1,067 research outputs found
Experimental realization of a Dirac monopole through the decay of an isolated monopole
We experimentally observe the decay dynamics of deterministically created
isolated monopoles in spin-1 Bose-Einstein condensates. As the condensate
undergoes a change between magnetic phases, the isolated monopole gradually
evolves into a spin configuration hosting a Dirac monopole in its synthetic
magnetic field. We characterize in detail the Dirac monopole by measuring the
particle densities of the spin states projected along different quantization
axes. Importantly, we observe the spontaneous emergence of nodal lines in the
condensate density that accompany the Dirac monopole. We also demonstrate that
the monopole decay accelerates in weaker magnetic field gradients.Comment: 10 pages, 7 figure
A Regularized Newton Method for Computing Ground States of Bose-Einstein condensates
In this paper, we propose a regularized Newton method for computing ground
states of Bose-Einstein condensates (BECs), which can be formulated as an
energy minimization problem with a spherical constraint. The energy functional
and constraint are discretized by either the finite difference, or sine or
Fourier pseudospectral discretization schemes and thus the original infinite
dimensional nonconvex minimization problem is approximated by a finite
dimensional constrained nonconvex minimization problem. Then an initial
solution is first constructed by using a feasible gradient type method, which
is an explicit scheme and maintains the spherical constraint automatically. To
accelerate the convergence of the gradient type method, we approximate the
energy functional by its second-order Taylor expansion with a regularized term
at each Newton iteration and adopt a cascadic multigrid technique for selecting
initial data. It leads to a standard trust-region subproblem and we solve it
again by the feasible gradient type method. The convergence of the regularized
Newton method is established by adjusting the regularization parameter as the
standard trust-region strategy. Extensive numerical experiments on challenging
examples, including a BEC in three dimensions with an optical lattice potential
and rotating BECs in two dimensions with rapid rotation and strongly repulsive
interaction, show that our method is efficient, accurate and robust.Comment: 25 pages, 6 figure
Computing Ground States of Spin-1 Bose-Einstein Condensates by the Normalized Gradient Flow
In this paper, we propose an efficient and accurate numerical method for
computing the ground state of spin-1 Bose-Einstein condensates (BEC) by using
the normalized gradient flow or imaginary time method. The key idea is to find
a third projection or normalization condition based on the relation between the
chemical potentials so that the three projection parameters used in the
projection step of the normalized gradient flow are uniquely determined by this
condition as well as the other two physical conditions given by the
conservation of total mass and total magnetization. This allows us to
successfully extend the most popular and powerful normalized gradient flow or
imaginary time method for computing the ground state of single component BEC to
compute the ground state of spin-1 BEC. An efficient and accurate
discretization scheme, the backward-forward Euler sine-pseudospectral method
(BFSP), is proposed to discretize the normalized gradient flow. Extensive
numerical results on ground states of spin-1 BEC with
ferromagnetic/antiferromagnetic interaction and harmonic/optical lattice
potential in one/three dimensions are reported to demonstrate the efficiency of
our new numerical method.Comment: 25 pages, 12 figure
Inert-states of spin-5 and spin-6 Bose-Einstein condensates
In this paper we consider spinor Bose-Einstein condensates with spin f=5 and
f=6 in the presence and absence of external magnetic field at the mean field
level. We calculate all of so-called inert-states of these systems.
Inert-states are very unique class of stationary states because they remain
stationary while Hamiltonian parameters change. Their existence comes from
Michel's theorem. For illustration of symmetry properties of the inert-states
we use method that allows classification of the systems as a polyhedron with 2f
vertices proposed by R. Barnett et al., Phys. Rev. Lett. 97, 180412 (2006).Comment: 19 pages, 4 figure
Newton-based alternating methods for the ground state of a class of multi-component Bose-Einstein condensates
The computation of the ground states of special multi-component Bose-Einstein
condensates (BECs) can be formulated as an energy functional minimization
problem with spherical constraints. It leads to a nonconvex quartic-quadratic
optimization problem after suitable discretizations. First, we generalize the
Newton-based methods for single-component BECs to the alternating minimization
scheme for multi-component BECs. Second, the global convergent alternating
Newton-Noda iteration (ANNI) is proposed. In particular, we prove the
positivity preserving property of ANNI under mild conditions. Finally, our
analysis is applied to a class of more general "multi-block" optimization
problems with spherical constraints. Numerical experiments are performed to
evaluate the performance of proposed methods for different multi-component
BECs, including pseudo spin-1/2, anti-ferromagnetic spin-1 and spin-2 BECs.
These results support our theory and demonstrate the efficiency of our
algorithms
Effective field theory for spinor dipolar Bose Einstein condensates
We show that the effective theory of long wavelength low energy behavior of a
dipolar Bose-Einstein condensate(BEC) with large dipole moments (treated as a
classical spin) can be modeled using an extended Non-linear sigma model (NLSM)
like energy functional with an additional non-local term that represents long
ranged anisotropic dipole-dipole interaction. Minimizing this effective energy
functional we calculate the density and spin-profile of the dipolar
Bose-Einstein condensate in the mean-field regime for various trapping
geometries. The resulting configurations show strong intertwining between the
spin and mass density of the condensate, transfer between spin and orbital
angular momentum in the form of Einstein-de Hass effect, and novel topological
properties. We have also described the theoretical framework in which the
collective excitations around these mean field solutions can be studied and
discuss some examples qualitatively.Comment: Latex + 3 eps figures, accepted for publication in a special issue of
EPJB on "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases
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