560 research outputs found
Efficient description of Bose-Einstein condensates in time-dependent rotating traps
Quantum sensors based on matter-wave interferometry are promising candidates
for high-precision gravimetry and inertial sensing in space. The favorable
source for the coherent matter waves in these devices are Bose-Einstein
condensates. A reliable prediction of their dynamics, which is governed by the
Gross-Pitaevskii equation, requires suitable analytical and numerical methods
which take into account the center-of-mass motion of the condensate, its
rotation and its spatial expansion by many orders of magnitude. In this
chapter, we present an efficient way to study their dynamics in time-dependent
rotating traps that meet this objective. Both, an approximate analytical
solution for condensates in the Thomas-Fermi regime and dedicated numerical
simulations on a variable adapted grid are discussed. We contrast and relate
our approach to previous alternative methods and provide further results, such
as analytical expressions for the one- and two-dimensional spatial density
distributions and the momentum distribution in the long-time limit that are of
immediate interest to experimentalists working in this field of research.Comment: 49 pages, 7 figures, preprint submitted to Advances in Atomic,
Molecular, and Optical Physics Volume 6
Accurate and efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates via the nonuniform FFT
In this paper, we propose efficient and accurate numerical methods for
computing the ground state and dynamics of the dipolar Bose-Einstein
condensates utilising a newly developed dipole-dipole interaction (DDI) solver
that is implemented with the non-uniform fast Fourier transform (NUFFT)
algorithm. We begin with the three-dimensional (3D) Gross-Pitaevskii equation
(GPE) with a DDI term and present the corresponding two-dimensional (2D) model
under a strongly anisotropic confining potential. Different from existing
methods, the NUFFT based DDI solver removes the singularity by adopting the
spherical/polar coordinates in Fourier space in 3D/2D, respectively, thus it
can achieve spectral accuracy in space and simultaneously maintain high
efficiency by making full use of FFT and NUFFT whenever it is necessary and/or
needed. Then, we incorporate this solver into existing successful methods for
computing the ground state and dynamics of GPE with a DDI for dipolar BEC.
Extensive numerical comparisons with existing methods are carried out for
computing the DDI, ground states and dynamics of the dipolar BEC. Numerical
results show that our new methods outperform existing methods in terms of both
accuracy and efficiency.Comment: 26 pages, 5 figure
An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates
In this paper, we propose an efficient and spectrally accurate numerical
method for computing the dynamics of rotating Bose-Einstein condensates (BEC)
in two dimensions (2D) and 3D based on the Gross-Pitaevskii equation (GPE) with
an angular momentum rotation term. By applying a time-splitting technique for
decoupling the nonlinearity and properly using the alternating direction
implicit (ADI) technique for the coupling in the angular momentum rotation term
in the GPE, at every time step, the GPE in rotational frame is decoupled into a
nonlinear ordinary differential equation (ODE) and two partial differential
equations with constant coefficients. This allows us to develop new
time-splitting spectral (TSSP) methods for computing the dynamics of BEC in a
rotational frame.The new numerical method is explicit, unconditionally stable,
and of spectral accuracy in space and second order accuracy in time. Moreover,
it is time reversible and time transverse invariant, and conserves the position
density in the discretized level if the GPE does. Extensive numerical results
are presented to confirm the above properties of the new numerical method for
rotating BEC in 2D and 3D.Comment: 21 pages; 7 figure
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