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Intensity modulated optical lattice potentials can change sign for an alkalimetal Rydberg atom, and the atoms are not always attracted to intensity minimain optical lattices with wavelengths near the CO$_2$ laser band. Here wedemonstrate that such IR lattices can be tuned so that the trapping potentialseen by the Rydberg atom can be made to vanish for atoms in \targeted" Rydbergstates. Such state selective trapping of Rydberg atoms can be useful incontrolled cold Rydberg collisions, cooling Rydberg states, andspecies-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 ofusing such optical lattices for state selective trapping of Rydberg atoms. Wealso develop exact analytic expressions for the lattice induced polarizabilityfor the $m_z = 0$ Rydberg states, and derive an accurate formula predictingtune-out wavelengths at which the optical trapping potential becomes invisibleto Rydberg atoms in targeted $l = 0$ states.

Tune-out wavelengths and landscape modulated polarizabilities of alkali Rydberg atoms in infrared optical lattices