88 research outputs found
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
On the stability of 2D dipolar Bose-Einstein condensates
We study the existence of energy minimizers for a Bose-Einstein condensate
with dipole-dipole interactions, tightly confined to a plane. The problem is
critical in that the kinetic energy and the (partially attractive) interaction
energy behave the same under mass-preserving scalings of the wave-function. We
obtain a sharp criterion for the existence of ground states, involving the
optimal constant of a certain generalized Gagliardo-Nirenberg inequality
Existence of minimizers in generalized Gross-Pitaevskii theory with the Lee-Huang-Yang correction
We study the dipolar Gross-Piteavskii functional with the Lee-Huang-Yang (LHY) correction term without trapping potential and in the regime where the dipole-dipole interaction dominates the repulsive short-range interaction. We show that, above a critical mass, the functional admits minimizers and we prove their regularity and exponential decay. We also estimate the critical mass in terms of the parameters of the system
Collective excitation frequencies and stationary states of trapped dipolar Bose-Einstein condensates in the Thomas-Fermi regime
We present a general method for obtaining the exact static solutions and
collective excitation frequencies of a trapped Bose-Einstein condensate (BEC)
with dipolar atomic interactions in the Thomas-Fermi regime. The method
incorporates analytic expressions for the dipolar potential of an arbitrary
polynomial density profile, thereby reducing the problem of handling non-local
dipolar interactions to the solution of algebraic equations.
We comprehensively map out the static solutions and excitation modes,
including non-cylindrically symmetric traps, and also the case of negative
scattering length where dipolar interactions stabilize an otherwise unstable
condensate. The dynamical stability of the excitation modes gives insight into
the onset of collapse of a dipolar BEC. We find that global collapse is
consistently mediated by an anisotropic quadrupolar collective mode, although
there are two trapping regimes in which the BEC is stable against quadrupole
fluctuations even as the ratio of the dipolar to s-wave interactions becomes
infinite. Motivated by the possibility of fragmented BEC in a dipolar Bose gas
due to the partially attractive interactions, we pay special attention to the
scissors modes, which can provide a signature of superfluidity, and identify a
long-range restoring force which is peculiar to dipolar systems. As part of the
supporting material for this paper we provide the computer program used to make
the calculations, including a graphical user interface.Comment: 23 pages, 11 figure
Vortex in a trapped Bose-Einstein condensate with dipole-dipole interactions
We calculate the critical rotation frequency at which a vortex state becomes
energetically favorable over the vortex-free ground state in a harmonically
trapped Bose-Einstein condensate whose atoms have dipole-dipole interactions as
well as the usual s-wave contact interactions. In the Thomas-Fermi
(hydrodynamic) regime, dipolar condensates in oblate cylindrical traps (with
the dipoles aligned along the axis of symmetry of the trap) tend to have lower
critical rotation frequencies than their purely s-wave contact interaction
counterparts. The converse is true for dipolar condensates in prolate traps.
Quadrupole excitations and centre of mass motion are also briefly discussed as
possible competing mechanisms to a vortex as means by which superfluids with
partially attractive interactions might carry angular momentumComment: 12 pages, 12 figure
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