Kaspar Sakmann- Dr. rer. nat.
- Researcher at Bosch Center for Artificial Intelligence
Kaspar Sakmann
- Dr. rer. nat.
- Researcher at Bosch Center for Artificial Intelligence
About
45
Publications
3,278
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1,298
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Introduction
I work at the Bosch Center for Artificial Intelligence as a deep learning researcher. I am interested in understanding and explaining the power of deep networks, particularly for generative modelling. My background is in theoretical and computational physics.
Current institution
Bosch Center for Artificial Intelligence
Current position
- Researcher
Additional affiliations
October 2012 - January 2015
Position
- PostDoc Position
Description
- Development of a 3d imaging system for ultracold gases experiments
Publications
Publications (45)
Bose-Einstein condensates (BECs) offer a fruitful, often uncharted ground for exploring physics of many-particle systems. In the present year of the MCTDHB project at the HLRS, we maintained and extended our investigations of BECs and interacting bosonic systems using the MultiConfigurational Time-Dependent Hartree for Bosons (MCTDHB) method and ru...
The many-body physics of trapped Bose-Einstein condensates (BECs) is very rich and demanding. During the past year of the MCTDHB project at the HLRS we continued to shed further light on it with the help of the MultiConfigurational Time-Dependent Hartree for Bosons (MCTDHB) method and using the MCTDHB and MCTDH-X software packages. Indeed, our resu...
Conservation of angular momentum is a fundamental symmetry in rotationally invariant quantum many-body systems. We show analytically that Gross-Pitaevskii mean-field dynamics violates this symmetry, provide its parametric dependence and quantify the degree of the violation numerically. The results are explained based on the time-dependent variation...
In their correspondence [arXiv:1610.07633] Drummond and Brand criticize our work [Nature Physics 15, 451 (2006)]. We show that their criticism is misleading and unfounded.
Here we report on further applications, developments, expansion, and proliferation of the Multi-Configurational Time-Dependent Hartree for Bosons (MCTDHB) method in the context of ultra-cold atomic systems. In this year we put our main efforts to understanding and generalizing vortices—two-dimensional (2D) and three-dimensional (3D) quantum objects...
During the past year of the MCTDHB project at the HLRS, we continued to strive and conquest further applications, developments, and expansion of the MultiConfigurational Time-Dependent Hartree for Bosons (MCTDHB) method in the context of ultracold atomic systems. We also announce the MCTDH-X package, the Multiconfigurational Time-Dependent Hartree...
The MCTDHB package has been applied to study the physics of trapped interacting many-boson systems by solving the underlying time-dependent (as well as the time-independent) many-boson Schrödinger equation. Here we report on four studies where novel physical ideas and phenomena have been proposed and discovered: (a) Universality of the fragmentatio...
The single-particle density is the most basic quantity that can be calculated
from a given many-body wave function. It provides the probability to find a
particle at a given position when the average over many realizations of an
experiment is taken. However, the outcome of single experimental shots of
ultracold atom experiments is determined by the...
Light field microscopy methods together with three-dimensional (3D) deconvolution can be used to obtain single-shot 3D images of atomic clouds. We demonstrate the method using a test setup that extracts 3D images from a fluorescent atomic vapor.
The quantum many-body dynamics of indistinguishable, interacting particles are described by the time-dependent many-body Schrödinger equation (TDSE). The TDSE constitutes a difficult problem and is not solvable analytically in most cases. The present review article expedites and benchmarks the capabilities of a novel theoretical method, the multico...
We derive a general linear-response many-body theory capable of computing
excitation spectra of trapped interacting bosonic systems, e.g., depleted and
fragmented Bose-Einstein condensates (BECs). To obtain the linear-response
equations we linearize the multiconfigurational time-dependent Hartree for
bosons (MCTDHB) method, which provides a self-co...
We review the multiconfigurational time-dependent Hartree method for bosons, which is a formally exact many-body theory for the propagation of the time dependent Schrödinger equation of N interacting identical bosons. In this approach, the time-dependent many-boson wavefunction is written as a sum of all permanents assembled from M orthogonal orbit...
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 α-decay, fusion and fission in nuclear physics, and photoassociation and photodissociation in biology and chemistry. A detailed theoretical description of the decay process in these systems is a very cum...
The exactly solvable quantum many-particle model with harmonic one- and
two-particle interaction terms is extended to include time-dependency. We show
that when the external trap potential and finite-range interparticle
interaction have a time-dependency the exact solutions of the corresponding
time-dependent many-boson Schr\"odinger equation are s...
The many-body Schr\"odinger dynamics of a one-dimensional bosonic Josephson
junction is investigated for up to ten thousand bosons and long times. The
initial states are fully condensed and the interaction strength is weak. We
report on a universal fragmentation dynamics on the many-body level: systems
consisting of different numbers of particles f...
![Figure 3: (Color online) Density [ ρ ( r, t )] in the relative...](profile/Andreas-Deuchert/publication/221665151/figure/fig1/AS:305463699755015@1449839629294/Color-online-Density-r-r-t-in-the-relative-coordinate-as-a-function-of-time-t_Q320.jpg)
We investigate the dynamics of two bosons trapped in an infinite
one-dimensional optical lattice potential within the framework of the
Bose-Hubbard model and derive an exact expression for the wavefunction at
finite time. As initial condition we chose localized atoms that are separated
by a distance of $d$ lattice sites and carry a center of mass q...
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 cum...
The multiconfigurational time-dependent Hartree method (MCTDH) [Chem. Phys.
Lett. {\bf 165}, 73 (1990); J. Chem. Phys. {\bf 97}, 3199 (1992)] is
celebrating nowadays entering its third decade of tackling numerically-exactly
a broad range of correlated multi-dimensional non-equilibrium quantum dynamical
systems. Taking in recent years particles' sta...
In this chapter, we discuss models that are popular in the description of ultracold bosons in (quasi-) periodic potentials, namely the Bose–Hubbard model and the discrete nonlinear Schrödinger equation. These two methods have in common that both employ Wannier functions as a single-particle basis. For our purposes it will be sufficient to restrict...
The quantum dynamics of one-dimensional bosonic Josephson junctions with attractive and repulsive interparticle interactions is studied using the Bose–Hubbard model and by numerically-exact computations of the full many-body Hamiltonian. A symmetry present in the Bose–Hubbard Hamiltonian dictates an equivalence between the evolution in time of attr...
A method to extend and optimize lattice models is presented. While conventional lattice models, such as the Bose–Hubbard model, use Wannier functions that are time-independent, we allow the Wannier functions of lattice models to depend on time. By deriving equations of motion for these new lattice models from the variational principle we show that...
We now turn to the description of the numerical methods used in this work. In Sect. 3.1 we give a self-contained explanation of the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. The MCTDHB method can be considered as the systematic many-body generalization of Gross–Pitaevskii theory. In Sect. 3.2 it is shown how the celebr...
In this thesis, trapped Bose-Einstein condensates were investigated based on the interacting many-body Schrödinger equation. Studies of this kind are (still) rare due to their computational complexity. Here, numerically exact results were obtained for the dynamics of up to one hundred identical bosons.
In this chapter we review the most important concepts of the theory of ultracold bosons. We begin with the many-body Hamiltonian, its different representations and show how the Schrödinger equation can be obtained from to the time-dependent variational principle. The representation of a many-body wave function in a finite basis set and its implicat...
We investigate the number fluctuations of spatially split many-boson systems
employing a theorem about the maximally and minimally attainable variances of
an observable. The number fluctuations of many-boson systems are given for
different numbers of lattice sites and both mean-field and many-body wave
functions. It is shown which states maximize t...
Lattice models are abundant in theoretical and condensed-matter physics.
Generally, lattice models contain time-independent hopping and interaction
parameters that are derived from the Wannier functions of the noninteracting
problem. Here, we present a new concept based on time-dependent Wannier
functions and the variational principle that leads to...
General Theory.- General Methods for the Quantum Dynamics of Identical Bosons.- Lattice Models for the Quantum Dynamics of Identical Bosons.- Reduced Density Matrices and Coherence of Trapped Interacting Bosons.- Exact Quantum Dynamics of a Bosonic Josephson Junction.- Quantum Dynamics of Attractive vs. Repulsive Bosonic Josephson Junctions: Bose-H...
In this thesis, the physics of trapped, interacting Bose-Einstein condensates is analyzed by solving the many-body Schrödinger equation. Particular emphasis is put on coherence, fragmentation and reduced density matrices. First, the ground state of a trapped Bose-Einstein condensate and its correlation functions are obtained. Then the dynamics of a...
The quantum dynamics of one-dimensional bosonic Josephson junctions with attractive and repulsive interparticle interactions is studied using the Bose-Hubbard model and by numerically-exact computations of the full many-body Hamiltonian. A symmetry present in the Bose-Hubbard Hamiltonian dictates an equivalence between the evolution in time of attr...
The quantum dynamics of a one-dimensional bosonic Josephson junction is studied by solving the time-dependent many-boson Schrödinger equation numerically exactly. Already for weak interparticle interactions and on short time scales, the commonly employed mean-field and many-body methods are found to deviate substantially from the exact dynamics. Th...
To solve the many-boson Schr\"odinger equation we utilize the Multiconfigurational time-dependent Hartree method for bosons (MCTDHB). To be able to attack larger systems and/or to propagate the solution for longer times, we implement a parallel version of the MCTDHB method thereby realizing the recently proposed [Streltsov {\it et al.} arXiv:0910.2...
To solve the many-boson Schr\"odinger equation we utilize the
Multiconfigurational time-dependent Hartree method for bosons (MCTDHB). To be
able to attack larger systems and/or to propagate the solution for longer
times, we implement a parallel version of the MCTDHB method thereby realizing
the recently proposed [Streltsov {\it et al.} arXiv:0910.2...
The quantum dynamics of a one-dimensional bosonic Josephson junction is studied by solving the time-dependent many-boson Schr\"odinger equation numerically exactly. Already for weak interparticle interactions and on short time scales, the commonly-employed mean-field and many-body methods are found to deviate substantially from the exact dynamics....
The first- and second-order correlation functions of trapped, interacting Bose-Einstein condensates are investigated numerically on a many-body level from first principles. Correlations in real space and momentum space are treated. The coherence properties are analyzed. The results are obtained by solving the many-body Schr\"odinger equation. It is...
We present an analytical method of calculating the mean first-passage times (MFPTs) for the magnetic moment of a uniaxial nanoparticle which is driven by a rapidly rotating, circularly polarized magnetic field and interacts with a heat bath. The method is based on the solution of the equation for the MFPT derived from the two-dimensional backward F...
A continuous configuration-interaction approach for condensates
in a ring is introduced. In its simplest form this approach
utilizes for attractive condensates the Gross-Pitaevskii
symmetry-broken solution and arrives at a ground state of correct
symmetry. Furthermore, the energy found is lower than the
Gross-Pitaevskii one and, with increasing num...
The two-dimensional backward Fokker-Planck equation is used to calculate the mean first-passage times (MFPTs) of the magnetic moment of a nanoparticle driven by a rotating magnetic field. It is shown that a magnetic field that is rapidly rotating in the plane {\it perpendicular} to the easy axis of the nanoparticle governs the MFPTs just in the sam...
The exact ground state of the many-body Schr\"odinger equation for $N$ bosons on a one-dimensional ring interacting via pairwise $\delta$-function interaction is presented for up to fifty particles. The solutions are obtained by solving Lieb and Liniger's system of coupled transcendental equations for finite $N$. The ground state energies for repul...
The quantum dynamics of a one-dimensional bosonic Josephson junction is studied by solving the time-dependent many-boson Schrödinger
equation numerically exactly. Already for weak interparticle interactions and on short time scales, the commonly-employed
mean-field and many-body methods are found to deviate substantially from the exact dynamics.
Questions
Questions (2)
There is now an open source package for the many-body dynamics of Bose-Einstein condensates. The package allows to go systematically beyond the Gross-Pitaevskii mean-field and thereby to check its validity. This is particularly interesting for trapped BECs where the geometry of the trap can lead to strongly correlated systems already at weak interactions.
Regards,
Kaspar
I would like to share some recent general results on quantum lattice models that I think are interesting to the condensed matter community.
In short, it is possible to optimize any lattice model of condensed matter physics that uses Wannier functions ab initio. The trick is to let the principle of least action determine the shape of the Wannier functions. We did that for the Bose-Hubbard model as an example. The parameters U and J are therefore determined variationally.
A short explanation of the concept and the article can be found here:
Please let me know if anyone is interested.
