Stark effect in the nonuniform field and its influence on the fine structure of Rydberg blockade

TL;DR

This paper investigates how nonuniform electric fields affect the energy levels of hydrogen-like atoms, revealing a significant impact on Rydberg blockade's fine spatial structure and deriving explicit formulas for energy shifts.

Contribution

It provides an explicit formula for energy level splitting in nonuniform fields and analyzes the Rydberg blockade's fine structure considering electric field gradients.

Findings

Energy shift proportional to the fourth power of principal quantum number

Derived explicit formula for energy levels in nonuniform fields

Confronted theoretical results with experimental data

Abstract

Splitting the energy levels of a hydrogen-like atom by the electric field nonuniform at the atomic scale is studied. This situation is important for the multi-level treatment of the phenomenon of Rydberg blockade [Yu.V. Dumin, J. Phys. B, v.47, p.175502 (2014)]. An explicit formula for the energy levels is derived. A typical value of the energy shift by the electric field gradient turns out to be proportional to the 4th power of the principal quantum number (i.e., the square of atomic size), as would be expected from a qualitative consideration. Finally, the fine spatial structure of the Rydberg blockade is analyzed when the electric-field-gradient term plays the dominant role, and the results are confronted with the experimental data.