191 research outputs found

### Mean-field model for Josephson oscillation in a Bose-Einstein condensate on an one-dimensional optical trap

Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study
the phase coherence in a repulsive Bose-Einstein condensate (BEC) trapped by a
harmonic and an one-dimensional optical lattice potential to describe the
experiment by Cataliotti {\it et al.} on atomic Josephson oscillation [Science
{\bf 293}, 843 (2001)]. The phase coherence is maintained after the BEC is set
into oscillation by a small displacement of the magnetic trap along the optical
lattice. The phase coherence in the presence of oscillating neutral current
across an array of Josephson junctions manifests in an interference pattern
formed upon free expansion of the BEC. The numerical response of the system to
a large displacement of the magnetic trap is a classical transition from a
coherent superfluid to an insulator regime and a subsequent destruction of the
interference pattern in agreement with the more recent experiment by Cataliotti
{\it et al.} [e-print cond-mat/0207139].Comment: 6 Latex pages, 6 PS and EPS figures, Accepted in European Physical
Journal

### Free expansion of attractive and repulsive Bose-Einstein condensed vortex states

Free expansion of attractive and repulsive Bose-Einstein condensed vortex
states formed in an axially symmetric trap is investigated using the numerical
solution of the time-dependent Gross-Pitaevskii equation. In a repulsive
condensate the vortex-core radius is much smaller than the radial
root-mean-square (rms) radius, which makes the experimental observation of the
vortex core difficult. The opposite is found to be true in an attractive
condensate which makes it a better candidate for experimental observation.
Also, in all cases the ratio of vortex-core radius to radial rms radius
increases as the angular momentum of the vortex increases. This makes the
vortex states with higher angular momenta more suitable for experimental
confirmation.Comment: 5 revtex pages, 7 postscript figure

### Study of a degenerate dipolar Fermi gas of 161Dy atoms

We study properties of a single-component (spin polarized) degenerate dipolar
Fermi gas of 161Dy atoms using a hydrodynamic description. Under
axially-symmetric trapping we suggest reduced one- (1D) and two-dimensional
(2D) description of the same for cigar and disk shapes, respectively. In
addition to a complete numerical solution of the hydrodynamic model we also
consider a variational approximation of the same. For a trapped system under
appropriate conditions, the variational approximation as well as the reduced 1D
and 2D models are found to yield results for shape, size and chemical potential
of the system in agreement with the full numerical solution of the
three-dimensional (3D) model. For the uniform system we consider anisotropic
sound propagation in 3D. An analytical result for anisotropic sound propagation
in uniform dipolar degenerate Fermi gas is found to be in agreement with
results of numerical simulation in 3D

### Collapse of attractive Bose-Einstein condensed vortex states in a cylindrical trap

Quantized vortex states of weakly interacting Bose-Einstein condensate of
atoms with attractive interatomic interaction in an axially symmetric harmonic
oscillator trap are investigated using the numerical solution of the
time-dependent Gross-Pitaevskii (GP) equation obtained by the semi-implicit
Crank-Nicholson method. Collapse of the condensate is studied in the presence
of deformed traps with a larger frequency along the radial as well as along the
axial directions. The critical number of atoms for collapse is calculated as a
function of vortex quantum $L$. The critical number increases with angular
momentum $L$ of the vortex state but tends to saturate for large $L$.Comment: 8 Latex pages, 5 postscript figures, Accepted in Phys. Rev.

### Mean-field model of interaction between bright vortex solitons in Bose-Einstein condensates

Using the explicit numerical solution of the axially-symmetric
Gross-Pitaevskii equation we study the dynamics of interaction among vortex
solitons in a rotating matter-wave bright soliton train in a radially trapped
and axially free Bose-Einstein condensate to understand certain features of the
experiment by Strecker et al.[2002 Nature 417 150]. In a soliton train,
solitons of opposite phase (phase delta = pi) repel and stay apart without
changing shape; solitons with delta = 0 attract, interact and coalesce, but
eventually come out; solitons with a general delta usually repel but interact
inelastically by exchanging matter. We study and suggest future experiments
with vortex solitons.Comment: 12 Revtex4 pages with 17 PS figures, Disscussion improved, References
added, Evolution of three-dimensional wave function of interacting solitons
plotte

### Bound states of attractive Bose-Einstein condensates in shallow traps in two and three dimensions

Using variational and numerical solutions of the mean-field Gross-Pitaevskii
equation for attractive interaction (with cubic or Kerr nonlinearity) we show
that a stable bound state can appear in a Bose-Einstein condensate (BEC) in a
localized exponentially-screened radially-symmetric harmonic potential well in
two and three dimensions. We also consider an axially-symmetric configuration
with zero axial trap and a exponentially-screened radial trap so that the
resulting bound state can freely move along the axial direction like a soliton.
The binding of the present states in shallow wells is mostly due to the
nonlinear interaction with the trap playing a minor role. Hence these BEC
states are more suitable to study the effect of the nonlinear force on the
dynamics. We illustrate the highly nonlinear nature of breathing oscillation of
these states. Such bound states could be created in BECs and studied in the
laboratory with present knowhow.Comment: 16 pages, 13 ps figures, Journal of Physics

### Josephson oscillation and induced collapse in an attractive Bose-Einstein condensate

Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study
the Josephson oscillation of an attractive Bose-Einstein condensate (BEC) in a
one-dimensional periodic optical-lattice potential. We find that the Josephson
frequency is virtually independent of the number of atoms in the BEC and of the
inter-atomic interaction (attractive or repulsive). We study the dependence of
Josephson frequency on the laser wave length and the strength of the
optical-lattice potential. For a fixed laser wave length (795 nm), the
Josephson frequency decreases with increasing strength as found in the
experiment of Cataliotti {\it et al.} [Science {\bf 293}, 843 (2001)]. For a
fixed strength, the Josephson frequency remains essentially unchanged for a
reasonable variation of laser wave length around 800 nm. However, for a fixed
strength, the Josephson oscillation is disrupted with the increase of laser
wave length beyond 2000 nm leading to a collapse of a sufficiently attractive
BEC. These features of Josephson oscillation can be tested experimentally with
present set ups.Comment: 7 pages, 12 ps and eps figures, Physical Review

### Bright vortex solitons in Bose Condensates

We suggest the possibility of observing and studying bright vortex solitons
in attractive Bose-Einstein condensates in three dimensions with a radial trap.
Such systems lie on the verge of critical stability and we discuss the
conditions of their stability. We study the interaction between two such
solitons. Unlike the text-book solitons in one dimension, the interaction
between two radially trapped and axially free three-dimensional solitons is
inelastic in nature and involves exchange of particles and deformation in
shape. The interaction remains repulsive for all phase delta between them
except for delta \approx 0.Comment: Version accepted in Few-Body System

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