  Intensity modulated optical lattice potentials can change sign for an alkali
metal Rydberg atom, and the atoms are not always attracted to intensity minima
in optical lattices with wavelengths near the CO$_2$ laser band. Here we
demonstrate that such IR lattices can be tuned so that the trapping potential
seen by the Rydberg atom can be made to vanish for atoms in \targeted" Rydberg
states. Such state selective trapping of Rydberg atoms can be useful in
controlled cold Rydberg collisions, cooling Rydberg states, and
species-selective trapping and transport of Rydberg atoms in optical lattices.
We tabulate wavelengths at which the trapping potential vanishes for the $n$s,
$n$p, and $n$d Rydberg states of Na and Rb atoms, and discuss advantages of
using such optical lattices for state selective trapping of Rydberg atoms. We
also develop exact analytic expressions for the lattice induced polarizability
for the $m_z = 0$ Rydberg states, and derive an accurate formula predicting
tune-out wavelengths at which the optical trapping potential becomes invisible
to Rydberg atoms in targeted $l = 0$ states.
