Hydrogen atom excitation in intense attosecond laser field: Gauge dependence of dipole approximation

It is assumed that, the atomic excitations probability can be calculated using first order perturbation theory and dipole approximations. The validity of the dipole approximations had been examined by comparing the results with the results obtained by exact calculations within the first order perturbation theory[2]. Figure 1 shows the time dependence of the transition probability in the dipole approximation. From these plots it is obvious that, the probabilities obtained in the length gauge are higher than that in the velocity gauge, in the interaction period (−τ/2<t<τ/2). After passing this time interval, transition probabilities for these two gauges became equal to each other precisely. Moreover those results are equal to the corresponding exact (without the dipole approximation) calculations results. (Figure 2) Though the time evolution of the same transition probabilities are different for these cases, the final results are the same for all three cases, excluding the 6s-6p0 transition. For the later case, only the length gauge give a false results, but the velocity gauge give the same result as the exact one, for the final value of the transition probability