843 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
The uncertainty product of an out-of-equilibrium many-particle system
In the present work we show, analytically and numerically, that the variance
of many-particle operators and their uncertainty product for an
out-of-equilibrium Bose-Einstein condensate (BEC) can deviate from the outcome
of the time-dependent Gross-Pitaevskii dynamics, even in the limit of infinite
number of particles and at constant interaction parameter when the system
becomes 100% condensed. We demonstrate our finding on the dynamics of the
center-of-mass position--momentum uncertainty product of a freely expanding as
well as of a trapped BEC. This time-dependent many-body phenomenon is explained
by the existence of time-dependent correlations which manifest themselves in
the system's reduced two-body density matrix used to evaluate the uncertainty
product. Our work demonstrates that one has to use a many-body propagation
theory to describe an out-of-equilibrium BEC, even in the infinite particle
limit.Comment: 26 pages, 5 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
Many-body effects in the excitation spectrum of weakly-interacting Bose-Einstein condensates in one-dimensional optical lattices
In this work, we study many-body excitations of Bose-Einstein condensates
(BECs) trapped in periodic one-dimensional optical lattices. In particular, we
investigate the impact of quantum depletion onto the structure of the
low-energy spectrum and contrast the findings to the mean-field predictions of
the Bogoliubov-de Gennes (BdG) equations. Accurate results for the many-body
excited states are obtained by applying a linear-response theory atop the
MCTDHB (multiconfigurational time-dependent Hartree method for bosons)
equations of motion, termed LR-MCTDHB. We demonstrate for condensates in a
triple well that even weak ground-state depletion of around leads to
visible many-body effects in the low-energy spectrum which deviate
substantially from the corresponding BdG spectrum. We further show that these
effects also appear in larger systems with more lattice sites and particles,
indicating the general necessity of a full many-body treatment
Many-body tunneling dynamics of Bose-Einstein condensates and vortex states in two spatial dimensions
In this work, we study the out-of-equilibrium many-body tunneling dynamics of
a Bose-Einstein condensate in a two-dimensional radial double well. We
investigate the impact of interparticle repulsion and compare the influence of
angular momentum on the many-body tunneling dynamics. Accurate many-body
dynamics are obtained by solving the full many-body Schr\"odinger equation. We
demonstrate that macroscopic vortex states of definite total angular momentum
indeed tunnel and that, even in the regime of weak repulsions, a many-body
treatment is necessary to capture the correct tunneling dynamics. As a general
rule, many-body effects set in at weaker interactions when the tunneling system
carries angular momentum.Comment: 26 pages, 9 figure
First principles derivation of a Rayleigh Gans Debye model for scattering from anisotropic inhomogeneities
Scattering problems are important in describing light propagation in wide
ranging media such as the atmosphere, colloidal solutions, metamaterials, glass
ceramic composites, transparent polycrystalline ceramics, and surfaces. The
Rayleigh Gans Debye (RGD) approximation has enjoyed great success in describing
a wide range of scattering phenomena. We derive a generalized RGD formulation
from the perturbation of Maxwell equations. In contrast to most treatments of
RGD scattering, our formulation can model any soft scattering phenomena in
linear media, including scattering by stochastic process, lossy media, and by
anisotropic inhomogeneities occurring at multiple length scales. Our
first-principles derivation makes explicit underlying assumptions and provides
jumping off points for more general treatments. The derivation also facilitates
a deeper understanding of soft scattering. It is demonstrated that sources of
scattering are not interfaces as is often presumed, but excess accelerating
charges emitting uncompensated radiation. Approximations to the equations are
also presented and discussed. For example, the scattering coefficient in the
large size RGD limit is shown to be proportional to the correlation length and
the variance of a projected phase shift
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
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