Merging quantum optics and quantum many-body atomic systems

A system joining the problems of quantum optics and quantum gases ultracold atoms trapped in an optical lattice inside a cavity is considered. Thus, the quantum natures of both the light and atomic motion play equally important roles in the process. This is in striking contrast to the majority of theoretical and experimental problems on ultracold gases, where the role of light is reduced to a classical auxiliary tool for trapping and manipulating intriguing atomic states.