3,663 research outputs found
Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases
We derive exact analytical results for the wave functions and energies of
harmonically trapped two-component Bose-Einstein condensates with weakly
repulsive interactions under rotation. The isospin symmetric wave functions are
universal and do not depend on the matrix elements of the two-body interaction.
The comparison with the results from numerical diagonalization shows that the
ground state and low-lying excitations consists of condensates of p-wave pairs
for repulsive contact interactions, Coulomb interactions, and the repulsive
interactions between aligned dipoles.Comment: 4 pages, 1 figure; revised version explains exact solutions in terms
of isospin symmetry and Hund's rul
Few-body precursor of the Higgs mode in a superfluid Fermi gas
We demonstrate that an undamped few-body precursor of the Higgs mode can be
investigated in a harmonically trapped Fermi gas. Using exact diagonalisation,
the lowest monopole mode frequency is shown to depend non-monotonically on the
interaction strength, having a minimum in a crossover region. The minimum
deepens with increasing particle number, reflecting that the mode is the
few-body analogue of a many-body Higgs mode in the superfluid phase, which has
a vanishing frequency at the quantum phase transition point to the normal
phase. We show that this mode mainly consists of coherent excitations of
time-reversed pairs, and that it can be selectively excited by modulating the
interaction strength, using for instance a Feshbach resonance in cold atomic
gases.Comment: 9 pages, 7 figure
Exact diagonalization results for an anharmonically trapped Bose-Einstein condensate
We consider bosonic atoms that rotate in an anharmonic trapping potential.
Using numerical diagonalization of the Hamiltonian, we identify the various
phases of the gas as the rotational frequency of the trap and the coupling
between the atoms are varied.Comment: 7 pages, RevTex, 10 figure
Comment on ``Fragmented Condensate Ground State of Trapped Weakly Interacting Bosons in Two Dimensions"
Recently Liu et al. [PRL 87, 030404 (2001)] examined the lowest state of a
weakly-interacting Bose-Einstein condensate. In addition to other interesting
results, using the method of the pair correlation function, they questioned the
validity of the mean-field picture of the formation of vortices and stated that
the vortices are generated at the center of the cloud. This is in apparent
contradiction to the Gross-Pitaevskii approach, which predicts that the
vortices successively enter the cloud from its outer parts as L/N (where N is
the number of atoms in the trap and hbar(L) is the angular momentum of the
system) increases. We have managed to reproduce the results of Liu et al.
however a more careful analysis presented below confirms the validity of the
mean-field approach.Comment: 1 page, RevTex, 2 figure
Slice Stretching Effects for Maximal Slicing of a Schwarzschild Black Hole
Slice stretching effects such as slice sucking and slice wrapping arise when
foliating the extended Schwarzschild spacetime with maximal slices. For
arbitrary spatial coordinates these effects can be quantified in the context of
boundary conditions where the lapse arises as a linear combination of odd and
even lapse. Favorable boundary conditions are then derived which make the
overall slice stretching occur late in numerical simulations. Allowing the
lapse to become negative, this requirement leads to lapse functions which
approach at late times the odd lapse corresponding to the static Schwarzschild
metric. Demanding in addition that a numerically favorable lapse remains
non-negative, as result the average of odd and even lapse is obtained. At late
times the lapse with zero gradient at the puncture arising for the puncture
evolution is precisely of this form. Finally, analytic arguments are given on
how slice stretching effects can be avoided. Here the excision technique and
the working mechanism of the shift function are studied in detail.Comment: 16 pages, 4 figures, revised version including a study on how slice
stretching can be avoided by using excision and/or shift
Tunable Wigner States with Dipolar Atoms and Molecules
We study the few-body physics of trapped atoms or molecules with electric or
magnetic dipole moments aligned by an external field. Using exact numerical
diagonalization appropriate for the strongly correlated regime, as well as a
classical analysis, we show how Wigner localization emerges with increasing
coupling strength. The Wigner states exhibit non-trivial geometries due to the
anisotropy of the interaction. This leads to transitions between different
Wigner states as the tilt angle of the dipoles with the confining plane is
changed. Intriguingly, while the individual Wigner states are well described by
a classical analysis, the transitions between different Wigner states are
strongly affected by quantum statistics. This can be understood by considering
the interplay between quantum-mechanical and spatial symmetry properties.
Finally, we demonstrate that our results are relevant to experimentally
realistic systems.Comment: 4 pages, 6 figure
Metastability of persistent currents in trapped gases of atoms
We examine the conditions that give rise to metastable, persistent currents
in a trapped Bose-Einstein condensate. A necessary condition for the stability
of persistent currents is that the trapping potential is not a monotonically
increasing function of the distance from the trap center. Persistent currents
also require that the interatomic interactions are sufficiently strong and
repulsive. Finally, any off-center vortex state is shown to be unstable, while
a driven gas shows hysteresis.Comment: 7 pages, RevTex, 5 figure
Mixtures of Bose gases under rotation
We examine the rotational properties of a mixture of two Bose gases.
Considering the limit of weak interactions between the atoms, we investigate
the behavior of the system under a fixed angular momentum. We demonstrate a
number of exact results in this many-body system.Comment: 4 pages, RevTex, 6 figure
Persistent currents in Bose gases confined in annular traps
We examine the problem of stability of persistent currents in a mixture of
two Bose gases trapped in an annular potential. We evaluate the critical
coupling for metastability in the transition from quasi-one to two-dimensional
motion. We also evaluate the critical coupling for metastability in a mixture
of two species as function of the population imbalance. The stability of the
currents is shown to be sensitive to the deviation from one-dimensional motion.Comment: 6 pages, 4 figure
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