State-Dependent Energy Shifts of Rydberg Atoms in a Ponderomotive Optical Lattice

We demonstrate the state dependence of the ponderomotive energy shift of Rydberg atoms in an optical lattice using microwave spectroscopy. Unique to Rydberg atoms, this dependence results from a state-dependent aspect ratio between Rydberg-atom size and lattice period. A semiclassical simulation reproduces all features observed in the microwave spectra and indicates the presence of trapped Rydberg atoms.

Figure 1

Effect of atom size on ponderomotive level shifts of Rydberg atoms in an optical lattice. (a) The level shifts are averages over the free-electron ponderomotive potential (dotted curve; maximum height ${\kappa }_{\mathrm{free}}$) weighted by the Rydberg electron’s density distribution. Hence, the lattice potentials of large Rydberg atoms tend to be shallower than those of small ones (sold curves; maximum height ${\alpha }_n{\kappa }_{\mathrm{free}}$, with state-dependent reduction factors $0<{\alpha }_n<1$). (b) Calculated frequency shift, $({\alpha }_{n+1}-{\alpha }_n){\kappa }_{\mathrm{free}}$, of the Rb $nS\to (n+1)S$ transition at a lattice maximum as a function of $n$.

Figure 2

Laser excitation spectra of the $50S$ Rydberg level for the dipole trap and optical lattice, obtained by scanning the upper transition laser. The dashed vertical line represents the approximate maximal lattice-induced shift. Inset: Diagram of laser beams used for Rydberg excitation and for creating the optical lattice.

Figure 3

Microwave spectra of the $50S\to 51S$ transition outside of the lattice and for three different lattice-induced shifts. The thick green line shows the results of a numerical simulation (see text). (For clarity, spectra are staggered vertically.)

Figure 4

Microwave spectra of the $62S\to 63S$ and $68S\to 71S$ transitions. (Spectra are staggered vertically.)