Momentum-resolved spectral function of ultracold bosons in two-dimensional optical lattices

Abstract

The excitations of strongly interacting bosons confined in a two-dimensional square lattice are studied. Using a combined Bogoliubov method and the quantum-rotor approach, the Hamiltonian of strongly interacting bosons is mapped onto the $U(1)$-phase action. This allows to calculate the momentum- and energy-resolved one-particle spectral function and its dependence on the presence of the superfluid phase. It is shown that the destruction of the ordered phase leads to the opening of the gap in the excitation spectrum in $\mathbf{k}=\mathbf{0}$. On the other hand, superfluidity manifests itself as a sharp coherence peak resulting from the emergence of the long-range order. Correlation effects lead to the appearance of a smearing of the band structure of incoherent particles although the remnants of the Bogoliubov excitations are still present in the coherent part of the spectrum.