Correlated Quantum Dynamics of Ultracold Few- to Many-Body Systems
This course is dedicated to the exploration of the quantum dynamics out of equilibrium for ultracold quantum gases ranging from the correlated quantum dynamics in optical lattices to the beyond mean-field behaviour of solitons. Following a brief introduction to the field of ultracold quantum gases and Bose-Einstein condensation we focus on the structure and dynamics of ultracold bosons in traps via a bottom up approach. Analytical models are presented and explained in order to provide a basis for the more complex non-integrable many-body systems. Our approach to investigate the non-equilibrium quantum dynamics for bosonic (fermionic) ensembles is the Multi-Layer Multi-Configuration Time-Dependent Hartree method for bosons (fermions) (ML-MCTDHB or ML-MCTDHF). Basic principles of this approach and the working equations are presented and analyzed. A series of applications will follow. Firstly we demonstrate in a `bottom-up approach' the correlated many-particle effects in the collective breathing dynamics for few- to many-boson systems in a harmonic trap. Many-body processes in black and grey matter-wave solitons are explored thereby demonstrating that quantum fluctuations limit the lifetime of the soliton contrast, which increases with increasing soliton velocity. For atomic ensembles in optical lattices we explore the interaction quench induced multimode dynamics leading to the emergence of density-wave tunneling, breathing and cradle-like processes. A particular far from equilibrium system is then studied at hand of the correlated quantum dynamics of a single atom collisionally coupled to a finite bosonic reservoir. In the last part of the presentation we provide some selective aspects of our recent investigations on atom-ion hybrid systems using the same methodology. First the ground state properties of ultracold trapped bosons with an immersed ionic impurity are discussed. Subsequently the capture dynamics of ultracold atoms in the presence of the impurity ion is explored.