Intensity landscape and the possibility of magic trapping of alkali-metal Rydberg atoms in infrared optical lattices

Motivated by compelling advances in manipulating cold Rydberg (Ry) atoms in optical traps, we consider the effect of the large extent of a Ry electron wave function on trapping potentials. We find that, when the Ry orbit lies outside inflection points in the laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron ac polarizability of the Ry electron is modulated by the intensity landscape and can accept both positive and negative values. We apply these insights to determining the magic wavelengths for Ry-ground-state transitions for alkali-metal atoms trapped in infrared optical lattices. We find magic wavelengths to be around $10\mu \mathrm{m}$ with exact values that depend on Ry-state quantum numbers.

Figure 1

Influence of Ry orbit size on the stability of atomic motion at the 1D lattice antinode for a toy model of a Ry atom. The vertical axis is the laser intensity $I\left(z\right)$. The electron cloud is localized in two “lumps”. The optical dipole force exerted on each lump is directed towards the nearby intensity minimum and is proportional to the local intensity slope $dI\left(z\right)/dz$. When the Ry orbit size is $2z_e<\lambda /4$ [panel (a)], the ${\mathbf{f}}_R$ and ${\mathbf{f}}_L$ acting on the localized lumps of electron density pull the atom away from the intensity maximum (unstable equilibrium). When $2z_e>\lambda /4$ [panel (b)], they act as restoring forces with the Ry atom stably resting at the intensity maximum.

Figure 2

The “landscape-modulated” polarizability ${\alpha }_r^{\mathrm{lsc}}$ for $ns$ states of Rb with $n=100$ (dashed orange line), 160 (dashed black line), and 180 (dashed blue line). The scalar ground-state polarizability ${\alpha }_g$ (solid red line) and the free-electron polarizability ${\alpha }_e$ (dashed gray line) are also shown. The magic wavelengths can be found for all $n\ge 154$ in the infrared wavelength range spanning the ${\mathrm{CO}}_2$ and the frequency-doubled ${\mathrm{CO}}_2$ laser bands.