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The energy spectrum of a system of Bose atoms in the superfluid phase in anoptical lattice of the graphene type has been studied. The dispersion laws forthe energy bands and the single particle spectral densities are calculated inthe random phase approximation and in the framework of the hard-core bosonformalism, and their changes at the transition from the normal phase to thesuperfluid one are described. As a result of this transformation, the number ofsubbands doubles. In the case of the subband energetic equivalence, the Diracpoints in the spectrum survive, and their number becomes twice as much. Whenthe subbands are energetically nonequivalent, the Dirac points are absent. Theshape of spectral densities is shown to be sensitive to the changes in thetemperature and the chemical potential position.

Investigation of the bosonic spectrum of two-dimensional optical graphene-type lattices. Superfluid phase