary Gross - Pitaevskii equation (GPE). The first
method, suggested by the work by Kondrat'ev and Miller (1966), applies to
one-dimensional (1D) GPE. It is based on the similarity between the GPE and the
integrable Gardner equation, all solutions of the latter equation (both
stationary and nonstationary ones) generating exact solutions to the GPE, with
the potential function proportional to the corresponding solutions. The second
method is based on the "inverse problem" for the GPE, i.e. construction of a
potential function which provides a desirable solution to the equation.
Systematic results are presented for 1D and 2D cases. Both methods are
illustrated by a variety of localized solutions, including solitary vortices,
for both attractive and repulsive nonlinearity in the GPE. The stability of the
1D solutions is tested by direct simulations of the time-dependent GPE
Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide
We investigate the one-dimensional expansion of a Bose-Einstein condensate in
an optical guide in the presence of a random potential created with optical
speckles. With the speckle the expansion of the condensate is strongly
inhibited. A detailed investigation has been carried out varying the
experimental conditions and checking the expansion when a single optical defect
is present. The experimental results are in good agreement with numerical
calculations based on the Gross-Pitaevskii equation.Comment: 5 pages, 5 figure
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