We investigate a strongly-correlated Bose gas in an optical lattice.
Extending the standard-basis operator method developed by Haley and Erdos to a
boson 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, the
excitation spectrum has a finite energy gap, reflecting the localized character
of atoms. In the superfluid phase, the excitation spectrum is shown to have an
itinerant-localized dual structure, where the gapless Bogoliubov mode (which
describes the itinerant character of superfluid atoms) and a band with a finite
energy gap coexist. We also show that the rf-tunneling current measurement
would give a useful information about the duality of a strongly-correlated
superfluid Bose gas near the superfluid-insulator transition.Comment: 10 pages, 4 figure