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In this article we present a new representation-free formalism, which can significantly simplify the analysis of interferometers comprised of atoms moving in time-dependent linear potentials.We present a methodology for the construction of two pairs of time-dependent functions that, once determined, lead to two conditions for the closing of the interferometer, and determine the phase and the contrast of the resultant interference. Using this new formalism, we explore the dependency of the interferometer phase on the interferometer time T for different atom interferometers. By now, it is well established that light pulse atom interferometers of the type first demonstrated by Kasevich and Chu (1991 Phys. Rev. Lett. 67, 181–4; 1992 Appl. Phys. B 54, 321–32), henceforth referred to as Mach– Zehnder (MZ) atom interferometers, have a phase scaling as T2. A few years ago, McDonald et al (2014 Europhys. Lett. 105, 63001) have experimentally demonstrated a novel type of atom interferometer, referred to as the continuous-acceleration bloch (CAB) interferometer, where the phase reveals a mixed scaling which is governed by a combination of T2 and T3. Moreover, we have recently proposed a different type of atom interferometer (Zimmermann et al 2017 Appl. Phys. B 123, 102), referred to as the T3-interferometer, which has a pure T3 scaling, as demonstrated theoretically. Finally, we conclude that the CAB interferometer can be shown to be a hybrid of the standardMZinterferometer and the T3-interferometer., publishedVersion

We show that the expectation value of the operator Ô ≡ exp (−cx̂²) + exp (−cpˆ²) defined by the position and momentum operators x̂ and pˆ with a positive parameter c can serve as a tool to identify quantum non-Gaussian states, that is states that cannot be represented as a mixture of Gaussian states. Our condition can be readily tested employing a highly efficient homodyne detection which unlike quantum-state tomography requires the measurements of only two orthogonal quadratures. We demonstrate that our method is even able to detect quantum non-Gaussian states with positive–definite Wigner functions. This situation cannot be addressed in terms of the negativity of the phase-space distribution. Moreover, we demonstrate that our condition can characterize quantum non-Gaussianity for the class of superposition states consisting of a vacuum and integer multiples of four photons under more than 50 % signal attenuation., publishedVersion

This cumulative thesis presents four publications (I)-(IV), Refs. [1-4], resulting from the author's research activities under the supervision of apl. Prof. Dr. M. A. Efremov at the Institut f��r Quantenphysik at Universit��t 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).