In this talk I will discuss the phase diagram and excitation spectra of correlated bosons with nearest and next-nearest neighbor interactions. The study of this system is motivated by the recent experiment on the Bose-Einstein condensation of chromium atoms with long-range dipolar interactions. The ground state phase diagram, calculated using the Gutzwiller Ansatz, shows, apart from the superfluid and the Mott insulator, two modulated phases, the charge density wave and the supersolid. Excitation spectra are also calculated which show a gap in the insulators, gapless, phonon mode in the superfluid and the supersolid, and a mode softening of superfluid excitations in the vicinity of the modulated phases. I will discuss the possibility of observing these phases in cold dipolar atoms and the ways to detect them.

LPTMS