564 research outputs found
Zero temperature correlations in trapped Bose-Einstein condensates
We introduce a family of correlated trial wave functions for the -particle
ground state of an interacting Bose gas in a harmonic trap. For large , the
correlations lead to a relative energy decrease of a fraction , compared
to mean field Gross-Pitaevskii theory. The kinetic energy in the weakly
confining direction turns out to be most sensitive to our correlations and,
remarkably, is higher by as much as a few per cent for condensates with atom
numbers of a few thousand. Thus, the predicted deviations from Gross-Pitaevskii
theory originating from ground state correlations might be observed in momentum
distribution measurements of small condensates.Comment: 10 pages, 3 figure
Non-Markovian quantum trajectories, instruments and time-continuous measurements
The linear and the nonlinear non-Markovian quantum state diffusion equation
(NMQSD) are well known tools for the description of certain non-Markovian open
quantum systems. In this work, we systematically investigate whether the
normalized linear NMQSD or the nonlinear NMQSD solutions can be generated by
means of a time-continuous measurement. By considering any conceivable
measurement scheme in the framework of instruments, we derive a necessary
criterion for a measurement interpretation of both equations. Concrete examples
show that the normalized linear NMQSD solutions are realizable only in the
Markovian limit in general. The application of the presented criterion to the
nonlinear NMQSD remains an open issue.Comment: 19 page
Exact open quantum system dynamics using the Hierarchy of Pure States (HOPS)
We show that the general and numerically exact Hierarchy of Pure States
method (HOPS) is very well applicable to calculate the reduced dynamics of an
open quantum system. In particular we focus on environments with a sub-Ohmic
spectral density (SD) resulting in an algebraic decay of the bath correlation
function (BCF). The universal applicability of HOPS, reaching from weak to
strong coupling for zero and non-zero temperature, is demonstrated by solving
the spin-boson model for which we find perfect agreement with other methods,
each one suitable for a special regime of parameters. The challenges arising in
the strong coupling regime are not only reflected in the computational effort
needed for the HOPS method to converge but also in the necessity for an
importance sampling mechanism, accounted for by the non-linear variant of HOPS.
In order to include non-zero temperature effects in the strong coupling regime
we found that it is highly favorable for the HOPS method to use the zero
temperature BCF and include temperature via a stochastic Hermitian contribution
to the system Hamiltonian.Comment: This document is the unedited Author's version of a Submitted Work
that was subsequently accepted for publication in the Journal of Chemical
Theory and Computation, copyright \c{opyright} American Chemical Society
after peer review. To access the final edited and published work see
http://pubs.acs.org/doi/abs/10.1021/acs.jctc.7b0075
Analytical results for Josephson dynamics of ultracold Bosons
We study the dynamics of ultracold Bosons in a double-well potential within
the two-mode Bose-Hubbard model by means of semiclassical methods. By applying
a WKB quantization we find analytical results for the energy spectrum, which
are in excellent agreement with numerical exact results. They are valid in the
energy range of plasma oscillations, both in the Rabi and the Josephson regime.
Adopting the reflection principle and the Poisson summation formula we derive
an analytical expression for the dynamics of the population imbalance depending
on the few relevant parameters of the system only. This allows us to discuss
its characteristic dynamics, especially the oscillation frequency, and the
collapse- and revival time, as a function of the model parameters, leading to a
deeper understanding of Josephson physics. We find that our fomulae match
previous experimental observations
Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems
We present a stochastic projection formalism for the description of quantum
dynamics in Bosonic or spin environments. The Schr\"odinger equation in
coherent state representation with respect to the environmental degrees of
freedom can be reformulated by employing the Feshbach partitioning technique
for open quantum systems based on the introduction of suitable non-Hermitian
projection operators. In this picture the reduced state of the system can be
obtained as a stochastic average over pure state trajectories. The
corresponding non-Markovian stochastic Schr\"odinger equations include a memory
integral over the past states. In the case of harmonic environments and linear
coupling the approach gives a new form of the established non-Markovian quantum
state diffusion (NMQSD) stochastic Schr\"odinger equation without functional
derivatives. Utilizing spin coherent states, the evolution equation for spin
environments resembles the Bosonic case with, however, a non-Gaussian average
for the reduced density operator
Time-dependent Semiclassics for Ultracold Bosons
We study the out-of-equilibrium dynamics of ultracold bosons in a double- and
triple-well potential within the Bose-Hubbard model by means of the
semiclassical Herman-Kluk propagator and compare the results to the frequently
applied "classical dynamics" calculation in terms of the truncated Wigner
approximation (TWA). For the double-well system we find the semiclassical
results in excellent agreement with the numerically exact ones, while the TWA
is not able to reproduce any revivals of the wave function. The triple-well
system turns out to be more difficult to handle due to the irregularity of the
corresponding classical phase space. Here, deviations of the TWA from the exact
dynamics appear even for short times, while better agreement is obtained using
the semiclassical approach presented in this article
Geometry of Gaussian quantum states
We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states
in multi mode continuous variable quantum systems. An analytical expression for
the Hilbert-Schmidt volume element is derived. Its corresponding probability
measure can be used to study typical properties of Gaussian states. It turns
out that although the manifold of Gaussian states is unbounded, an ensemble of
Gaussian states distributed according to this measure still has a normalizable
distribution of symplectic eigenvalues, from which unitarily invariant
properties can be obtained. By contrast, we find that for an ensemble of
one-mode Gaussian states based on the Bures measure the corresponding
distribution cannot be normalized. As important applications, we determine the
distribution and the mean value of von Neumann entropy and purity for the
Hilbert-Schmidt measure
Detection of space-time fluctuations by a model matter interferometer
In papers on primary state diffusion (Percival 1994, 1995), numerical
estimates suggested that fluctuations in the space-time metric on the scale of
the Planck time (10^-44s) could be detected using atom interferometers. In this
paper we first specify a stochastic metric obtained from fluctuations that
propagate with the velocity of light, and then develop the non-Markovian
quantum state diffusion theory required to estimate the resulting decoherence
effects on a model matter interferometer. Both commuting and non-commuting
fluctuations are considered. The effects of the latter are so large that if
they applied to some real atom interferometry experiments they would have
suppressed the observed interference. The model is too crude to conclude that
such fluctuations do not exist, but it does demonstrate that the small
numerical value of the Planck time does not alone prevent experimental access
to Planck-scale phenomena in the laboratory.Comment: TeX, 23 pages, submitted to Proc. Roy. Soc. Lon
Revealing the nature of non-equilibrium phase transitions with quantum trajectories
A damped and driven collective spin system is analyzed by using quantum state
diffusion. This approach allows for a mostly analytical treatment of the
investigated non-equilibrium quantum many body dynamics, which features a phase
transition in the thermodynamical limit. The exact results obtained in this
work, which are free of any finite size defects, provide a complete
understanding of the model. Moreover, the trajectory framework gives an
intuitive picture of the two phases occurring, revealing a spontaneously broken
symmetry and allowing for a qualitative and quantitative characterization of
the phases. We determine exact critical exponents, investigate finite size
scaling, and explain a remarkable non-algebraic behaviour at the transition in
terms of torus hopping.Comment: 5 pages, 5 figure
Collision model approach to steering of an open driven qubit
We investigate quantum steering of an open quantum system by measurements on
its environment in the framework of collision models. As an example we consider
a coherently driven qubit dissipatively coupled to a bath. We construct local
non-adaptive and adaptive as well as nonlocal measurement scenarios specifying
explicitly the measured observable on the environment. Our approach shows
transparently how the conditional evolution of the open system depends on the
type of the measurement scenario and the measured observables. These can then
be optimized for steering. The nonlocal measurement scenario leads to maximal
violation of the used steering inequality at zero temperature. Further, we
investigate the robustness of the constructed scenarios against thermal noise.
We find generally that steering becomes harder at higher temperatures.
Surprisingly, the system can be steered even when bipartite entanglement
between the system and individual subenvironments vanishes
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