Dependence of Rydberg-Atom Optical Lattices on the Angular Wave Function

We investigate the dependence of optical-lattice trapping potentials for Rydberg atoms on the angular portion of the atomic wave function. While ground-state atoms are pointlike in relation to an optical-lattice field, Rydberg-atom wave functions extend over a substantial fraction of the lattice period, which leads to a dependence of the lattice trapping potential on the angular portion of the spatial wave function. The angular dependence of the potential is measured using various ($j$, $m_j$) levels of ${}^{85}\mathrm{Rb}$ Rydberg $nD$ states ($50\le n\le 65$) prepared in a one-dimensional optical lattice (wavelength 1064 nm) and a transverse dc electric field. The measured optical-lattice depths are found to be in agreement with theoretical results.

Figure 1

Optical excitation spectrum of the $50D$ Rydberg level in the lattice and a transverse dc electric field. The Stark components, labeled 1–5, exhibit structures on the high-frequency side that reflect lattice-induced shifts of the optical transitions. Inset: ground and Rydberg levels in the lattice. The arrows indicate how the maxima in the experimental spectrum correlate with the shapes of the lattice potentials.

Figure 2

Optical excitation spectra for level 2 of Fig. 1 in a transverse dc field and a noninverted lattice and inverted lattice. Spectral features, indicated by arrows, enable a measurement of the Rydberg-state lattice depth (${\kappa }_{\mathrm{Ryd}}$).

Figure 3

Symbols: Measured vs calculated POL potential depths for the levels listed in Table . The error bars reflect systematic and measurement uncertainties. Line: a linear fit to the data points.

Figure 4

Calculated depth of the $65D$ POL potentials ${\kappa }_{\mathrm{Ryd}}$ in units of the free-electron POL depth ${\kappa }_{\mathrm{free}}$ for various Stark levels as a function of the dc field. The level labeling follows the scheme used in Fig. 1. Negative POL depths correspond to cases in which the Rydberg-atom center of mass is attracted to intensity maxima in the lattice.