A theoretical study of interacting bosons in a periodic optical lattice is presented. Instead of the commonly used tight-binding approach (applicable near the Mott-insulating regime of the phase diagram), the present work starts from the exact single-particle states of bosons in a cubic optical lattice, satisfying the Mathieu equation, an approach that can be particularly useful at large boson fillings. The effects of short-range interactions are incorporated using a self-consistent Hartree-Fock approximation, and predictions for experimental observables such as the superfluid transition temperature, condensate fraction, and boson momentum distribution are presented.
Publication Source (Journal or Book title)
Physical Review A - Atomic, Molecular, and Optical Physics
Lü, Q., Patton, K., & Sheehy, D. (2014). Self-consistent Hartree-Fock approach for interacting bosons in optical lattices. Physical Review A - Atomic, Molecular, and Optical Physics, 90 (6) https://doi.org/10.1103/PhysRevA.90.063625