In this thesis, we have investigated strongly correlated bosonic gases in an
optical lattice, mostly based on a bosonic version of dynamical mean field theory
and its real-space extension. Emphasis is put on possible novel quantum
phenomena of these many-body systems and their corresponding underlying
physics, including quantum magnetism, pair-superfluidity, thermodynamics,
many-body cooling, new quantum phases in the presence of long-range interactions,
and excitational properties. Our motivation is to simulate manybody
phenomena relevant to strongly correlated materials with ultracold lattice
gases, which provide an excellent playground for investigating quantum
systems with an unprecedented level of precision and controllability. Due to
their high controllability, ultracold gases can be regarded as a quantum simula-
tor of many-body systems in solid-state physics, high energy astrophysics, and
quantum optics. In this thesis, specifically, we have explored possible novel
quantum phases, thermodynamic properties, many-body cooling schemes, and
the spectroscopy of strongly correlated many-body quantum systems. The
results presented in this thesis provide theoretical benchmarks for exploring
quantum magnetism in upcoming experiments, and an important step towards
studying quantum phenomena of ultracold gases in the presence of long-range
interactions.