Magic wavelengths for the $5s\text{–}18s$ transition in rubidium

Magic wavelengths, for which there is no differential ac Stark shift for the ground and excited state of the atom, allow trapping of excited Rydberg atoms without broadening the optical transition. This is an important tool for implementing quantum gates and other quantum information protocols with Rydberg atoms, and reliable theoretical methods to find such magic wavelengths are thus extremely useful. We use a high-precision all-order method to calculate magic wavelengths for the $5s\text{−}18s$ transition of rubidium, and compare the calculation to experiment by measuring the light shift for atoms held in an optical dipole trap at a range of wavelengths near a calculated magic value.

Figure 1

Magic wavelengths $\lambda$ (in nm) for the $18s$ state in rubidium, determined as crossing of the $5s$ and $18s$ dynamic polarizabilities (in a.u.). Two magic wavelengths near the $18s\text{−}6p_{1/2}$ and $18s\text{−}6p_{3/2}$ resonances are shown.

Figure 2

Determination of the uncertainty in the Rb $18s\text{−}5s$ magic wavelength.

Figure 3

(a) Measured $5s\text{−}18s$ light shift near the $6p_{3/2}\text{−}18s$ transition with a dispersive fit to the data. Inset is an example single-shot fluorescence spectrum with a Gaussian fit to extract the transition frequency (in terms of the probe detuning from the intermediate $5p_{1/2}$ state). (b) Zoomed in on the region of the magic wavelength with a $1/x$ power law fit to the data (blue) and calculated polarizability (red) with width equal to the $18s$ polarizability uncertainty. Shaded regions are the uncertainties on the calculated (red) and experimentally extracted (blue) magic wavelengths.