Quantum non-Gaussianity and universality of one-dimensional three-body bound states

This cumulative thesis presents four publications (I)-(IV), (I) L. Happ, M. A. Efremov, H. N. Nha, and W. P. Schleich, Sufficient condition for a quantum state to be genuinely quantum non-Gaussian, New J. Phys. 20, 023046 (2018). (II) L. Happ, M. Zimmermann, S. I. Betelu, W. P. Schleich, and M. A. Efremov, Universality in a one-dimensional three-body system, Phys. Rev. A 100, 012709 (2019). (III) L. Happ, M. Zimmermann, and M. A. Efremov, Universality of excited three-body bound states in one dimension, J. Phys. B: At. Mol. Opt. Phys. 55, 015301 (2022). (IV) L. Happ and M. A. Efremov, Proof of universality in one-dimensional few-body systems including anisotropic interactions, J. Phys. B: At. Mol. Opt. Phys. 54, 21LT01 (2021), resulting from the author's research activities under the supervision of apl. Prof. Dr. M. A. Efremov at the Institut für Quantenphysik at Universität Ulm. These publications range over the scope of two subfields of quantum physics, namely quantum information theory and few-body physics. Accordingly, we have organized this thesis in two parts, each of which has its own introduction, conclusion and outlook. The first part is centered around publication (I) which concludes the author's work in the field of quantum information theory. This publication aims at classifying quantum states, in particular it presents a novel sufficient condition to determine whether a quantum state is genuinely quantum non-Gaussian. The class of non-Gaussian states are important in many aspects of quantum information, e.g. entanglement distillation or enhancing quantum teleportation. The condition relies on an upper border for the possible measurement outcomes of a hermitian operator. This operator consists of two orthogonal phase space quadratures and can therefore be measured employing standard techniques in quantum optics experiments. Unlike many other criteria on non-Gaussianity, our condition is shown to be powerful in detecting the non-Gaussian character of quantum states even when the experiment is subject to significant imperfections of the measurement devices. The second part of the thesis is based on the publications (II)-(IV) and contains the main part of the author's research which is placed in the field of few-body physics. Here, the main focus lies on universal behavior, a property which allows to apply the corresponding results to physical systems of various fields, e.g. ultracold atoms or systems of nuclear particles. At the heart of our studies is a mass-imbalanced quantum mechanical three-body system confined to one spatial dimension. In contrast to the three-dimensional case, the situation in one spatial dimension is much less studied and requires research efforts on a more fundamental level. In particular, in publication (II) we have analyzed the energy spectrum and wave functions of three-body bound states in this system. More precisely, we have proved that in the weakly-interacting limit, the three-body results for a large class of short-range two-body interactions show universal behavior and converge to those obtained for the zero-range contact interaction. The publications (III) and (IV) follow up on these results, and we have revealed how several properties of finite-range two-body interactions, which cannot be modeled by the contact interaction, affect the aforementioned universality of the three-body results. These properties correspond to relevant situations in experiments of ultracold atoms, and include interactions that are resonant but not necessarily weak (III), and interactions with anisotropic features (IV).