Temperature-dependent excitation spectra of ultra-cold bosons in optical lattices

Trapping ultra-cold atoms in optical lattices provides a unique environment for investigating quantum phase transitions between strongly correlated superfluid and Mott insulator phases. One of the major complications in the analysis of experiments is establishing of criteria for identifying the superfluid phase. Sharp features occurring while entering ordered state have been recognized as a signature of superfluidity. In the present work it is shown that sharp peaks are not necessarily a reliable diagnostic of phase coherence in these systems. Using the combined Bogoliubov method and the quantum rotor approach for phase variables, we calculate the momentum and energy-resolved single-particle spectral function $A(\mathbf{k}\omega)$ at arbitrary temperature $T$ and its shape in the presence of the superfluid phase. We find that in the two-dimensional system even at $T>0$, where condensate fraction vanishes, the remnants of the sharp coherence peak in $A(\mathbf{k}\omega)$ are present. In contrast, such a feature is not observed for the bosons loaded in the three-dimensional lattice.