Statistical mechanics is one of the most comprehensive theories in physics. From a boiling pot of water to the complex dynamics of quantum many-body systems it provides a successful connection between the microscopic dynamics of atoms and molecules a
nd the macroscopic properties of matter. However, statistical mechanics only describes the thermal equilibrium situation of a system, and there is no general framework to describe how equilibrium is reached or under which circumstances it can be reached at all. This problem is particularly challenging in quantum mechanics, where unitarity appears to render the very concept of thermalization counterintuitive. With the rapid experimental progress in the control and probing of ultracold quantum gases this question has become within reach of detailed experimental investigations. In these notes we present a series of experiments with ultracold one-dimensional Bose gases, which provide novel insights into this fundamental question.
Optics and interferometry with matter waves is the art of coherently manipulating the translational motion of particles like neutrons, atoms and molecules. Coherent atom optics is an extension of techniques that were developed for manipulating emph{i
nternal} quantum states. Applying these ideas to translational motion required the development of techniques to localize atoms and transfer population coherently between distant localities. In this view position and momentum are (continuouse) quantum mechanical degree of freedom analogous to discrete internal quantum states. In our contribution we start with an introduction into matter-wave optics in section 1, discuss coherent atom optics and atom interferometry techniques for molecular beams in section 2 and for trapped atoms in section 3. In section 4 we then describe tools and experiments that allow us to probe the evolution of quantum states of many-body systems by atom interference.
The experimental realisation of large scale many-body systems has seen immense progress in recent years, rendering full tomography tools for state identification inefficient, especially for continuous systems. In order to work with these emerging phy
sical platforms, new technologies for state identification are required. In this work, we present first steps towards efficient experimental quantum field tomography. We employ our procedure to capture ultracold atomic systems using atom chips, a setup that allows for the quantum simulation of static and dynamical properties of interacting quantum fields. Our procedure is based on cMPS, the continuous analogues of matrix product states (MPS), ubiquitous in condensed-matter theory. These states naturally incorporate the locality present in realistic physical settings and are thus prime candidates for describing the physics of locally interacting quantum fields. The reconstruction procedure is based on two- and four-point correlation functions, from which we predict higher-order correlation functions, thus validating our reconstruction for the experimental situation at hand. We apply our procedure to quenched prethermalisation experiments for quasi-condensates. In this setting, we can use the quality of our tomographic reconstruction as a probe for the non-equilibrium nature of the involved physical processes. We discuss the potential of such methods in the context of partial verification of analogue quantum simulators.
