121 research outputs found
Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions
The occupation of more than one single-particle state and hence the emergence
of fragmentation is a many-body phenomenon universal to systems of spatially
confined interacting bosons. In the present study, we investigate the effect of
the range of the interparticle interactions on the fragmentation degree of one-
and two-dimensional systems. We solve the full many-body Schr\"odinger equation
of the system using the recursive implementation of the multiconfigurational
time-dependent Hartree for bosons method, R-MCTDHB. The dependence of the
degree of fragmentation on dimensionality, particle number, areal or line
density and interaction strength is assessed. It is found that for contact
interactions, the fragmentation is essentially density independent in two
dimensions. However, fragmentation increasingly depends on density the more
long-ranged the interactions become. The degree of fragmentation is increasing,
keeping the particle number fixed, when the density is decreasing as
expected in one spatial dimension. We demonstrate that this remains,
nontrivially, true also for long-range interactions in two spatial dimensions.
We, finally, find that within our fully self-consistent approach, the
fragmentation degree, to a good approximation, decreases universally as
when only is varied.Comment: 8 pages of RevTex4-1, 5 figure
Phases, many-body entropy measures and coherence of interacting bosons in optical lattices
Already a few bosons with contact interparticle interactions in small optical
lattices feature a variety of quantum phases: superfluid, Mott-insulator and
fermionized Tonks gases can be probed in such systems. To detect these phases
-- pivotal for both experiment and theory -- as well as their many-body
properties we analyze several distinct measures for the one-body and many-body
Shannon information entropies. We exemplify the connection of these entropies
with spatial correlations in the many-body state by contrasting them to the
Glauber normalized correlation functions. To obtain the ground-state for
lattices with commensurate filling (i.e. an integer number of particles per
site) for the full range of repulsive interparticle interactions we utilize the
multiconfigurational time-dependent Hartree method for bosons (MCTDHB) in order
to solve the many-boson Schr\"odinger equation. We demonstrate that all
emergent phases -- the superfluid, the Mott insulator, and the fermionized gas
can be characterized equivalently by our many-body entropy measures and by
Glauber's normalized correlation functions. In contrast to our many-body
entropy measures, single-particle entropy cannot capture these transitions.Comment: 11 pages, 7 figures, software available at http://ultracold.or
Decay modes of two repulsively interacting bosons
We study the decay of two repulsively interacting bosons tunneling through a
delta potential barrier by direct numerical solution of the time-dependent
Schr\"odinger equation. The solutions are analyzed according to the regions of
particle presence: both particles inside the trap (in-in), one particle in and
one particle out (in-out), and both particles outside (out-out). It is shown
that the in-in probability is dominated by exponential decay, and its decay
rate is predicted very well from outgoing boundary conditions.
Up to a certain range of interaction strength the decay of in-out probability
is dominated by the single particle decay mode.
The decay mechanisms are adequately described by simple models.Comment: 18 pages, 13 figure
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
Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well
We examine the spectral structure and many-body dynamics of two and three
repulsively interacting bosons trapped in a one-dimensional double-well, for
variable barrier height, inter-particle interaction strength, and initial
conditions. By exact diagonalization of the many-particle Hamiltonian, we
specifically explore the dynamical behaviour of the particles launched either
at the single particle ground state or saddle point energy, in a
time-independent potential. We complement these results by a characterisation
of the cross-over from diabatic to quasi-adiabatic evolution under finite-time
switching of the potential barrier, via the associated time-evolution of a
single particle's von Neumann entropy. This is achieved with the help of the
multiconfigurational time-dependent Hartree method for indistinguishable
particles (\textsc{Mctdh-x}) -- which also allows us to extrapolate our results
for increasing particle numbers.Comment: 20 pages, 14 figure
Orbital Josephson effect and interactions in driven atom condensates on a ring
In a system of ac-driven condensed bosons we study a new type of Josephson
effect occurring between states sharing the same region of space and the same
internal atom structure. We first develop a technique to calculate the long
time dynamics of a driven interacting many-body system. For resonant
frequencies, this dynamics can be shown to derive from an effective
time-independent Hamiltonian which is expressed in terms of standard creation
and annihilation operators. Within the subspace of resonant states, and if the
undriven states are plane waves, a locally repulsive interaction between bosons
translates into an effective attraction. We apply the method to study the
effect of interactions on the coherent ratchet current of an asymmetrically
driven boson system. We find a wealth of dynamical regimes which includes Rabi
oscillations, self-trapping, and chaotic behavior. In the latter case, a full
many-body calculation deviates from the mean-field results by predicting large
quantum fluctuations of the relative particle number.Comment: Published versio
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