3 research outputs found
Precision measurements of s-wave scattering lengths in a two-component Bose-Einstein condensate
We use collective oscillations of a two-component Bose-Einstein condensate
(2CBEC) of \Rb atoms prepared in the internal states and for the precision measurement of
the interspecies scattering length with a relative uncertainty of
. We show that in a cigar-shaped trap the three-dimensional
(3D) dynamics of a component with a small relative population can be
conveniently described by a one-dimensional (1D) Schr\"{o}dinger equation for
an effective harmonic oscillator. The frequency of the collective oscillations
is defined by the axial trap frequency and the ratio , where
is the intra-species scattering length of a highly populated component
1, and is largely decoupled from the scattering length , the total atom
number and loss terms. By fitting numerical simulations of the coupled
Gross-Pitaevskii equations to the recorded temporal evolution of the axial
width we obtain the value , where is the Bohr
radius. Our reported value is in a reasonable agreement with the theoretical
prediction but deviates significantly from the
previously measured value \cite{Mertes07} which is commonly
used in the characterisation of spin dynamics in degenerate \Rb atoms. Using
Ramsey interferometry of the 2CBEC we measure the scattering length
which also deviates from the previously reported value
\cite{Mertes07}. We characterise two-body losses for the
component 2 and obtain the loss coefficients
and
.Comment: 11 pages, 8 figure
Mean-field dynamics of two-mode Bose-Einstein condensates in highly anisotropic potentials: Interference, dimensionality, and entanglement
We study the mean-field dynamics and the reduced-dimension character of
two-mode Bose-Einstein condensates (BECs) in highly anisotropic traps. By means
of perturbative techniques, we show that the tightly confined (transverse)
degrees of freedom can be decoupled from the dynamical equations at the expense
of introducing additional effective three-body, attractive, intra- and
inter-mode interactions into the dynamics of the loosely confined
(longitudinal) degrees of freedom. These effective interactions are mediated by
changes in the transverse wave function. The perturbation theory is valid as
long as the nonlinear scattering energy is small compared to the transverse
energy scales. This approach leads to reduced-dimension mean-field equations
that optimally describe the evolution of a two-mode condensate in general
quasi-1D and quasi-2D geometries. We use this model to investigate the relative
phase and density dynamics of a two-mode, cigar-shaped Rb BEC. We study
the relative-phase dynamics in the context of a nonlinear Ramsey interferometry
scheme, which has recently been proposed as a novel platform for high-precision
interferometry. Numerical integration of the coupled, time-dependent,
three-dimensional, two-mode Gross-Pitaevskii equations for various atom numbers
shows that this model gives a considerably more refined analytical account of
the mean-field evolution than an idealized quasi-1D description.Comment: 35 pages, 10 figures. Current version is as publishe