Discrete time method for the problem interaction electromagnetic wave-atom at very high frequencies

In this Letter considers a new method to the solution of time-dependent Schrödinger equation specially arising in interaction laser radiation-atom at very high frequencies. The discrete time is introduced and the problem with the time-dependent Schrödinger equation is reduced to solving the eigenvalue equation. Constant phase δ corresponding the origin of time becomes, in this way, an important unknown parameter. The physical reason for such approach is the model for laser phase noise. It is present in reality and usually not included into considerations. The sodium atom in the ground state is immersed in alternating (AC) electromagnetic field with frequency in extreme ultraviolet (XUV, wavelengths shorter than 100 nm) region. The AC Stark shift and polarizability are considered and the estimation of the AC Stark shift is given. Our examinations show that energy shift has anomalously strong dependence of δ and laser phase noise introduces significant uncertainty in experimental observation of AC Stark shift. Modification of 3s atomic wave function at high enough strength of electric filed due the phase noise is also shown.