Multiorbital mean-field approach for bosons, spinor bosons, and Bose-Bose and Bose-Fermi mixtures in real-space optical lattices

Cold atoms in optical lattices are described in real space by the multiorbital mean-field approach. We consider four typical systems: (i) spinless identical bosons, (ii) spinor identical bosons, (iii) Bose-Bose mixtures, and (iv) Bose-Fermi mixtures, and derive in each case the corresponding multiorbital mean-field energy functional and working equations. The general equations as well as those obtained by explicitly utilizing the translational symmetry of lattices are presented. We discuss the effects of particle-particle interactions and translational symmetry on properties of the solutions.