Magnus expansion for laser-matter interaction: Application to generic few-cycle laser pulses

We treat the interaction of an atom with a short intense few-cycle laser pulse by the use of the Magnus expansion of the time-evolution operator. Terms of the Magnus expansion up to the third order in the pulse duration are evaluated explicitly, and expressions for the transition probability between atomic eigenstates are given. The transition operators up to this order are particularly simple, involving only momentum and position shifts arising from the laser field alone. The connection to other existing approaches is established. For a variety of generic short-pulse forms the results of the Magnus approximation are in excellent agreement with time-dependent transition probabilities obtained from accurate ab initio numerical calculations. However, the limitation of the Magnus expansion for pulses having both vanishing momentum and position shifts is demonstrated also.