High-order correction calculation for survival of Rydberg atoms in intense laser fields

•Confirm the effects of the higher-order terms on the calculation of Rydberg He atoms in external fields.•Confined the Magnus expansion up to the fourth order and used it to obtain analytical expressions of different order time evolution operators.•To calculate the Rydberg atomic survival probability with using the high order corrected time evolution operators in external fields with different parameters. Using a method based on the Magnus expansion, the survival of Rydberg atoms in intense laser fields is studied. Usually, for atoms in intense laser fields, effects beyond the electric dipole approximation need to be considered. In the past few years, researchers have primarily paid attention to the nondipole effects induced by the electric quadrupole term of the optical field. The quadrupole term plays a more important role than the electric dipole term in the calculation of the survival probability of Rydberg atoms in intense laser fields even though the magnitude of the former is smaller than that of the latter in terms of the multipole expansion of the optical vector potential. Meanwhile, the effects of higher-order corrections beyond the quadrupole term remain ambiguous. In this paper, we confirm that corrections containing higher-order terms, except for the quadrupole term, can be neglected in the calculation of the transitions of Rydberg atoms in external fields. We then use the second-order time evolution operator containing the quadrupole term to study the scaling law of the transition probability of Rydberg He in laser fields with different parameters.