94 research outputs found

### Variance as a sensitive probe of correlations enduring the infinite particle limit

Bose-Einstein condensates made of ultracold trapped bosonic atoms have become
a central venue in which interacting many-body quantum systems are studied. The
ground state of a trapped Bose-Einstein condensate has been proven to be 100%
condensed in the limit of infinite particle number and constant interaction
parameter [Lieb and Seiringer, Phys. Rev. Lett. {\bf 88}, 170409 (2002)]. The
meaning of this result is that properties of the condensate, noticeably its
energy and density, converge to those obtained by minimizing the
Gross-Pitaevskii energy functional. This naturally raises the question whether
correlations are of any importance in this limit. Here, we demonstrate both
analytically and numerically that even in the infinite particle limit many-body
correlations can lead to a substantial modification of the \textit{variance} of
any operator compared to that expected from the Gross-Pitaevskii result. The
strong deviation of the variance stems from its explicit dependence on terms of
the reduced two-body density matrix which otherwise do not contribute to the
energy and density in this limit. This makes the variance a sensitive probe of
many-body correlations even when the energy and density of the system have
already converged to the Gross-Pitaevskii result. We use the center-of-mass
position operator to exemplify this persistence of correlations. Implications
of this many-body effect are discussed.Comment: 20 pages, 6 figure

### Impact of the range of the interaction on the quantum dynamics of a bosonic Josephson junction

The out-of-equilibrium quantum dynamics of a bosonic Josephson junction (BJJ)
with long-range interaction is studied in real space by solving the
time-dependent many-body Schr\"odinger equation numerically accurately using
the multiconfigurational time-dependent Hartree method for bosons. Having the
many-boson wave-function at hand we can examine the impact of the range of the
interaction on the properties of the BJJ dynamics, viz. density oscillations
and their collapse, self trapping, depletion and fragmentation, as well as the
position variance, both at the mean-field and many-body level. Explicitly, the
frequency of the density oscillations and the time required for their collapse,
the value of fragmentation at the plateau, the maximal and the minimal values
of the position variance in each cycle of oscillation and the overall pace of
its growth are key to our study. We find competitive effect between the
interaction and the confining trap. The presence of the tail part of the
interaction basically enhances the effective repulsion as the range of the
interaction is increased starting from a short, finite range. But as the range
becomes comparable with the trap size, the system approaches a situation where
all the atoms feel a constant potential and the impact of the tail on the
dynamics diminishes. There is an optimal range of the interaction in which
physical quantities of the junction are attaining their extreme values.Comment: Contribution to the Special Issue of Chemical Physics dedicated to
Professor Hans-Dieter Meyer on the occasion of his 70th birthday; few typos
correcte

### Many-Body Quantum Dynamics of a Bosonic Josephson Junction with a Finite-Range Interaction

The out-of-equilibrium quantum dynamics of a Bose gas trapped in an
asymmetric double well and interacting with a finite-range interaction has been
studied in real space by solving the time-dependent many-body Schr\"odinger
equation numerically accurately using the multiconfigurational time-dependent
Hartree method for bosons (MCTDHB). We have focused on the weakly interacting
limit where the system is essentially condensed. We have examined the impact of
the range of the interaction on the dynamics of the system, both at the
mean-field and many-body levels. Explicitly, we have studied the maximal and
the minimal values of the many-body position variance in each cycle of
oscillation, and the overall pace of its growth. We find that the range of the
interaction affects the dynamics of the system differently for the right well
and the left well. We have also examined the infinite-particle limit and find
that even there, the impact of the range of the interaction can only be
described by a many-body theory such as MCTDHB

### Condensates in annuli: Dimensionality of the variance

Static and dynamic properties of Bose-Einstein condensates in annular traps
are investigated by solving the many-boson Schr\"odinger equation numerically
accurately using the multiconfigurational time-dependent Hartree for bosons
method. We concentrate on weakly-interacting bosons exhibiting low depletion.
Analysis of the mean-field position variance, which accounts for the shape of
the density only, and the many-body position variance, which incorporates a
tiny amount of excitations through the reduced two-particle density matrix,
shows that the former behaves essentially as a quasi-one-dimensional quantity
whereas the latter as a two-dimensional quantity. This brings another dimension
to the physics of bosons in ring-shaped traps.Comment: 24 pages, 8 figure

### Morphology of an interacting three-dimensional trapped Bose-Einstein condensate from many-particle variance anisotropy

The variance of the position operator is associated with how wide or narrow a
wave-packet is, the momentum variance is similarly correlated with the size of
a wave-packet in momentum space, and the angular-momentum variance quantifies
to what extent a wave-packet is non-spherically symmetric. We examine an
interacting three-dimensional trapped Bose-Einstein condensate at the limit of
an infinite number of particles, and investigate its position, momentum, and
angular-momentum anisotropies. Computing the variances of the three Cartesian
components of the position, momentum, and angular-momentum operators we present
simple scenarios where the anisotropy of a Bose-Einstein condensate is
different at the many-body and mean-field levels of theory, despite having the
same many-body and mean-field densities per particle. This suggests a way to
classify correlations via the morphology of 100\% condensed bosons in a
three-dimensional trap at the limit of an infinite number of particles.
Implications are briefly discussed.Comment: 23 pages, 3 figure

### Uncertainty product of an out-of-equilibrium Bose-Einstein condensate

The variance and uncertainty product of the position and momentum
many-particle operators of structureless bosons interacting by a long-range
inter-particle interaction and trapped in a single-well potential are
investigated. In the first example, of an out-of-equilibrium interaction-quench
scenario, it is found that, despite the system being fully condensed, already
when a fraction of a particle is depleted differences with respect to the
mean-field quantities emerge. In the second example, of the pathway from
condensation to fragmentation of the ground state, we find out that, although
the cloud's density broadens while the system's fragments, the position
variance actually decreases, the momentum variance increases, and the
uncertainty product is not a monotonous function but has a maximum. Implication
are briefly discussed.Comment: 14 pages, 3 figure

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