Axel U. J. Lode
ContactDepartment of PhysicsUniversity of Basel Klingelbergstrasse 82 CH4056 Basel, Switzerland CV as .pdf MCTDHX Homepage: ultracold.org mctdhx.org mctdh.bf schroedinger.org

Research interests:
Development and Applications of the MCTDHX package
MCTDHX is a modern implementation of the MultiConfigurational TimeDependent Hartree method for indistinguishable particles X . It is a program to solve the timedependent manybody Schrödinger equation numerically exactly for Hamiltonians with generally timedependent or timeindependent one and/or twobody potentials for bosons or fermions. A graphical user interface named Guantum facilitates the usage of the MCTDHX package. For further reading and download, please click here.
Study of 2D and 3D Interacting Ultracold ManyBody Systems
Since recent developments of especially MCTDHX made computations in 2 and 3 dimensions feasible, I study bosonic and fermionic systems' properties in the crossover from weak to strong interactions as well as with and without angular momentum. The MCTDHX idea can be adopted also for the case of optical lattices, i.e., Hubbard Hamiltonians. Contrary to other methods in the field, large 2D and 3D lattice systems can be treated on an accurate beyondmeanfield manybody level.
Tunneling Dynamics in Open Ultracold ManyBody Systems
One of my research interests is the tunneling process in systems of interacting indistinguishable particles which are not completely trapped, i.e., systems in which there is no/less than the particle number of bound states. So far it was found for bosons that the initial coherence will be destroyed throughout the dynamics, that the decay times are determined by the interactions, the particle number, and the potential threshold. The mechanism of the loss of coherence is driven by simultaneously happening singleparticle processes. The pace of these processes depends on the chemical potentials of subsystems made of a different number of particles. In all the systems several natural orbitals are needed to qualitatively describe the dynamics. The timedependent GrossPitaevskii approximation fails to cover the dynamics qualitatively and quantitatively. The devised model consideration was recently shown to also apply for fermionic particles with Coulomb interactions.
New Analysis Tools and Measures for Quantum ManyBody Systems and their Dynamics
One very general problem about quantum manybody physics is that even knowing the full solution to a problem might sometimes not be enough: The solution might be so complicated that one needs an appropriate tool to grasp the useful information contained in this solution. I try to tackle this question by developing new tools and measures to analyse and classify the plethora of phenomena in quantum manybody dynamics. Recently implemented and tested measures for quantum dynamics include several genuine manybody entropies, single shot simulations, and highorder correlation functions.
Useful Software
Picture Gallery
Video Gallery
MCTDHX on Youtube
Phantom vortices playlistVortex reconnections playlist
MCTDHB introduction at the Annual Colloquium of the HGS MathComp.
MCTDHB introduction in a group seminar coinciding with the birthday of Lorenz Cederbaum.
MCTDHB introduction in the MCTDH group seminar.
MCTDHB introduction in a talk at the Technion in Haifa.
Movie depicting the first order momentum correlation function of the ejected bosons in the decay by tunneling to open space.
Movie illustrating the timeadaptivity of MCTDHB orbitals in the decay by tunneling to open space.
Movie showing a decomposition of the momentum distribution to a fraction corresponding to a harmonic oscillator and a peak structure for the decay by tunneling to open space.
Movie of the depletion of an expanding BEC of 10000 atoms visualized with the second order correlation function.
Movie of the vortex formation in a stirred 2D BEC.
Talks / Workshops / Conferences
 Data Driven Modelling and Optimization, Warsaw, 2008
 Shared and Distributed Memory Parallel Programming, HLRS Stuttgart, Germany, 2009
 Parallel Computing, Heidelberg, Germany, 2010
 Quantum Hybrid Systems, Heidelberg, Germany, 2010
 Minerva Winter School on LightMatter Interaction, Haifa, Israel, 2010
 7th VIHPS Tuning Workshop, HLRS Stuttgart, Germany, 2011
 Quantum Science and Technologies, Rovereto, Italy, 2011
 FiniteTemperature NonEquilibrium Superfluid Systems, Heidelberg, Germany, 2011
 CQD Colloquium Pretalk, Heidelberg, Germany, 2012
 Talk at the Technion, Haifa, Israel, 2012
 Talk at the Quantum Technologies Conference III, Warsaw, Poland, 2013
 CQD Colloquium Pretalk, Heidelberg, Germany, 2013
 Talk in the Condensed Matter Theory Group, Basel, 2013
 Talk at the 16th HLRS Review workshop, Stuttgart, Germany, 2013
 Talk in the Quantum Optics and Statistics Group, Freiburg, Germany, 2013
 Lecture "A Laymans Guide to MCTDHB" at CEPOF, São Carlos, São Paulo, Brazil, lecture notes, 2014
 Talk at IFSC, USP, São Carlos, São Paulo, Brazil, 2014
 Talk at IFUSP, USP, São Paulo, São Paulo, Brazil, 2014
 Talk at IFSC, USP, São Carlos, São Paulo, Brazil, 2015
 Talk at QNano Group, IFSC USP, São Paulo, São Paulo, Brazil, 2015
 Talk at the QSIT meeting in Arosa, Switzerland, 2015
 Talk at the Computational ManyBody physics in the era of artificial gauge fields workshop, Munich, Germany, 2015
 Talk at the ETH Zürich, Switzerland, 2015
 Talk in the Quantum Optics and Statistics Group, Freiburg, Germany, 2015
 Talk at the FU Berlin, Berlin, Germany, 2015
 Talk at the Manybody Physics in Synthetic Quantum Systems conference, Stellenbosch, South Africa, 2016
 Talk in the Quantum Optics and Statistics Group, Freiburg, Germany, 2016
 Talk at the Ultrafast Xray Science Laboratory, LBNL, Berkeley, USA 2016
Grants/Scholarships/Prizes
 Interanational Graduiertenkolleg 710 Complex processes: Modeling, Simulation and Optimization: PhD Scholarship, 2009
 SophieBernthsen Award of the RuprechtKarlsUniversität Heidelberg, 2011
 Minerva Short Term Research Grant, 2012
 Springer Theses award, 2014
Publications
Show all abstracts.1.  Fragmented Superradiance of a BoseEinstein Condensate in an Optical Cavity 
Axel U. J. Lode and Christoph Bruder. This paper shows how the interactions between laserpumped superradiant atoms in an optical cavity lead to the emergence of fragmentation and the breakdown of the Dicke model description of the system. Phys. Rev. Lett. 118, 013603 (2017); arXiv:1606.06058; .
The Dicke model and the superradiance of twolevel systems in a radiation field have many applications. Recently, a Dicke quantum phase transition has been realized with a BoseEinstein condensate in a cavity. We numerically solve the manybody Schrödinger equation and study correlations in the ground state of interacting bosons in a cavity as a function of the strength of a driving laser. Beyond a critical strength, the bosons occupy multiple modes macroscopically while remaining superradiant. This fragmented superradiance can be detected by analyzing the variance of singleshot measurements.
 
2.  Phantom vortices: hidden angular momentum in ultracold dilute BoseEinstein condensates 
Storm E. Weiner, Marios C. Tsatsos, Lorenz S. Cederbaum, and Axel U. J. Lode. This paper discusses how the slow acquisition of angular momentum leads to the fragmentation of twodimensional BECs and the occurence of phantom vortices, a new manybody mode of quantized vorticity. Scientific Reports 7, 40122 (2017); arXiv:1409.7670 [condmat.quantgas].
Vortices are essential to angular momentum in quantum systems such as ultracold atomic gases. The existence of quantized vorticity in bosonic systems stimulated the development of the GrossPitaevskii meanfield approximation. However, the true dynamics of angular momentum in finite, interacting manybody systems like trapped BoseEinstein condensates is enriched by the emergence of quantum correlations whose description demands more elaborate methods. Herein we theoretically investigate the full manybody dynamics of the acquisition of angular momentum by a gas of ultracold bosons in two dimensions using a standard rotation procedure. We demonstrate the existence of a novel mode of quantized vorticity, which we term the phantom vortex. Contrary to the conventional meanfield vortex, can be detected as a topological defect of spatial coherence, but not of the density. We describe previously unknown manybody mechanisms of vortex nucleation and show that angular momentum is hidden in phantom vortices modes which so far seem to have evaded experimental detection. This phenomenon is likely important in the formation of the Abrikosov lattice and the onset of turbulence in superfluids.
 
3.  Dynamics of Hubbard Hamiltonians with the multiconfigurational timedependent Hartree method for indistinguishable particles 
Axel U. J. Lode and Christoph Bruder. This paper applies the philosophy of the multiconfigurational timedependent Hartree for indistinguishable particles to solve the timedependent Schrödinger equation with Hubbard Hamiltonians Phys. Rev. A 94, 013616 (2016); http://arxiv.org/abs/1604.08809.
We apply the multiconfigurational timedependent Hartree method for indistinguishable particles (MCTDHX) to systems of bosons or fermions in lattices described by Hubbard type Hamiltonians with longrange or shortrange interparticle interactions. The wavefunction is expanded in a variationally optimized timedependent manybody basis generated by a set of effective creation operators that are related to the original particle creation operators by a timedependent unitary transform. We use the timedependent variational principle for the coefficients of this transform as well as the expansion coefficients of the wavefunction in the timedependent manybody basis as variational parameters to derive equations of motion. The convergence of MCTDHX is shown by comparing its results to the exact diagonalization of one, two, and threedimensional lattices filled with bosons with contact interactions. We use MCTDHX to study the buildup of correlations in the longtime splitting dynamics of a BoseEinstein condensate loaded into a large twodimensional lattice subject to a barrier that is ramped up in the center. We find that the system is split into two parts with emergent timedependent correlations that depend on the ramping time  for most barrierraisingtimes the system becomes twofold fragmented, but for some of the very fast ramps, the system shows revivals of coherence.
 
4.  The multiconfigurational timedependent Hartree method for bosons with internal degrees of freedom: Theory and composite fragmentation of multicomponent BoseEinstein condensates 
Axel U. J. Lode This paper applies the multiconfigurational timedependent Hartree method for bosons with internal degrees of freedom and describes the composite fragmentation of harmonically trapped bosons as a function of the spatial separation between their two internal states. Phys. Rev. A 93, 063601 (2016); http://arxiv.org/abs/1602.05791.
In this paper the multiconfigurational timedependent Hartree for bosons method (MCTDHB) is derived for the case of N identical bosons with internal degrees of freedom. The theory for bosons with internal degrees of freedom constitutes a generalization of the MCTDHB method that substantially enriches the manybody physics that can be described. We demonstrate that the numerically exact solution of the timedependent manybody Schr\"odinger equation for interacting bosonic particles with internal degrees of freedom is now feasible. We report on the MCTDHB equations of motion for bosons with internal degrees of freedom and their implementation for a general manybody Hamiltonian with onebody and twobody terms that, both, may depend on the internal states of the considered particles. To demonstrate the capabilities of the theory and its software implementation integrated in the MCTDHX software, we apply MCTDHB to the emergence of fragmentation of parabolically trapped bosons with two internal states: we study the groundstate of N=100 parabolically confined bosons as a function of the splitting between the statedependent minima of the two parabolic potentials. To quantify the coherence of the system we compute its normalized onebody correlation function. We find that the coherence within each internal state of the atoms is maintained, while it is lost between the different internal states. This is a hallmark of a new kind of fragmentation which is absent in bosons without internal structure. We term the emergent phenomenon "composite fragmentation".
 
5.  Multiconfigurational timedependent Hartree method for fermions: Implementation, exactness, and fewfermion tunneling to open space 
Elke Fasshauer and Axel U. J. Lode. This paper introduces a new implementation of MCTDHF, shows its exactness and discusses the physics of charged fermions tunneling through a barrier to open space. Phys. Rev. A 93, 033635 (2016); arXiv:1510.02984.
We report on an implementation of the multiconfigurational timedependent Hartree method (MCTDH) for spinpolarized fermions (MCTDHF). Our approach is based on a mapping for operators in Fock space that allows a compact and efficient application of the Hamiltonian and solution of the MCTDHF equations of motion. Our implementation extends, builds on, and exploits the recursive implementation of MCTDH for bosons (rmctdhb) package. Together with rmctdhb, the present implementation of MCTDHF forms the mctdhx package. We benchmark the accuracy of the algorithm with the harmonic interaction model and a timedependent generalization thereof. These models consider parabolically trapped particles that interact through a harmonic interaction potential. We demonstrate that MCTDHF is capable of solving the timedependent manyfermion Schrödinger equation to an arbitrary degree of precision and can hence yield numerically exact results even in the case of Hamiltonians with timedependent onebody and twobody potentials. We study the problem of two initially parabolically confined and charged fermions tunneling through a barrier to open space. We demonstrate the validity of a model proposed previously for the manybody tunneling to open space of bosonic particles with contact interactions [Proc. Natl. Acad. Sci. USA 109, 13521 (2012)]. The manyfermion tunneling can be built up from sequentially happening singlefermion tunneling processes. The characteristic momenta of these processes are determined by the chemical potentials of trapped subsystems of smaller particle numbers: The escaped fermions convert the different chemical potentials into kinetic energy. Using the twobody correlation function, we present a detailed picture of the sequentiality of the process and are able to tell tunneling from overthebarrier escape.
 
6.  Manybody entropies, correlations, and emergence of statistical relaxation in interaction quench dynamics of ultracold bosons 
Axel U. J. Lode, Barnali Chakrabarti, and Venkata K. B. Kota. This paper introduces several genuine manybody measures for entropy and discusses their timeevolution for interaction quench dynamics of ultracold bosons. Phys. Rev. A 92, 033622 (2015); arXiv:1501.02611 [condmat.quantgas].
We study the quantum manybody dynamics and the entropy production triggered by an interaction quench in a system of N=10 interacting identical bosons in an external onedimensional harmonic trap. The multiconfigurational timedependent Hartree method for bosons (MCTDHB) is used for solving the timedependent Schrödinger equation at a high level of accuracy. We consider manybody entropy measures such as the Shannon information entropy, number of principal components, and occupation entropy that are computed from the timedependent manybody basis set used in MCTDHB. These measures quantify relevant physical features such as irregular or chaotic dynamics, statistical relaxation, and thermalization. We monitor the entropy measures as a function of time and assess how they depend on the interaction strength. For larger interaction strength, the manybody information and occupation entropies approach the value predicted for the Gaussian orthogonal ensemble of random matrices. This implies statistical relaxation. The basis states of MCTDHB are explicitly timedependent and optimized by the variational principle in a way that minimizes the number of significantly contributing ones. It is therefore a nontrivial fact that statistical relaxation prevails in MCTDHB computations. Moreover, we demonstrate a fundamental connection between the production of entropy, the buildup of correlations and loss of coherence in the system. Our findings imply that meanfield approaches such as the timedependent GrossPitaevskii equation cannot capture statistical relaxation and thermalization because they neglect correlations. Since the coherence and correlations are experimentally accessible, their present connection to manybody entropies can be scrutinized to detect statistical relaxation. In this work we use the recent recursive software implementation of the MCTDHB (RMCTDHB).
 
7.  Condensate fragmentation as a sensitive measure of the quantum manybody behavior of bosons with longrange interactions 
Uwe R. Fischer, Axel U. J. Lode, and Budhaditya Chatterjee. This manuscript investigates the degree of fragmentation in ultracold bosons in one and two spatial dimensions in dependence on the functional shape of the interparticle interaction potential. Phys. Rev. A 91, 063621 (2015); arXiv:1502.04889 [condmat.quantgas].
The occupation of more than one singleparticle state, and hence the emergence of fragmentation, is a manybody phenomenon occurring for systems of spatially confined strongly interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one and twodimensional systems in single wells. We solve the full manybody Schrödinger equation of the system using the recursive implementation of the multiconfigurational timedependent Hartree for bosons method (RMCTDHB). The dependence of the degree of fragmentation on dimensionality, particle number, areal or line density, and interaction strength is assessed. For contact interactions, it is found that the fragmentation is essentially density independent in two dimensions. However, fragmentation increasingly depends on density the more long ranged the interactions become. At fixed particle number N, the degree of fragmentation is increasing when the density is decreasing, as expected in one spatial dimension. We demonstrate that this, nontrivially, remains true also for longrange interactions in two spatial dimensions. We, finally, find that fragmentation in a single well is a mesoscopic phenomenon: Within our fully selfconsistent approach, the degree of fragmentation, to a good approximation, decreases universally as N^(0.5) when only N is varied.
 
8.  Vortex reconnections in anisotropic trapped threedimensional BoseEinstein condensates 
Tomos Wells, Axel U. J. Lode, Vanderlei S. Bagnato, and Marios C. Tsatsos. This paper investigates the reconnection dynamics of two coherent perpendicular vortices in a threedimensional sample of ultracold bosons. J. Low Temp. Phys 180, 133 (2015); arXiv:1410.2859 [condmat.quantgas].
Quantum vortex reconnections can be considered as a fundamental unit of interaction in complex turbulent quantum gases. Understanding the dynamics of single vortex reconnections as elementary events is an essential precursor to the explanation of the emergent properties of turbulent quantum gases. It is thought that a lone pair of quantum vortex lines will inevitably interact given a sufficiently long time. This paper investigates aspects of reconnections of quantum vortex pairs imprinted in a Bose–Einstein condensate with 101 bosons held in an anisotropic threedimensional trap using an exact manybody treatment. In particular, the impact of the interaction strength and the trap anisotropy in the reconnection time is studied. It is found that interaction strength has no effect on reconnection time over short time scales and that the trap anisotropy can cause the edge of the condensate to interfere with the reconnection process. It is also found that the initially coherent system fragments very slowly, even for a relatively large interaction strength, and therefore the system tends to stay condensed during the reconnections.
 
9.  Resonances and Dynamical Fragmentation in a Stirred BoseEinstein Condensate 
Marios C. Tsatsos and Axel U. J. Lode. This paper investigates the resonant behavior of a twodimensional stirred sample of ultracold bosons and establishes a connection of fragmentation and vortex nucleation in the system. J. Low Temp. Phys. 181, 171 (2015); arXiv:1410.0414 [condmat.quantgas].
Superfluids are distinguished from ordinary fluids by the quantized manner in which the rotation is manifested in them. Precisely, quantized vortices are known to appear in the bulk of a superfluid subject to external rotation. In this work we study a trapped ultracold Bose gas of N=101 atoms interacting with finiterange potential in two spatial dimensions that is stirred by a rotating beam. We use the multiconfigurational Hartree method for bosons, which goes beyond the mainstream meanfield theory, to calculate the dynamics of the gas in real time. As the gas is rotated, the wavefunction of the system changes symmetry and topology. We see a series of resonances, i.e., peaks in the total energy, as the stirring frequency is increased. Fragmentation and a change of the symmetry of the density of the gas accompany the appearance of these resonances. We conclude that fragmentation of the gas appears handinhand with resonant absorption of energy and angular momentum from the external agent of rotation.
 
10.  Breaking the resilience of a twodimensional BoseEinstein condensate to fragmentation 
Shachar Klaiman, Axel U. J. Lode, Alexej I. Streltsov, Lorenz S. Cederbaum, and Ofir E. Alon. This paper discusses how to obtain a fragmented BEC by dynamically transforming radially symmetric single well to double well potentials. Phys. Rev. A 90, 043620 (2014); arXiv:1409.0323 [condmat.quantgas].
A twodimensional BoseEinstein condensate (BEC) split by a radial potential barrier is investigated. We
determine on an accurate manybody level the system's groundstate phase diagram as well as a timedependent
phase diagram of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the
timedependent splitting process leads to substantial fragmentation. We demonstrate the dynamical fragmentation
of a BEC despite its ground state being condensed. The results are analyzed using a meanfield model and suggest
that a large manifold of lowlying fragmented excited states can significantly impact the dynamics of trapped
twodimensional BECs.
 
11.  Controlling the Velocities and Number of Emitted Particles in the Tunneling to Open Space Dynamics 
Axel U. J. Lode, Shachar Klaiman, Ofir E. Alon, Alexej I. Streltsov, and Lorenz S. Cederbaum. This paper discusses how manybody tunneling to open space can be controlled by manipulating the potential threshold and the interparticle repulsion. Phys. Rev. A 89, 053620 (2014); arXiv:1309.4253 [quantph].
A scheme to control the manyboson tunneling process to open space is derived and demonstrated. The number of ejected particles and their velocities can be controlled by two parameters, the threshold of the potential and the interparticle interaction. Since these parameters are fully under experimental control, this is also the case for the number of ejected particles and their emission spectrum. The process of tunneling to open space can hence be used, for example, for the quantum simulation of complicated tunneling ionization processes and atom lasers. To understand the manybody tunneling process, a generalization of the model introduced in [Proc. Natl. Acad. Sci. USA, 109, 13521 (2012)] for tunneling in the absence of a threshold is put forward and proven to apply for systems with a nonzero threshold value. It is demonstrated that the model is applicable for general interparticle interaction strengths, particle numbers and threshold values. The model constructs the manybody process from singleparticle emission processes. The rates and emission momenta of the singleparticle processes are determined by the chemical potentials and energy differences to the threshold value of the potential for systems with different particle numbers. The chemical potentials and these energy differences depend on the interparticle interaction. Both the number of confined particles and their rate of emission thus allow for a control by the manipulation of the interparticle interaction and the threshold. Numerically exact results for two, three and one hundred bosons are shown and discussed. The devised control scheme for the manybody tunneling process performs very well for the dynamics of the momentum density, the correlations, the coherence and of the final state, i.e., the number of particles that remain confined in the potential.
 
12.  How an interacting manybody system tunnels through a potential barrier to open space 
Axel U. J. Lode, Alexej I. Streltsov, Kaspar Sakmann, Ofir E. Alon, and Lorenz S. Cederbaum. This manuscript explains in detail how the tunneling of an initially coherent interacting ultracold atomic sample through a potential barrier to open space works. Proc. Natl. Acad. Sci. USA, 109, 13521 (2012); arXiv:1202.3447 [condmat.quantgas].
The tunneling process in a manybody system is a phenomenon which lies at the very heart of quantum mechanics. It appears in nature in the form of αdecay, 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 cumbersome problem, either because of very complicated or even unknown interparticle interactions or due to a large number of constituent particles. In this work, we theoretically study the phenomenon of quantum manybody tunneling in a transparent and controllable physical system, an ultracold atomic gas. We analyze a full, numerically exact manybody solution of the Schrödinger equation of a onedimensional 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 manyparticle decay process is a quantum interference of singleparticle 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 manybody correlations between the emitted and trapped fractions of the wave function in the respective processes.
 
13.  Numerically exact quantum dynamics of bosons with timedependent interactions of harmonic type 
Axel U. J. Lode, Kaspar Sakmann, Ofir E. Alon, Lorenz S. Cederbaum, and Alexej I. Streltsov. This manuscript assesses the capability of MCTDHB to provide numerically exact solutions of the full timedependent manyboson Schrödinger equation Phys. Rev. A 86, 063606 (2012); arXiv:1207.5128 [condmat.quantgas].
The exactly solvable quantum manyparticle model with harmonic one and twoparticle interaction terms is extended to include time dependency. We show that when the external trap potential and interparticle interaction have a time dependency, the numerically exact solutions of the corresponding timedependent manyboson Schrödinger equation are still available. We use these exact solutions to benchmark the recently developed multiconfigurational timedependent Hartree method for bosons (MCTDHB) [ Phys. Rev. Lett. 99 030402 (2007); Phys. Rev. A 77 033613 (2008)]. In particular, we benchmark the MCTDHB method for (i) the ground state; (ii) the breathing manybody dynamics activated by a quench scenario where the interparticle interaction strength is suddenly turned on to a finite value; (iii) the nonequilibrium dynamic for driven scenarios where both the trap and interparticleinteraction potentials are timedependent. Excellent convergence of the ground state and dynamics is demonstrated. The great relevance of the selfconsistency and time adaptivity, which are the intrinsic features of the MCTDHB method, is demonstrated by contrasting the MCTDHB predictions and those obtained within the standard full configuration interaction method spanning a Fock space of the same size, but utilizing as oneparticle basis set the fixedshape eigenstates of the oneparticle potential. Connections of the model's results to ultracold BoseEinstein condensed systems are addressed.
 
14.  NumericallyExact Schrödinger Dynamics of Closed and Open Many Boson Systems with the MCTDHB Package 
Axel U. J. Lode, Kaspar Sakmann, Rostislav A. Doganov, Julian Grond, Ofir E. Alon, Alexej I. Streltsov, and Lorenz S. Cederbaum. This review article discusses the capabilities, various applications and the parallelization of the MCTDHB program package. Springer, High Performance Computing in Science and Engineering '13, pp 8192, Nagel, Wolfgang E.; Körner, Dietmar H.; Resch, Michael M.
This review article discusses the capabilities, various applications and the parallelization of the MCTDHB program package.
 
15.  Thesis: Tunneling Dynamics in Open Ultracold Bosonic Systems 
Axel U. J. Lode My thesis discusses the tunneling dynamics in open ultracold bosonic systems. Link to Springer Theses website; Link.
This thesis explores the quantum manybody tunneling dynamics of open ultracold
bosonic systems with the recently developed multiconfigurational timedependent
Hartree for bosons (MCTDHB) method. The capabilities of MCTDHB
to provide solutions to the full timedependent manybody problem are assessed
in a benchmark using the analytically solvable harmonic interaction Hamiltonian
and a generalization of it with timedependent both one and twobody
potentials. In a comparison with numerically exact MCTDHB results, it is shown
that e.g. lattice methods fail qualitatively to describe the tunneling dynamics. A
model assembling the manybody physics of the process from basic simultaneously
happening singleparticle processes is derived and verified with a numerically
exact MCTDHB description. The generality of the model is demonstrated
even for strong interactions and large particle numbers. The ejection of the
bosons from the source occurs with characteristic velocities. These velocities are
defined by the chemical potentials of systems with different particle numbers
which are converted to kinetic energy. The tunneling process is accompanied
by fragmentation: the ejected bosons lose their coherence with the source and
among each other. It is shown that the various aspects of the tunneling dynamics’
can be controlled well with the interaction and the potential threshold.
 
16.  Exact decay and tunnelling dynamics of interacting fewboson systems 
Axel U.J. Lode, Alexej I. Streltsov, Ofir E. Alon, HansDieter Meyer, and Lorenz S. Cederbaum. This paper discusses the decay of a fewboson system modeled described numerically exactly with the multiconfigurational timedependent Hartree method and absorbing boundary conditions. J. Phys. B: At. Mol. Opt. Phys. 42, 044018 (2009)
The decay and tunnelling dynamics of repulsive fewboson systems through a onedimensional potential barrier is studied from first principles. To this end, we solve the numerically exact timedependent fewboson Schrödinger equation by utilizing the successful multiconfiguration timedependent Hartree method. Benchmark results for a wide range of interactions are reported. Deviations from the timedependent Gross–Pitaevskii approach are identified. Counterintuitively, the meanfield approach can overestimate the tunnelling times even for relatively weaklyinteracting fewboson systems. Implications are discussed.
 
17.  Wave chaos as signature for depletion of a BoseEinstein condensate 
Iva Březinova, Axel U. J. Lode, Alexej I. Streltsov, Ofir E. Alon, Lorenz S. Cederbaum, and Joachim Burgdörfer. This paper shows that the occurence of chaos in the GrossPitevskii equation is a sign of the occurence of depletion or fragmentation on the manybody level. Phys. Rev. A 86, 013630 (2012); arXiv:1202.5869 [condmat.quantgas].
We study the expansion of repulsively interacting BoseEinstein condensates (BECs) in shallow onedimensional potentials. We show for these systems that the onset of wave chaos in the GrossPitaevskii equation (GPE), that is, the onset of exponential separation in Hilbert space of two nearby condensate wave functions, can be used as an indication for the onset of depletion of the BEC and the occupation of excited modes within a manybody description. Comparison between the multiconfigurational timedependent Hartree for bosons method and the GPE reveals a close correspondence between the manybody effect of depletion and the meanfield effect of wave chaos for a wide range of singleparticle external potentials. In the regime of wave chaos the GPE fails to account for the finescale quantum fluctuations because manybody effects beyond the validity of the GPE are nonnegligible. Surprisingly, despite the failure of the GPE to account for the depletion, coarsegrained expectation values of the singleparticle density such as the overall width of the atomic cloud agree very well with the manybody simulations. The timedependent depletion of the condensate could be investigated experimentally, for example, via decay of coherence of the expanding atom cloud.
 
18.  Elastic scattering of a BoseEinstein condensate at a potential landscape 
Iva Březinova, Axel U. J. Lode, Alexej I. Streltsov, Lorenz S. Cederbaum, Ofir E. Alon, Lee A. Collins, Barry I. Schneider, and Joachim Burgdörfer. This paper demonstrates the importance of depletion and fragmentation in scattering a BoseEinstein condensate from a shallow optical or disorder potential. J. Phys. Conf. Ser. 488, 012032 (2014); arXiv:1310.0622 [condmat.quantgas].
We investigate the elastic scattering of BoseEinstein condensates at shallow periodic and disorder potentials. We show that the collective scattering of the macroscopic quantum object couples to internal degrees of freedom of the BoseEinstein condensate such that the BoseEinstein condensate gets depleted. As a precursor for the excitation of the BoseEinstein condensate we observe wave chaos within a meanfield theory.
 
19.  Excitation spectra of manybody systems by linear response: General theory and applications to trapped condensates 
Julian Grond, Alexej I. Streltsov, Axel U. J. Lode, Kaspar Sakmann, Lorenz S. Cederbaum, and Ofir E. Alon. This paper introduces and tests a linear response theory on top of the multiconfigurational timedependent Hartree method for bosons. Phys. Rev. A 88, 023606 (2013); arXiv:1307.1667 [condmat.quantgas].
We derive a general linearresponse manybody theory capable of computing excitation spectra of trapped interacting bosonic systems, e.g., depleted and fragmented BoseEinstein condensates (BECs). To obtain the linearresponse equations we linearize the multiconfigurational timedependent Hartree for bosons (MCTDHB) method, which provides a selfconsistent description of manyboson systems in terms of orbitals and a state vector (configurations), and is in principle numericallyexact. The derived linearresponse manybody theory, which we term LRMCTDHB, is applicable to systems with interaction potentials of general form. From the numerical implementation of the LRMCTDHB equations and solution of the underlying eigenvalue problem, we obtain excitations beyond available theories of excitation spectra, such as the Bogoliubovde Gennes (BdG) equations. The derived theory is first applied to study BECs in a onedimensional harmonic potential. The LRMCTDHB method contains the BdG excitations and, also, predicts a plethora of additional manybody excitations which are out of the realm of standard linear response. In particular, our theory describes the exact energy of the higher harmonic of the first (dipole) excitation not contained in the BdG theory. We next study a BEC in a very shallow onedimensional doublewell potential. We find with LRMCTDHB lowlying excitations which are not accounted for by BdG, even though the BEC has only little fragmentation and, hence, the BdG theory is expected to be valid. The convergence of the LRMCTDHB theory is assessed by systematically comparing the excitation spectra computed at several different levels of theory.
 
20.  Recursive formulation of the multiconfigurational timedependent Hartree method for fermions, bosons and mixtures thereof in terms of onebody density operators 
Ofir E. Alon, Alexej I. Streltsov, Kaspar Sakmann, Axel U. J. Lode, Julian Grond, and Lorenz S. Cederbaum. This paper builds recursively from onebody operators the equations of motion of the multiconfigurational timedependent Hartree method for three (different) kinds of indistinguishable particles. Chemical Physics Volume 401, Pages 214 (2012); arXiv:1109.4429 [quantph].
The multiconfigurational timedependent Hartree method (MCTDH) [H.D. Meyer, U. Manthe, L.S. Cederbaum, Chem. Phys. Lett. 165, 73 (1990); U. Manthe, H.D. Meyer, L.S. Cederbaum, J. Chem. Phys. 97, 3199 (1992)] is celebrating nowadays entering its third decade of tackling numericallyexactly a broad range of correlated multidimensional nonequilibrium quantum dynamical systems. Taking in recent years particles’ statistics explicitly into account, within the MCTDH for fermions (MCTDHF) and for bosons (MCTDHB), has opened up further opportunities to treat larger systems of interacting identical particles, primarily in laseratom and coldatom physics. With the increase of experimental capabilities to simultaneously trap mixtures of two, three, and possibly even multiple kinds of interacting composite identical particles together, we set up the stage in the present work and specify the MCTDH method for such cases. Explicitly, the MCTDH method for systems with three kinds of identical particles interacting via all combinations of two and threebody forces is presented, and the resulting equationsofmotion are briefly discussed. All four possible mixtures (Fermi–Fermi–Fermi, Bose–Fermi–Fermi, Bose–Bose–Fermi and Bose–Bose–Bose) are presented in a unified manner. Particular attention is paid to represent the coefficients’ part of the equationsofmotion in a compact recursive form in terms of onebody density operators only. The recursion utilizes the recently proposed Combinadicbased mapping for fermionic and bosonic operators in Fock space [A.I. Streltsov, O.E. Alon, L.S. Cederbaum, Phys. Rev. A 81, 022124 (2010)], successfully applied and implemented within MCTDHB. Our work sheds new light on the representation of the coefficients’ part in MCTDHF and MCTDHB without resorting to the matrix elements of the manybody Hamiltonian with respect to the timedependent configurations. It suggests a recipe for efficient implementation of the schemes derived here for mixtures which is suitable for parallelization.
 
21.  What to do with targeted IL2. 
H. N. Lode, R. Xiang, P. Perri, U. Pertl, A. Lode, S. D. Gillies, and R. A. Reisfeld. This article assesses the usage of IL2 immunocytokines for an immunotherapy of various sorts of cancer. Drugs Today, 36(5): 321 (2000)
A common strategy in immunotherapy of cancer is the induction of an increased immunogenicity of syngeneic malignancies. A novel approach to achieve this goal is the targeting of cytokines into the tumor microenvironment with antibodycytokine fusion proteins, called immunocytokines. This report summarizes therapeutic efficacy and immune mechanisms involved in targeting IL2 to syngeneic tumors and describes their extended use as a synergistic treatment modality for cancer vaccines and antiangiogenesis. Treatment of established melanoma and colon carcinoma metastases with IL2 immunocytokines resulted in eradication of disease, followed by a vaccination effect protecting mice from lethal challenges with wildtype tumor cells. In a syngeneic neuroblastoma model, targeted IL2 elicited effective antitumor responses mediated by NK cells in the absence of a Tcell memory. Interestingly, targeted IL2 was effective in amplification of memory immune responses previously induced by cancer vaccines. Furthermore, a synergistic effect achieved by combining targeted IL2immunotherapy with an antiangiogenic inhibitor of integrin alphavbeta3 extends the potential of this immunotherapeutic strategy in combination with antiangiogenesis as demonstrated in three syngeneic tumor models. Based on these findings, targeted IL2 may provide an effective tool for the adjuvant treatment of cancer either applied as a single strategy or in combination with cancer vaccines and antiangiogenic strategies.
