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We investigate a strongly-correlated Bose gas in an optical lattice.Extending the standard-basis operator method developed by Haley and Erdos to aboson Hubbard model, we calculate excitation spectra in the superfluid phase,as well as in the Mott insulating phase, at T=0. In the Mott phase, theexcitation spectrum has a finite energy gap, reflecting the localized characterof atoms. In the superfluid phase, the excitation spectrum is shown to have anitinerant-localized dual structure, where the gapless Bogoliubov mode (whichdescribes the itinerant character of superfluid atoms) and a band with a finiteenergy gap coexist. We also show that the rf-tunneling current measurementwould give a useful information about the duality of a strongly-correlatedsuperfluid Bose gas near the superfluid-insulator transition.Comment: 10 pages, 4 figure

Itinerant-localized dual character of a strongly correlated superfluid Bose gas in an optical lattice