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

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.