# Tug-of-war model and tuned-out Rydberg

Tug-of-war model for a Rydberg atom in optical lattice.  I(z) is the lattice intensity dependence and the atom is made out of a nucleus and two lumps of electronic wave function. For a certain distance between the lumps ($\lambda/4$),  optical forces on the two lumps cancel each other no matter what the atomic position is.

Finally a chance for a Rydberg atom to tune out, chill out and be all it ever wanna be. Would not it be great to just sail through life hurdles without ever noticing them? Now Rydberg atoms can just do that easily and naturally, thanks to the latest theoretical understanding coming from our group.

We find special "tune-out conditions" that guarantee that Rydberg atom motion remains uninhibited by optical lattice. This is illustrated by  the tug-of-war Figure to the left. Here a 1D Rydberg atom is made out of a nucleus and two rigidly placed lumps of electronic density.  The total dipole optical force vanishes  when the diameter of the orbit is equal to half the lattice constant.

For the 3D case, realistic atoms, and all the technical details, see our publication:
Tune-out wavelengths and landscape-modulated polarizabilities of alkali-metal Rydberg atoms in infrared optical lattices, T. Topcu, A. Derevianko, Phys. Rev. A 88, 053406 (2013) arXiv:1308.6258

Here is the abstract:
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 CO2 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 ns, np, and nd 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.