The properties of a Rydberg atom immersed in an ultracold environment were investigated. Two scenarios were considered, one of which involves the neighbouring ground-state atoms arranged in a spatially structured configuration, while the other involves them distributed randomly in space. To calculate the influence of the multiple ground-state atoms on the Rydberg atom, Fermi-pseudopotential was used, which simplified greatly the numerical effort. In many cases, the few-body interaction can be written down analytically which reveals the symmetry properties of the system. In the structured case, we report the first prediction of the formation of ``Rydberg Borromean trimers''. The few-body interactions and the dynamics of the linear A-B-A trimer, where A is the ground-state atom and B is the Rydberg atom, were investigated in the framework of normal mode analysis. This exotic ultralong-range triatomic bound state exists despite that the Rydberg-ground-state interaction is repulsive. Their lifetimes were estimated using both quantum scattering calculations and semi-classical approximations which are found to be typically sub-microseconds. In the disordered case, the Rydberg-excitation spectra of a frozen-gas were simulated, where the nuclear degrees of freedom can be ignored. The systematic change of the spectral shape with respect to the density of the gas and the excitation of the Rydberg atom were found and studied. Some parts of the spectral shape can be described by simple scaling laws with exponents given by the basic properties of the atomic species such as the polarizability and the zero-energy electron-atom scattering length.

The advent of laser cooling of atoms led to the discovery of ultra-cold matter, with temperatures below liquid Helium, which displays a variety of new physical phenomena. Physics of Ultra-Cold Matter gives an overview of this recent area of science, with a discussion of its main results and a description of its theoretical concepts and methods. Ultra-cold matter can be considered in three distinct phases: ultra-cold gas, Bose Einstein condensate, and Rydberg plasmas. This book gives an integrated view of this new area of science at the frontier between atomic physics, condensed matter, and plasma physics. It describes these three distinct phases while exploring the differences, as well as the sometimes unexpected similarities, of their respective theoretical methods. This book is an informative guide for researchers, and the benefits are a result from an integrated view of a very broad area of research, which is limited in previous books about this subject. The main unifying tool explored in this book is the wave kinetic theory based on Wigner functions. Other theoretical approaches, eventually more familiar to the reader, are also given for extension and comparison. The book considers laser cooling techniques, atom-atom interactions, and focuses on the elementary excitations and collective oscillations in atomic clouds, Bose-Einstein condensates, and Rydberg plasmas. Linear and nonlinear processes are considered, including Landau damping, soliton excitation and vortices. Atomic interferometers and quantum coherence are also included.