Absence of Far-Detuned Attractive Optical Traps for Alkali Rydberg Atoms

Neutral-atom quantum simulation is susceptible to entanglement between the atom's internal electronic state and its center-of-mass position. In many alkali Rydberg platforms, the'spin-motion coupling'is exacerbated by the free expansion required to avoid ponderomotive anti-trapping from optical fields. A recent proposal (arXiv:2505.01071) claims sufficiently excited Rydberg states could be trapped in a monochromatic, far-detuned, circularly polarized optical field by harnessing a large vector polarizability. We disprove the proposal through analytic calculation and measurement of the vector polarizability of the $54S$, $54P$, and $53D$ orbitals of Cesium. Regarding the optical angular frequency $\omega$, we analytically derive that the scalar, vector, and tensor polarizabilities scale as $\omega^{-2}$, $\omega^{-3}$, and $\omega^{-4}$, as opposed to the proposed scaling of $\omega^{-2}$, $\omega^{-1}$, and $\omega^{-2}$. We refine the sum-over-states expression for vector and tensor polarizability to be numerically stable and predict negligible vector and tensor polarizabilities far detuned from resonances, in agreement with our measurements. However, we find vector polarizability can enhance a recent proposal for near-detuned attractive trapping. Furthermore, we evaluate the breakdown of the electric-dipole approximation and derive no effect stronger than ponderomotive repulsion. We conclude that an attractive, monochromatic, far-detuned optical trap for alkali Rydberg states is not possible, regardless of the beam geometry.