Excitation spectrum of Mott shells in optical lattices

We theoretically study the excitation spectrum of confined macroscopic optical lattices in the Mott-insulating limit. For large systems, a fast numerical method is proposed to calculate the ground state filling and excitation energies. We introduce many-particle on-site energies capturing multi-band effects and discuss tunnelling on a perturbative level using an effectively restricted Hilbert space. Results for small one-dimensional lattices obtained by this method are in good agreement with the exact multi-band diagonalization of the Hamiltonian. Spectral properties associated with the formation of regions with constant filling, so-called Mott shells, are investigated and interfaces between the shells with strong particle fluctuations are characterized by gapless local excitations

Localization and delocalization of ultracold bosonic atoms in finite optical lattices

We study bosonic atoms in small optical lattices by exact diagonalization and observe a striking similarity to the superfluid to Mott insulator transition in macroscopic systems. The momentum distribution, the formation of an energy gap, and the pair correlation function show only a weak size dependence. For noncommensurate filling we reveal in deep lattices a mixture of localized and delocalized particles, which is sensitive to lattice imperfections. Breaking the lattice symmetry causes a Bose-glass-like behavior. We discuss the nature of excited states and orbital effects by using an exact diagonalization technique that includes higher bands.Comment: 8 pages, 10 figures. Published versio

Self-Trapping of Bosons and Fermions in Optical Lattices

We theoretically investigate the enhanced localization of bosonic atoms by fermionic atoms in three-dimensional optical lattices and find a self-trapping of the bosons for attractive boson-fermion interaction. Because of this mutual interaction, the fermion orbitals are substantially squeezed, which results in a strong deformation of the effective potential for bosons. This effect is enhanced by an increasing bosonic filling factor leading to a large shift of the transition between the superfluid and the Mott-insulator phase. We find a nonlinear dependency of the critical potential depth on the boson-fermion interaction strength. The results, in general, demonstrate the important role of higher Bloch bands for the physics of attractively interacting quantum gas mixtures in optical lattices and are of direct relevance to recent experiments with 87Rb - 40K mixtures, where a large shift of the critical point has been found.Comment: 4 pages, 4 figures. Published versio