257 research outputs found
Dissipation-managed soliton in a quasi-one-dimensional Bose-Einstein condensate
We use the time-dependent mean-field Gross-Pitaevskii equation to study the
formation of a dynamically-stabilized dissipation-managed bright soliton in a
quasi-one-dimensional Bose-Einstein condensate (BEC). Because of three-body
recombination of bosonic atoms to molecules, atoms are lost (dissipated) from a
BEC. Such dissipation leads to the decay of a BEC soliton. We demonstrate by a
perturbation procedure that an alimentation of atoms from an external source to
the BEC may compensate for the dissipation loss and lead to a
dynamically-stabilized soliton. The result of the analytical perturbation
method is in excellent agreement with mean-field numerics. It seems possible to
obtain such a dynamically-stabilized BEC soliton without dissipation in
laboratory.Comment: 5 pages, 3 figure
Black soliton in a quasi-one-dimensional trapped fermion-fermion mixture
Employing a time-dependent mean-field-hydrodynamic model we study the
generation of black solitons in a degenerate fermion-fermion mixture in a
cigar-shaped geometry using variational and numerical solutions. The black
soliton is found to be the first stationary vibrational excitation of the
system and is considered to be a nonlinear continuation of the vibrational
excitation of the harmonic oscillator state. We illustrate the stationary
nature of the black soliton, by studying different perturbations on it after
its formation.Comment: 7 pages, 10 figure
Simulation of a stationary dark soliton in a trapped zero-temperature Bose-Einstein condensate
We discuss a computational mechanism for the generation of a stationary dark
soliton, or black soliton, in a trapped Bose-Einstein condensate using the
Gross-Pitaevskii (GP) equation for both attractive and repulsive interaction.
It is demonstrated that the black soliton with a "notch" in the probability
density with a zero at the minimum is a stationary eigenstate of the GP
equation and can be efficiently generated numerically as a nonlinear
continuation of the first vibrational excitation of the GP equation in both
attractive and repulsive cases in one and three dimensions for pure harmonic as
well as harmonic plus optical-lattice traps. We also demonstrate the stability
of this scheme under different perturbing forces.Comment: 7 pages, 15 ps figures, Final version accepted in J Low Temp Phy
Coupled Bose-Einstein condensate: Collapse for attractive interaction
We study the collapse in a coupled Bose-Einstein condensate of two types of
bosons 1 and 2 under the action of a trap using the time-dependent
Gross-Pitaevskii equation. The system may undergo collapse when one, two or
three of the scattering lengths for scattering of boson with ,
, are negative representing an attractive interaction. Depending
on the parameters of the problem a single or both components of the condensate
may experience collapse.Comment: 5 pages and 9 figures, small changes mad
Weakly bound atomic trimers in ultracold traps
The experimental three-atom recombination coefficients of the atomic states
Na, Rb and Rb,
together with the corresponding two-body scattering lengths, allow predictions
of the trimer bound state energies for such systems in a trap. The
recombination parameter is given as a function of the weakly bound trimer
energies, which are in the interval for large
positive scattering lengths, . The contribution of a deep-bound state to our
prediction, in the case of Rb, for a particular trap, is
shown to be relatively small.Comment: 5 pages, 1 figur
Mean-field description of collapsing and exploding Bose-Einstein condensates
We perform numerical simulation based on the time-dependent mean-field
Gross-Pitaevskii equation to understand some aspects of a recent experiment by
Donley et al. on the dynamics of collapsing and exploding Bose-Einstein
condensates of Rb atoms. They manipulated the atomic interaction by an
external magnetic field via a Feshbach resonance, thus changing the repulsive
condensate into an attractive one and vice versa. In the actual experiment they
changed suddenly the scattering length of atomic interaction from positive to a
large negative value on a pre-formed condensate in an axially symmetric trap.
Consequently, the condensate collapses and ejects atoms via explosion. We find
that the present mean-field analysis can explain some aspects of the dynamics
of the collapsing and exploding Bose-Einstein condensates.Comment: 9 Latex pages, 10 ps and eps files, version accepted in Physical
Review A, minor changes mad
Scaling limit of virtual states of triatomic systems
For a system with three identical atoms, the dependence of the wave
virtual state energy on the weakly bound dimer and trimer binding energies is
calculated in a form of a universal scaling function. The scaling function is
obtained from a renormalizable three-body model with a pairwise Dirac-delta
interaction. It was also discussed the threshold condition for the appearance
of the trimer virtual state.Comment: 9 pages, 3 figure
Cooper pair dispersion relation for weak to strong coupling
Cooper pairing in two dimensions is analyzed with a set of renormalized
equations to determine its binding energy for any fermion number density and
all coupling assuming a generic pairwise residual interfermion interaction. \
Also considered are Cooper pairs (CPs) with nonzero center-of-mass momentum
(CMM)--usually neglected in BCS theory--and their binding energy is expanded
analytically in powers of the CMM up to quadratic terms. A Fermi-sea-dependent
{\it linear} term in the CMM dominates the pair excitation energy in weak
coupling (also called the BCS regime) while the more familiar quadratic term
prevails in strong coupling (the Bose regime). The crossover, though strictly
unrelated to BCS theory {\it per se,} is studied numerically as it is expected
to play a central role in a model of superconductivity as a Bose-Einstein
condensation of CPs where the transition temperature vanishes for all
dimensionality for quadratic dispersion, but is {\it nonzero} for all
for linear dispersion.Comment: 11 pages plus 3 figures, revised version accepted in Physical Review
Bose-Einstein condensate collapse: a comparison between theory and experiment
We solve the Gross-Pitaevskii equation numerically for the collapse induced
by a switch from positive to negative scattering lengths. We compare our
results with experiments performed at JILA with Bose-Einstein condensates of
Rb-85, in which the scattering length was controlled using a Feshbach
resonance. Building on previous theoretical work we identify quantitative
differences between the predictions of mean-field theory and the results of the
experiments. Besides the previously reported difference between the predicted
and observed critical atom number for collapse, we also find that the predicted
collapse times systematically exceed those observed experimentally. Quantum
field effects, such as fragmentation, that might account for these
discrepancies are discussed.Comment: 4 pages, 2 figure
Linear to quadratic crossover of Cooper pair dispersion relation
Cooper pairing is studied in three dimensions to determine its binding energy
for all coupling using a general separable interfermion interaction. Also
considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM). A
coupling-independent {\it linear} term in the CMM dominates the pair excitation
energy in weak coupling and/or high fermion density, while the more familiar
quadratic term prevails only in the extreme low-density (i.e., vacuum) limit
for any nonzero coupling. The linear-to-quadratic crossover of the CP
dispersion relation is analyzed numerically, and is expected to play a central
role in a model of superconductivity (and superfluidity) simultaneously
accommodating a BCS condensate as well as a Bose-Einstein condensate of CP
bosons.Comment: 13 pages plus 2 figure
- …