title: From few- to many-body physics in low-dimensional quantum gases
Creators: name: Brauneis, Fabian
Publisher: name: UNSPECIFIED
Year: 2024

description: Macroscopic systems exhibit complex behavior that cannot be understood by studying their few-body components alone. A key challenge in modern physics is to uncover how many-body phenomena emerge from the underlying few-body world. One approach to this problem is to study properties of the system as the particle number increases. Motivated by recent experimental advancements enabling such investigations in ultracold atom systems, this thesis contributes to three goals of the field "few-to-many-body crossover": 1) Advance numerical investigations of this crossover by improving theoretical tools. 2) Connect many-body concepts with the description of few-to-many systems. 3) Explore basic physics of few-body systems to facilitate new many-body research.

We contribute to the first goal by comparing different renormalization methods for the one-dimensional contact interaction. Although this interaction requires no regularization, renormalized interactions have been shown to significantly improve the convergence of ab initio calculations. This expands the accessible parameter space, allowing one to study systems with stronger interactions and larger particle numbers. Our results address a gap in the literature by contrasting commonly used renormalized interactions in cold atom setups, providing valuable guidance for selecting the most suitable renormalization scheme.

Next, we study a one-dimensional system of bosons with a repulsively interacting impurity. Impurities are important for few-to-many studies because they act as probes of the environment. We introduce an experimentally motivated Hamiltonian and connect its energy spectrum to a quasi-particle known as the Bose polaron, thereby achieving the second goal. The connection with this many-body concept offers an intuitive understanding of the system. It enables the exploration of the few-to-many-body crossover in cold-atom polaron problems beyond conventional observables.

In a separate study, we investigate an attractive impurity interacting with bosons in one dimension. The attractive interaction complicates many-body studies of this system as the impurity forms a bound state with the bosons. Therefore, our focus is on characterizing this state. For example, we derive the maximum number of bosons that can be bound to the impurity. This few-body analysis addresses the third goal by providing key insights for many-body research on one-dimensional attractive impurities.

In the final part of this thesis, we examine a two-dimensional system of attractively interacting bosons. Previous research has demonstrated that this system exhibits intriguing universal behavior. Given that most experiments are performed in harmonic traps, we study the influence of such confinement. Specifically, we investigate the transition from a trap-dominated state to an interaction-dominated one. Inspired by the many-body concept of phases, we introduce an observable that can be used as an indicator of the transition in few-to-many systems, contributing to the second goal. Furthermore, we also add to the third goal by studying finite range effects in the few-body sector.