Investigating multi-photon processes via single electron approach from the low frequency perspective

In this study, we basically studied the interaction between a laser field and an atom. Making use of the Floquet double perturbation approach introduced by Pont et al., we computed energy levels for the Hydrogen atom, which is simplest atomic system that includes one electron. With the help of this method, Pont et al. calculated the coefficients depending on the Alternating Current (AC) quasienergy, ω^2 forces and the field strength F for an atom irradiated by a strong field with a low ω frequency, and expressed the energy eigenvalues in terms of these coefficients. The aforementioned coefficients are represented by β_2n^((2m)) and rational numbers that can be obtained precisely in the case of real and atomic hydrogen. In this investigation, we repeated the analytical calculation of these coefficients in detail and calculated the coefficients for the ground state atomic hydrogen in an electromagnetic field by using the parameters described below. Pont et al. in their study, in the low frequency region F^2n's calculations related to the 〖Re(E〗_ac) value in the β_2n^((2m))coefficients for the n = 1 and the m = 1 value of the ω frequency, in the equation 〖E_ac (F,ω)=Ʃ〗_m Ʃ_n β_2n^((2m)) F^2n ω^2m to open the series. The I (intensity) value of the field strength used is 〖10〗^13 W/〖cm〗^2 and the wavelength is 616 nm. ω=0.074 a.u frequency corresponding to a wavelength of 616 nm and the β in the series in which we opened. We re-obtained the result 〖Re(E〗_ac)=-0.502776 obtained by Pont, M et al. by writing the frequency values in their places and using the Mathematica 12.3 software. In addition, we changed the values of m, which takes places in the power of the ω^2m frequency, from 0 to 4 while taking into account the n = 0 as well as n = 1 values of F^2n in the same frequency and intensity region. When we consider the E_ac values in the β_2n^((2m)) coefficients by repeating the same steps, we observed a larger shift in the value of 〖Re(E〗_ac) as we increase m from 0 to 4. However, we achieved that the shift in the quasienergy for m≥4 values is small enough to be neglected.