arXiv subjects

Axel U. J. Lode

Publications and source records attributed to Axel U. J. Lode.

At least 19 recordsLinked to original sources

arXiv2024

Condensates Breaking Up Under Rotation

The ground state of a rotating Bose-Einstein condensate trapped in a two-dimensional anharmonic--anisotropic potential is analyzed numerically at the limit of an infinite number of particles. We find that the density breaks up along the $x$ direction in position space and along the $p_y$ direction in momentum space together with the acquisition of angular momentum. Side by side, the anisotropies of the many-particle position variances along the $x$ and $y$ directions and of the many-particle momentum variances along the $p_y$ and $p_x$ directions become opposite when computed at the many-body and mean-field levels of theory. All in all, the rotating bosons are found to possess unique correlations at the limit of an infinite number of particles, both in position and momentum spaces, although their many-body and mean-field energies per particle and densities per particle coincide and the condensate fraction is 100\%. Implications are briefly discussed.

cond-mat.quant-gas↗

arXiv2022

Accuracy of quantum simulators with ultracold dipolar molecules: a quantitative comparison between continuum and lattice descriptions

With rapid progress in control and manipulation of ultracold magnetic atoms and dipolar molecules, the quantum simulation of lattice models with strongly interacting dipole-dipole interactions (DDI) and high densities is now within experimental reach. This rapid development raises the issue about the validity of quantum simulation in such regimes. In this study, we address this question by performing a full quantitative comparison between the continuum description of a one-dimensional gas of dipolar bosons in an optical lattice, and the single-band Bose-Hubbard lattice model that it quantum simulates. By comparing energies and density distributions, and by calculating direct overlaps between the continuum and lattice many-body wavefunctions, we demonstrate that in regimes of strong DDI and high densities the continuum system fails to recreate the desired lattice model. Two-band Hubbard models become necessary to reduce the discrepancy observed between continuum and lattice descriptions, but appreciable deviations in the density profile still remain. Our study elucidates the role of strong DDI in generating physics beyond lowest-band descriptions and should offer a guideline for the calibration of near-term dipolar quantum simulators.

cond-mat.quant-gas↗

arXiv2022

Fragmentation and correlations in a rotating Bose-Einstein condensate undergoing breakup

The theoretical investigation of rotating Bose-Einstein condensates has mainly focused on the emergence of quantum vortex states and the condensed properties of such systems. In the present work, we concentrate on other facets by examining the impact of rotation on the ground state of weakly interacting bosons confined in anharmonic potentials computed both at the mean-field level and particularly at the many-body level of theory. For the many-body computations, we employ the well-established many-body method known as the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We present how various degrees of fragmentation can be generated following the breakup of the ground state densities in anharmonic traps without ramping up a potential barrier for strong rotations. The breakup of the densities is found to be associated with the acquisition of angular momentum in the condensate due to the rotation. In addition to fragmentation, the presence of many-body correlations is examined by computing the variances of the many-particle position and momentum operators. For strong rotations, the many-body variances become smaller than their mean-field counterparts, and one even finds a scenario with opposite anisotropies of the mean-field and many-body variances. Further, it is observed that for higher discrete symmetric systems of order k, namely three-fold and four-fold symmetry, breakup to k sub-clouds and emergence of k-fold fragmentation take place. All in all, we provide a thorough many-body investigation of how and which correlations build up when a trapped Bose-Einstein condensate breaks up under rotation.

cond-mat.quant-gas↗

arXiv2022

Pauli crystal melting in shaken optical traps

Pauli crystals are ordered geometric structures that emerge in trapped noninteracting fermionic systems due to their underlying Pauli repulsion. The deformation of Pauli crystals - often called melting - has been recently observed in experiments, but the mechanism that leads to it remains unclear. We address this question by studying the melting dynamics of N=6 fermions as a function of periodic driving and experimental imperfections in the trap (anisotropy and anharmonicity) by employing a combination of numerical simulations and Floquet theory. Surprisingly, we reveal that the melting of Pauli crystals is not simply a direct consequence of an increase in system energy, but is instead related to the trap geometry and the population of the Floquet modes. We show that the melting is absent in traps without imperfections and triggered only by a sufficiently large shaking amplitude in traps with imperfections.

cond-mat.quant-gas↗

arXiv2021

Mott transition in a cavity-boson system: A quantitative comparison between theory and experiment

The competition between short-range and cavity-mediated infinite-range interactions in a cavity-boson system leads to the existence of a superfluid phase and a Mott-insulator phase within the self-organized regime. In this work, we quantitatively compare the steady-state phase boundaries of this transition measured in experiments and simulated using the Multiconfigurational Time-Dependent Hartree Method for Indistinguishable Particles. To make the problem computationally feasible, we represent the full system by the exact many-body wave function of a two-dimensional four-well potential. We argue that the validity of this representation comes from the nature of both the cavity-atomic system and the Bose-Hubbard physics. Additionally we show that the chosen representation only induces small systematic errors, and that the experimentally measured and theoretically predicted phase boundaries agree reasonably. We thus demonstrate a new approach for the quantitative numerical determination of the superfluid--Mott-insulator phase boundary.

cond-mat.quant-gas↗

arXiv2021

Fermionization via cavity-assisted infinite-range interactions

We study a one-dimensional array of bosons with infinite-range interactions mediated by a laser-driven dissipative optical cavity. The cavity-mediated infinite-range interactions open up a new pathway to fermionization, hitherto only known for dipolar bosons due to their long-range interactions. In parameter ranges attainable in state-of-the-art experiments, we systematically compare observables for bosons and fermions with infinite-range interactions. At large enough laser pump power, many observables, including density distributions in real and momentum space, correlation functions, eigenvalues of the one-body density matrix, and superradiance order parameter, become identical for bosons and fermions. We map out the emergence of this cavity-induced fermionization as a function of pump power and contact interactions. We discover that cavity-mediated interactions can compensate a reduction by several orders of magnitude in the strength of the contact interactions needed to trigger fermionization.

cond-mat.quant-gas↗

arXiv2021

Many-body density and coherence of trapped cold bosons

Many-body densities and correlation functions are of paramount importance for understanding quantum many-body physics. Here, we present a method to compute them; our approach is general and based on the action of bosonic or fermionic annihilation field operators on the many-body wavefunction. We analyze $N = 6$ quasi-one-dimensional harmonically-trapped bosons with weak to strong contact interaction strength up to the Tonks-Girardeau limit with infinite repulsion using the MultiConfigurational Time-Dependent Hartree method for indistinguishable particles (MCTDH-X). We compare our MCTDH-X solutions to the analytical ones in the infinite repulsion regime as well as to the so-called correlated pair wavefunction approach and find a good agreement. Since numerical approximations are not bound to the cases where analytical solutions are known, we thus demonstrate a general method to investigate high-order reduced density matrices and correlation functions in systems for which analytical solutions are unknown. We trace the build-up of correlation features in the crossover from weak interactions to the Tonks-Girardeau limit and find that the higher-order correlation functions and densities resemble those in the Tonks-Girardeau limit for way smaller interactions than anticipated from just the one-body density.

cond-mat.quant-gas↗

arXiv2020

Dynamics of Ultracold Bosons in Artificial Gauge Fields: Angular Momentum, Fragmentation, and the Variance of Entropy

We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schrödinger equation using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X). We find that the artificial gauge field implants angular momentum in the system. Fragmentation -- multiple macroscopic eigenvalues of the reduced one-body density matrix -- emerges in sync with the dynamics of angular momentum: the bosons in the many-body state develop non-trivial correlations. Fragmentation and angular momentum are experimentally difficult to assess; here, we demonstrate that they can be probed by statistically analyzing the variance of the image entropy of single-shot images that are the standard projective measurement of the state of ultracold atomic systems.

cond-mat.quant-gas↗

arXiv2020

Optimized Observable Readout from Single-shot Images of Ultracold Atoms via Machine Learning

Single-shot images are the standard readout of experiments with ultracold atoms -- the tarnished looking glass into their many-body physics. The efficient extraction of observables from single-shot images is thus crucial. Here, we demonstrate how artificial neural networks can optimize this extraction. In contrast to standard averaging approaches, machine learning allows both one- and two-particle densities to be accurately obtained from a drastically reduced number of single-shot images. Quantum fluctuations and correlations are directly harnessed to obtain physical observables for bosons in a tilted double-well potential at an unprecedented accuracy. Strikingly, machine learning also enables a reliable extraction of momentum-space observables from real-space single-shot images and vice versa. This obviates the need for a reconfiguration of the experimental setup between in-situ and time-of-flight imaging, thus potentially granting an outstanding reduction in resources.

cond-mat.quant-gas↗

arXiv2020

Interpretable and unsupervised phase classification

Fully automated classification methods that yield direct physical insights into phase diagrams are of current interest. Here, we demonstrate an unsupervised machine learning method for phase classification which is rendered interpretable via an analytical derivation of its optimal predictions and allows for an automated construction scheme for order parameters. Based on these findings, we propose and apply an alternative, physically-motivated, data-driven scheme which relies on the difference between mean input features. This mean-based method is computationally cheap and directly interpretable. As an example, we consider the physically rich ground-state phase diagram of the spinless Falicov-Kimball model.

cond-mat.dis-nn↗

arXiv2020

Detecting One-Dimensional Dipolar Bosonic Crystal Orders via Full Distribution Functions

We explore the groundstates of a few dipolar bosons in optical lattices with incommensurate filling. The competition of kinetic, potential, and interaction energies leads to the emergence of a variety of crystal state orders with characteristic one- and two-body densities. We probe the transitions between these orders and construct the emergent state diagram as a function of the dipolar interaction strength and the lattice depth. We show that the crystal state orders can be observed using the full distribution functions of the particle number extracted from simulated single-shot images.

cond-mat.quant-gas↗

arXiv2020

Pathway to chaos through hierarchical superfluidity in a cavity-BEC system

We explore the role of atomic correlations in a harmonically trapped Bose-Einstein condensate coupled to a dissipative cavity, where both the atoms and the cavity are blue detuned from the external pumping laser. Using a genuine many-body approach that goes beyond mean-field, we extract density distributions and many-body correlations to unveil a pathway to chaos at large pump power through a hierarchical self-organization of the atoms, where the atoms transition from a single-well optical lattice to a double-well optical lattice. Correlated states of the atoms emerge and are characterized by local superfluid correlations in phases which are globally superfluid or Mott insulating. Local superfluid-Mott transitions are precluded by a dynamical instability to chaos which occurs via quasiperiodic attractors. Our results explain the mechanism behind the dynamical instabilities observed in experiments.

cond-mat.quant-gas↗

arXiv2020

Multiconfigurational time-dependent Hartree approaches for indistinguishable particles

In this Colloquium, the wavefunction-based Multiconfigurational Time-Dependent Hartree approaches to the dynamics of indistinguishable particles (MCTDH-F for Fermions and MCTDH-B for Bosons) are reviewed. MCTDH-B and MCTDH-F or, together, MCTDH-X are methods for describing correlated quantum systems of identical particles by solving the time-dependent Schrödinger equation from first principles. MCTDH-X is used to accurately model the dynamics of real-world quantum many-body systems in atomic, molecular, and optical physics. The key feature of these approaches is the time-dependence and optimization of the single-particle states employed for the construction of a many-body basis set, which yields nonlinear working equations. We briefly describe the historical developments that have lead to the formulation of the MCTDH-X methods and motivate the necessity for wavefunction-based approaches. We sketch the derivation of the unified MCTDH-F and MCTDH-B equations of motion for complete and also specific restricted configuration spaces. The strengths and limitations of the MCTDH-X approach are assessed via benchmarks against an exactly solvable model and via convergence checks. We highlight some applications to instructive and experimentally-realized quantum many-body systems: the dynamics of atoms in Bose-Einstein condensates in magneto-optical and optical traps and of electrons in atoms and molecules. We discuss the current development and frontiers in the field of MCTDH-X: theories and numerical methods for indistinguishable particles, for mixtures of multiple species of indistinguishable particles, the inclusion of nuclear motion for the nonadiabatic dynamics of atomic and molecular systems, as well as the multilayer and second-quantized-representation approaches, and the orbital-adaptive time-dependent coupled-cluster theory are discussed.

cond-mat.quant-gas↗

arXiv2020

Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well

We examine the spectral structure and many-body dynamics of two and three repulsively interacting bosons trapped in a one-dimensional double-well, for variable barrier height, inter-particle interaction strength, and initial conditions. By exact diagonalization of the many-particle Hamiltonian, we specifically explore the dynamical behaviour of the particles launched either at the single particle ground state or saddle point energy, in a time-independent potential. We complement these results by a characterisation of the cross-over from diabatic to quasi-adiabatic evolution under finite-time switching of the potential barrier, via the associated time-evolution of a single particle's von Neumann entropy. This is achieved with the help of the multiconfigurational time-dependent Hartree method for indistinguishable particles (\textsc{Mctdh-x}) -- which also allows us to extrapolate our results for increasing particle numbers.

quant-ph↗

arXiv2020

MCTDH-X: The multiconfigurational time-dependent Hartree method for indistinguishable particles software

We introduce and describe the multiconfigurational time-depenent Hartree for indistinguishable particles (MCTDH-X) software. This powerful tool allows the investigation of ground state properties and dynamics of interacting quantum many-body systems in different spatial dimensions. The MCTDH-X software is a set of programs and scripts to compute, analyze, and visualize solutions for the time-dependent and time-independent many-body Schrödinger equation for indistinguishable quantum particles. As the MCTDH-X software represents a general solver for the Schrödinger equation, it is applicable to a wide range of problems in the fields of atomic, optical, molecular physics as well as condensed matter systems. In particular, it can be used to study light-matter interactions, correlated dynamics of electrons, as well as some aspects related to quantum information and computing. The MCTDH-X software solves a set of non-linear coupled working equations based on the application of the variational principle to the Schrödinger equation. These equations are obtained by using an ansatz for the many-body wavefunction that is a time-dependent expansion in a set of time-dependent many-body basis states. The time-dependence of the basis set enables MCTDH-X to deal with quantum dynamics at a superior accuracy as compared to, for instance, exact diagonalization approaches. Herein, we give an introduction to the MCTDH-X software via an easy-to-follow tutorial with a focus on accessibility. We use the double well to illustrate the fermionization of bosonic particles, the crystallization of fermionic particles, characteristics of the superfluid and Mott-insulator quantum phases in Hubbard models, and even dynamical quantum phase transitions. Our tutorial guides the potential user to apply the MCTDH-X software also to more complex systems.

cond-mat.quant-gas↗

arXiv2018

Superfluid--Mott insulator transition of ultracold superradiant bosons in a cavity

We investigate harmonically-trapped, laser-pumped bosons with infinite-range interactions induced by a dissipative high-finesse red-detuned optical cavity with numerical and analytical methods. We obtain multiple cavity and atomic observables as well as the full phase diagram of the system using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X) approach. Besides the transition from an unorganized normal phase to a superradiant phase where atoms self-organize, we focus on an in-depth investigation of the self-organized superfluid to self-organized Mott insulator phase transition in the superradiant phase as a function of the cavity-atom coupling. The numerical results are substantiated by an analytical study of an effective Bose-Hubbard model. We numerically analyze cavity fluctuations and emergent strong correlations between atoms in the many-body state across the Mott transition via the atomic density distributions and Glauber correlation functions. Unexpectedly, the weak harmonic trap leads to features like a lattice switching between the two symmetry-broken $\mathbb{Z}_2$ configurations of the untrapped system and a reentrance of superfluidity in the Mott insulating phase. Our analytical considerations quantitatively explain the numerically observed correlation features.

cond-mat.quant-gas↗

arXiv2018

Correlations of strongly interacting ultracold dipolar bosons in optical lattices

Strongly interacting dipolar bosons in optical lattices exhibit diverse quantum phases that are rich in physics. As the strength of the long-range boson-boson interaction increases, the system transitions across different phases: from a superfluid, through a Mott-insulator to a Tonks gas and, eventually, a crystal state. The signature of these phases and their transitions can be unequivocally identified by an experimentally detectable order parameter, recently described in arXiv:1708.07409. Herein, we calculate the momentum distributions and the normalized Glauber correlation functions of dipolar bosons in a one-dimensional optical lattice in order to characterize all their phases. To understand the behavior of the correlations across the phase transitions, we first investigate the eigenfunctions and eigenvalues of the one-body reduced density matrix as the function of the dipolar interaction strength. We then analyze the real- and momentum-space Glauber correlation functions, thereby gaining a spatially and momentum-resolved insight into the coherence properties of these quantum phases. We find an intriguing structure of non-local correlations that, independently of other system parameters, reveal the phase transitions of the system. In particular, spatial localization with synchronous momentum delocalization accompanies the formation of correlated islands in the density. Moreover, our study showcases that precise control of intersite correlations is possible through manipulation of the depth of the lattice, while intrasite correlations are influenced solely by changing the dipolar interaction strength.

cond-mat.quant-gas↗

arXiv2018

Order parameter and detection for crystallized dipolar bosons in lattices

We explore the ground-state properties of bosons with dipole-dipole interactions in a one-dimensional optical lattice. Remarkably, a crystallization process happens for strong dipolar interactions. Herein, we provide a detailed characterization and a way to measure the resulting crystal phase. Using the eigenvalues of the reduced one-body density matrix we define an order parameter that yields a phase diagram in agreement with an analysis of the density and two-body density. We demonstrate that the phase diagram can be detected experimentally using the variance of single-shot measurements.

cond-mat.quant-gas↗