  We suggest to view ultracold atoms in a time-periodically shifted optical
lattice as a "dressed matter wave", analogous to a dressed atom in an
electromagnetic field. A possible effect lending support to this concept is a
transition of ultracold bosonic atoms from a superfluid to a Mott-insulating
state in response to appropriate "dressing" achieved through time-periodic
lattice modulation. In order to observe this effect in a laboratory experiment,
one has to identify conditions allowing for effectively adiabatic motion of a
many-body Floquet state.
