Theoretical study on Stark effect of Rydberg atom in super low frequency electric field measurement

Super low frequency electric field measurements are crucial in analysing electromagnetic compatibility, assessing equipment status, and other related fields. Rydberg atom-based super low frequency electric field measurements are performed by observing the Stark shift in the spectrum of the Rydberg state. In a specific range of field strength (E < E_avoid, where E_avoid is the threshold to avoid crossing electric fields), the Rydberg atomic spectrum experiences a quadratic frequency shift in relation to the field strength, with the coefficient being determined by the atomic polarisability α. The authors establish a dynamic equation for the interaction between the external electric field and the atomic system, and present the Stark structure diagram of the Caesium Rydberg atom. The mathematical formulae for α and E_avoid in different Rydberg states are also obtained: α = A × (n*)⁶ + B × (n*)⁷ and E_avoid = C/(n*)⁵ + D/(n*)⁷, where A(B) = 2.2503 × 10⁻⁹(7.49,948 × 10⁻¹¹) and C(D) = 1.68,868 × 10⁸(2.45,991 × 10⁹). The error of α and E_avoid compared with the experimental values does not exceed 8% and is even lower in the low Rydberg states. Accurately calculating the values of α and E_avoid is crucial in incorporating the Rydberg atom quantum coherence effect into super low frequency electric field measurements in new power systems.