  We explore quantum many-body physics of a driven Bose-Einstein condensate in
optical lattices. The laser field induces a gap in the generalized Bogoliubov
spectrum proportional to the effective Rabi frequency. The lowest lying modes
in a driven condensate are characterized by zero group velocity and non-zero
current. Thus, the laser field induces roton modes, which carry interaction in
a driven condensate. We show that collective excitations below the energy of
the laser-induced gap remain undamped, while above the gap they are
characterized by a significantly suppressed Landau damping rate.

Quantum Gases;Quantum Physics