Quantum simulations generated by ultra-cold atoms inoptical lattices

Ultra-cold bosonic atoms trapped in optical lattice potentials have an important role in quantum simulation studies. The adjustable optical lattice parameters and interactions between bosons allow phase transitions to be controlled in such systems. Interphase transitions are widely used in quantum computing. In particular, the Mott insulator phase, where tunneling between lattice sites is suppressed, is matched with qubits. The Bose-Hubbard model is used to analyze the behavior of bosons in the optical lattice potentials. In this thesis, the three-well Bose-Hubbard model, which has many application areas, was theoretically considered. The effects of interatomic dipolar interactions and time-dependent tunneling amplitudes on phase transitions were investigated. Numerical results for the superfluid and Mott insulator phases, which are compatible with the literature, have been obtained.