79 research outputs found
Tree-body loss of of trapped ultracold Rb atoms due to a Feshbach resonance
The loss of ultracold trapped atoms in the vicinity of a Feshbach resonance
is treated as a two-stage reaction, using the Breit-Wigner theory. The first
stage is the formation of a resonant diatomic molecule, and the second one is
its deactivation by inelastic collisions with other atoms. This model is
applied to the analysis of recent experiments on Rb, leading to an
estimated value of cms for the deactivation rate
coefficient.Comment: LaTeX, 4 pages with 1 figures, uses REVTeX4, uses improved
experimental dat
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
Very high precision bound state spectroscopy near a Rb Feshbach resonance
We precisely measured the binding energy of a molecular state near the
Feshbach resonance in a Rb Bose-Einstein condensate (BEC). Rapid
magnetic field pulses induced coherent atom-molecule oscillations in the BEC.
We measured the oscillation frequency as a function of B-field and fit the data
to a coupled-channels model. Our analysis constrained the Feshbach resonance
position [155.041(18) G], width [10.71(2) G], and background scattering length
[-443(3) a] and yielded new values for , , and . These
results improved our estimate for the stability condition of an attractive BEC.
We also found evidence for a mean-field shift to the binding energy.Comment: 5 pages, 2 figures, submitted to PR
Characterization of elastic scattering near a Feshbach resonance in rubidium 87
The s-wave scattering length for elastic collisions between 87Rb atoms in the
state |f,m_f>=|1,1> is measured in the vicinity of a Feshbach resonance near
1007 G. Experimentally, the scattering length is determined from the mean-field
driven expansion of a Bose-Einstein condensate in a homogeneous magnetic field.
The scattering length is measured as a function of the magnetic field and
agrees with the theoretical expectation. The position and the width of the
resonance are determined to be 1007.40 G and 0.20 G, respectively.Comment: 4 pages, 2 figures minor revisions: added Ref.6, included error bar
Dynamic depletion in a Bose condensate via a sudden increase of the scattering length
We examine the time-dependent quantum depletion of a trapped Bose condensate
arising from a rapid increase of the scattering length. Our solution indicates
that a significant buildup of incoherent atoms can occur within a
characteristic time short compared with the harmonic trap period. We discuss
how the depletion density and the characteristic time depend on the physical
parameters of the condensate
Hydrodynamic modes of a 1D trapped Bose gas
We consider two regimes where a trapped Bose gas behaves as a one-dimensional
system. In the first one the Bose gas is microscopically described by 3D mean
field theory, but the trap is so elongated that it behaves as a 1D gas with
respect to low frequency collective modes. In the second regime we assume that
the 1D gas is truly 1D and that it is properly described by the Lieb-Liniger
model. In both regimes we find the frequency of the lowest compressional mode
by solving the hydrodynamic equations. This is done by making use of a method
which allows to find analytical or quasi-analytical solutions of these
equations for a large class of models approaching very closely the actual
equation of state of the Bose gas. We find an excellent agreement with the
recent results of Menotti and Stringari obtained from a sum rule approach.Comment: 15 pages, revtex, 1 figure
A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
We consider the problem of identifying sharp criteria under which radial
(finite energy) solutions to the focusing 3d cubic nonlinear
Schr\"odinger equation (NLS) scatter,
i.e. approach the solution to a linear Schr\"odinger equation as . The criteria is expressed in terms of the scale-invariant quantities
and , where denotes the
initial data, and and denote the (conserved in time) mass and
energy of the corresponding solution . The focusing NLS possesses a
soliton solution , where is the ground-state solution to a
nonlinear elliptic equation, and we prove that if and
, then the
solution is globally well-posed and scatters. This condition is sharp in
the sense that the soliton solution , for which equality in these
conditions is obtained, is global but does not scatter. We further show that if
, then the solution blows-up in finite time. The
technique employed is parallel to that employed by Kenig-Merle \cite{KM06a} in
their study of the energy-critical NLS
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
Dynamics of quantum quenching for BCS-BEC systems in the shallow BEC regime
The problem of coupled Fermi-Bose mixtures of an ultracold gas near a narrow
Feshbach resonance is approached through the time-dependent and complex
Ginzburg-Landau (TDGL) theory. The dynamical system is constructed using
Ginzburg-Landau-Abrikosov-Gor'kov (GLAG) path integral methods with the single
mode approximation for the composite Bosons, and the equilibrium states are
obtained in the BEC regime for adiabatic variations of the Feshbach detuning
along the stationary solutions of the dynamical system. Investigations into the
rich superfluid dynamics of this system in the shallow BEC regime yields the
onset of multiple interference patterns in the dynamics as the system is
quenched from the deep-BEC regime. This results in a partial collapse and
revival of the coherent matter wave field of the BEC, whose temporal profile is
reported.Comment: 24 pages, 7 figures. Submitted to European Journal of Physics Plu
An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation
We study nonlinear mean-field dynamics of ultracold molecule formation in the
case when the external field configuration is defined by the level-crossing
Demkov-Kunike model, characterized by a bell-shaped coupling and finite
variation of the detuning. Analyzing the fast sweep rate regime of the strong
interaction limit, which models a situation when the peak value of the coupling
is large enough and the resonance crossing is sufficiently fast, we construct a
highly accurate ansatz to describe the temporal dynamics of the molecule
formation in the mentioned interaction regime. The absolute error of the
constructed approximation is less than 3*10^-6 for the final transition
probability while at certain time points it might increase up to 10^-3.
Examining the role of the different terms in the constructed approximation, we
prove that in the fast sweep rate regime of the strong interaction limit the
temporal dynamics of the atom-molecule conversion effectively consists of the
process of resonance crossing, which is governed by a nonlinear equation,
followed by atom-molecular coherent oscillations which are basically described
by a solution of the linear problem, associated with the considered nonlinear
one.Comment: Accepted for publication in J. Contemp. Phys. (Armenian National
Academy of Sciences) 8 pages, 4 figure
- …