Many-body physics of ultracold bosons: numerical simulations, single-shot images, and machine learning
Miriam Büttner, Michael Thoss, Heinz‐Peter Breuer
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.
•Jul 22, 2026•0 citations