The relationship between natural orbitals, one-body coherences, and two-body correlations is explored for bosonic many-body systems of definite parity with two occupied single-particle states. We show that the strength of local two-body correlations at the parity-symmetry center characterizes the number-state distribution and controls the structure of nonlocal two-body correlations. A recipe for the experimental reconstruction of the natural-orbital densities and quantum depletion is derived. These insights into the structure of the many-body wave function are applied to the predicted quantum-fluctuation-induced decay of dark solitons.
The relationship between natural orbitals, one-body coherences, and two-body correlations is explored for bosonic many-body systems of definite parity with two occupied single-particle states. We show that the strength of local two-body correlations at the parity-symmetry center characterizes the number-state distribution and controls the structure of nonlocal two-body correlations. A recipe for the experimental reconstruction of the natural-orbital densities and quantum depletion is derived. These insights into the structure of the many-body wave function are applied to the predicted quantum-fluctuation-induced decay of dark solitons.
We perform a comparative beyond-mean-field study of black and gray solitonic excitations in a finite ensemble of ultracold bosons confined to a one-dimensional box. An optimized density-engineering potential is developed and employed together with phase imprinting to cleanly initialize gray solitons. By means of ab initio simulations with the multiconfiguration time-dependent Hartree method for bosons, we demonstrate that quantum fluctuations limit the lifetime of the soliton contrast, which increases with increasing soliton velocity. A natural orbital analysis reveals a two-stage process underlying the decay of the soliton contrast. The broken parity symmetry of gray solitons results in a local asymmetry of the orbital mainly responsible for the decay, which leads to a characteristic asymmetry of remarkably localized two-body correlations. The emergence and decay of these correlations as well as their displacement from the instantaneous soliton position are analyzed in detail. Finally, the role of phase imprinting for the many-body dynamics is illuminated and additional nonlocal correlations in pairs of counterpropagating gray solitons are observed.
In this thesis, the behavior of ultracold bosonic systems in external potentials is investigated. Such systems are typically realized as Bose-Einstein condensates, where dilute atomic gases cooled to extremely low temperatures exhibit collective quantum behavior. Because of the large degree of control they allow over the external potential and over the interaction parameters of the many-body system, Bose-Einstein condensates constitute a testing ground for the dedicated study of coherence, correlations, and quantum phase transitions in interacting bosonic systems. This thesis presents an investigation of the many-body physics of ultracold bosons, focusing specifically on how the many-body properties of these ultracold bosonic systems change with changing external potential, how they manifest themselves in experimentally accessible observables, and how these properties can be analyzed using both numerical many-body methods and data-driven approaches. The first part of this thesis focuses on the theoretical description of ultracold bosonic systems in external trapping potentials. Using the multiconfigurational time-dependent Hartree method for bosons (MCTDH-X), numerically exact simulations were performed that allow the calculation of reduced density matrices, natural orbitals, and correlation functions. These quantities were used to analyze the coherence properties and fragmentation of trapped bosonic systems. In particular, double-well systems were investigated as model scenarios in which the gradual formation of a central barrier leads to a redistribution of natural occupations and a transition from a condensed to a fragmented many-body state. In this context, we demonstrate the usefulness of single-shot images, which represent projective measurements of the many-body wave function, for the experimental investigation of the many-body physics of fragmenting system. Single-shot images can be simulated numerically using MCTDH-X, but they are more commonly obtained through experimental measurements. The possibility of extracting many-body information in an experimental context, where said many-body information is not otherwise accessible, is discussed. Supervised machine learning models were trained on simulated single-shot data sets to investigate whether information about the underlying many-body state can be inferred directly from measurement outcomes. The results show that machine learning models are capable of learning patterns in the single-shot images that correlate with properties of the underlying many-body state and can therefore predict density-related quantities with good accuracy. The second part of this thesis focuses on a joint theoretical and experimental investigation of a system of ultracold bosons coupled to an optical cavity. In this system, the atoms interact with a dynamically generated optical potential produced by the cavity field. We use a new theoretical framework that combines a mean-field treatment of the cavity field with a many-body description of the atomic degrees of freedom to be able to capture the emergence of a superradiant self-organized phase and the subsequent transition to a self-organized Mott-insulating state. Our simulations show good agreement with the experimental results, and we discuss where the use of a beyond mean-field treatment in the simulations becomes essential in describing the physics of the different involved phases and quantum states. In summary, the results presented in this thesis demonstrate how numerical many-body simulations and machine learning methods can be used to analyze experimentally accessible observables and to gain insight into the many-body physics of ultracold bosonic systems.
In this thesis, the behavior of ultracold bosonic systems in external potentials is investigated. Such systems are typically realized as Bose-Einstein condensates, where dilute atomic gases cooled to extremely low temperatures exhibit collective quantum behavior. Because of the large degree of control they allow over the external potential and over the interaction parameters of the many-body system, Bose-Einstein condensates constitute a testing ground for the dedicated study of coherence, correlations, and quantum phase transitions in interacting bosonic systems. This thesis presents an investigation of the many-body physics of ultracold bosons, focusing specifically on how the many-body properties of these ultracold bosonic systems change with changing external potential, how they manifest themselves in experimentally accessible observables, and how these properties can be analyzed using both numerical many-body methods and data-driven approaches. The first part of this thesis focuses on the theoretical description of ultracold bosonic systems in external trapping potentials. Using the multiconfigurational time-dependent Hartree method for bosons (MCTDH-X), numerically exact simulations were performed that allow the calculation of reduced density matrices, natural orbitals, and correlation functions. These quantities were used to analyze the coherence properties and fragmentation of trapped bosonic systems. In particular, double-well systems were investigated as model scenarios in which the gradual formation of a central barrier leads to a redistribution of natural occupations and a transition from a condensed to a fragmented many-body state. In this context, we demonstrate the usefulness of single-shot images, which represent projective measurements of the many-body wave function, for the experimental investigation of the many-body physics of fragmenting system. Single-shot images can be simulated numerically using MCTDH-X, but they are more commonly obtained through experimental measurements. The possibility of extracting many-body information in an experimental context, where said many-body information is not otherwise accessible, is discussed. Supervised machine learning models were trained on simulated single-shot data sets to investigate whether information about the underlying many-body state can be inferred directly from measurement outcomes. The results show that machine learning models are capable of learning patterns in the single-shot images that correlate with properties of the underlying many-body state and can therefore predict density-related quantities with good accuracy. The second part of this thesis focuses on a joint theoretical and experimental investigation of a system of ultracold bosons coupled to an optical cavity. In this system, the atoms interact with a dynamically generated optical potential produced by the cavity field. We use a new theoretical framework that combines a mean-field treatment of the cavity field with a many-body description of the atomic degrees of freedom to be able to capture the emergence of a superradiant self-organized phase and the subsequent transition to a self-organized Mott-insulating state. Our simulations show good agreement with the experimental results, and we discuss where the use of a beyond mean-field treatment in the simulations becomes essential in describing the physics of the different involved phases and quantum states. In summary, the results presented in this thesis demonstrate how numerical many-body simulations and machine learning methods can be used to analyze experimentally accessible observables and to gain insight into the many-body physics of ultracold bosonic systems.
Strongly interacting finite ensembles of dipolar bosons in commensurately filled one-dimensional 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 and a Tonks–Girardeau gas to a crystal state. The signature of these phases and their transitions can be unequivocally identified by an experimentally detectable order parameter, recently described in Phys. Rev. A 98 235301 (2018 [ 33 ]). 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 a 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 observables, reveal the phase transitions of the system. In particular, spatial localization and momentum delocalization accompany the formation of correlated islands in the density as interactions become stronger. Our study showcases that precise control of intersite correlations is possible through the manipulation of the depth of the lattice, while intrasite correlations can be influenced by changing the dipolar interaction strength.
We study the correlation properties of the ground states of few ultracold bosons, trapped in double wells of varying barrier height in one dimension. Extending previous results on the signature of the transition from a Bose-condensed state via fragmentation to the hard-core limit, we provide a deeper understanding of that transition by relating it to the loss of coherence in the one-body density matrix and to the emerging long-range tail in the momentum spectrum. These are accounted for in detail by discussing the natural orbitals and their occupations. Our discussion is complemented by an analysis of the two-body correlation function.
We present a fully quantum many-body treatment of dark solitons formed by ultracold bosonic atoms in one-dimensional optical lattices. Using time-evolving block decimation to simulate the single-band Bose-Hubbard Hamiltonian, we consider the quantum dynamics of density and phase engineered dark solitons as well as the quantum evolution of mean-field dark solitons injected into the quantum model. The former approach directly models how one may create quantum entangled dark solitons in experiment. While we have already presented results regarding the latter approach elsewhere [R. V. Mishmash and L. D. Carr, Phys. Rev. Lett. 103, 140403 (2009)], we expand upon those results in this work. In both cases, quantum fluctuations cause the dark soliton to fill in and may induce an inelasticity in soliton-soliton collisions. Comparisons are made to the Bogoliubov theory which predicts depletion into an anomalous mode that fills in the soliton. Our many-body treatment allows us to go beyond the Bogoliubov approximation and calculate explicitly the dynamics of the system's natural orbitals.