Theoretical Study of Quantum Phase Transition in Bosonic Gases trapped by Both Periodic and Quasi-periodic Optical Lattices

Abstract

We qualitatively study the microscopic properties of a bosonic condensate in a periodic optical lattice through the homogeneous Bose-Hubbard model, and in a quasi-periodic lattice through the inhomogeneous Bose-Hubbard model. Both models are solved analytically through the Mean Field Approach. We emphasize the didactic aspect of the study with descriptive richness in the mathematical aspect.

Keywords:
Bose-Hubbard Hamiltonian; Optical Lattices; Quantum Phase Transitions