  We show how it is possible to more than double the on-site interaction energy
of neutral atoms in optical potentials by the technique of radio-frequency (rf)
dressing, while maintaining interwell dynamics. We calculate Bose-Hubbard
parameters for rf dressed optical lattices and arrays of rf dressed dipole
traps. We show that decreasing the distance between wells, by the interpolation
of wells confining different m_F states, increases the interaction energy more
than decreasing the height of the classically forbidden region between existing
wells. The schemes we propose have negligible Landau-Zener losses caused by
atomic motion; this was a dominant effect in the first experimental
demonstration of the modification of an optical potential by radio-frequency
dressing.
