Abstract
A study was conducted to access quantum phase transitions (QPT) at near-absolute-zero temperatures by changing an external parameter or a coupling constant driven by quantum fluctuations. These studies investigated QPTs in interacting many-body-problems for strongly correlated electronic systems in condensed matter physics and for a weakly interacting ultracold atomic system. The investigations revealed that the many-body dynamics can be described from a Mott-insulating phase to a superfluid phase in a gas of ultracold atoms with periodic potentials by using a Bose-Hubbard model that included an on-site two-atom interaction and hopping between neighboring sites. It was also revealed that engineered composites of optical cavities, few-level atoms, and laser light can form a strongly interacting many-body system to investigate the concepts and methods in condensed matter physics as required by quantum optics.