552 research outputs found
Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation
A two-dimensional Bose-Einstein condensate (BEC) split by a radial potential
barrier is investigated. We determine on an accurate many-body level the
system's ground-state phase diagram as well as a time-dependent phase diagram
of the splitting process. Whereas the ground state is condensed for a wide
range of parameters, the time-dependent splitting process leads to substantial
fragmentation. We demonstrate for the first time the dynamical fragmentation of
a BEC despite its ground state being condensed. The results are analyzed by a
mean-field model and suggest that a large manifold of low-lying fragmented
excited states can significantly impact the dynamics of trapped two-dimensional
BECs.Comment: 5+eps pages, 4 figure
Fragmentation and correlations in a rotating Bose-Einstein condensate undergoing breakup
The theoretical investigation of rotating Bose-Einstein condensates has
mainly focused on the emergence of quantum vortex states and the condensed
properties of such systems. In the present work, we concentrate on other facets
by examining the impact of rotation on the ground state of weakly interacting
bosons confined in anharmonic potentials computed both at the mean-field level
and particularly at the many-body level of theory. For the many-body
computations, we employ the well-established many-body method known as the
multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We
present how various degrees of fragmentation can be generated following the
breakup of the ground state densities in anharmonic traps without ramping up a
potential barrier for strong rotations. The breakup of the densities is found
to be associated with the acquisition of angular momentum in the condensate due
to the rotation. In addition to fragmentation, the presence of many-body
correlations is examined by computing the variances of the many-particle
position and momentum operators. For strong rotations, the many-body variances
become smaller than their mean-field counterparts, and one even finds a
scenario with opposite anisotropies of the mean-field and many-body variances.
Further, it is observed that for higher discrete symmetric systems of order k,
namely three-fold and four-fold symmetry, breakup to k sub-clouds and emergence
of k-fold fragmentation take place. All in all, we provide a thorough many-body
investigation of how and which correlations build up when a trapped
Bose-Einstein condensate breaks up under rotation
Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances
We study the quench dynamics of a two-component ultracold Fermi gas from the
weak into the strong interaction regime, where the short time dynamics are
governed by the exponential growth rate of unstable collective modes. We obtain
an effective interaction that takes into account both Pauli blocking and the
energy dependence of the scattering amplitude near a Feshbach resonance. Using
this interaction we analyze the competing instabilities towards Stoner
ferromagnetism and pairing.Comment: 4+epsilon pages, 4 figure
Wave chaos as signature for depletion of a Bose-Einstein condensate
We study the expansion of repulsively interacting Bose-Einstein condensates
(BECs) in shallow one-dimensional potentials. We show for these systems that
the onset of wave chaos in the Gross-Pitaevskii equation (GPE), i.e. the onset
of exponential separation in Hilbert space of two nearby condensate wave
functions, can be used as indication for the onset of depletion of the BEC and
the occupation of excited modes within a many-body description. Comparison
between the multiconfigurational time-dependent Hartree for bosons (MCTDHB)
method and the GPE reveals a close correspondence between the many-body effect
of depletion and the mean-field effect of wave chaos for a wide range of
single-particle external potentials. In the regime of wave chaos the GPE fails
to account for the fine-scale quantum fluctuations because many-body effects
beyond the validity of the GPE are non-negligible. Surprisingly, despite the
failure of the GPE to account for the depletion, coarse grained expectation
values of the single-particle density such as the overall width of the atomic
cloud agree very well with the many-body simulations. The time dependent
depletion of the condensate could be investigated experimentally, e.g., via
decay of coherence of the expanding atom cloud.Comment: 12 pages, 10 figure
Optimal Monte Carlo Updating
Based on Peskun's theorem it is shown that optimal transition matrices in
Markov chain Monte Carlo should have zero diagonal elements except for the
diagonal element corresponding to the largest weight. We will compare the
statistical efficiency of this sampler to existing algorithms, such as
heat-bath updating and the Metropolis algorithm. We provide numerical results
for the Potts model as an application in classical physics. As an application
in quantum physics we consider the spin 3/2 XY model and the Bose-Hubbard model
which have been simulated by the directed loop algorithm in the stochastic
series expansion framework.Comment: 6 pages, 5 figures, replaced with published versio
How does an interacting many-body system tunnel through a potential barrier to open space?
The tunneling process in a many-body system is a phenomenon which lies at the
very heart of quantum mechanics. It appears in nature in the form of
alpha-decay, fusion and fission in nuclear physics, photoassociation and
photodissociation in biology and chemistry. A detailed theoretical description
of the decay process in these systems is a very cumbersome problem, either
because of very complicated or even unknown interparticle interactions or due
to a large number of constitutent particles. In this work, we theoretically
study the phenomenon of quantum many-body tunneling in a more transparent and
controllable physical system, in an ultracold atomic gas. We analyze a full,
numerically exact many-body solution of the Schr\"odinger equation of a
one-dimensional system with repulsive interactions tunneling to open space. We
show how the emitted particles dissociate or fragment from the trapped and
coherent source of bosons: the overall many-particle decay process is a quantum
interference of single-particle tunneling processes emerging from sources with
different particle numbers taking place simultaneously. The close relation to
atom lasers and ionization processes allows us to unveil the great relevance of
many-body correlations between the emitted and trapped fractions of the
wavefunction in the respective processes.Comment: 18 pages, 4 figures (7 pages, 2 figures supplementary information
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