We study the excitation to Rydberg states in the interaction of the hydrogen atom with a short strong laser pulse. Utilizing solutions of the time-dependent Schrödinger equation we find that the parity of the populated angular momentum states agrees with the selection rules for multiphoton resonant absorption at low intensities, if the pulse length is not too short. In contrast, the parity effect cannot be observed for ultrashort pulses as well as for long pulses at high intensities. We further identify signatures of the population in the excited states via the line emissions from the populated np states after the end of the pulse exhibiting the parity effect.

We analyze the role of the difference between the central frequencies of the spectral distributions of the vector potential and the electric field of a short laser pulse. The frequency shift arises when the electric field is determined as the derivative of the vector potential to ensure that both quantities vanish at the beginning and end of the pulse. We derive an analytical estimate of the frequency shift and show how it affects various light induced processes, such as excitation, ionization and high harmonic generation. Since observables depend on the frequency spectrum of the electric field, the shift should be taken into account when setting the central frequency of the vector potential to avoid potential misinterpretation of numerical results for processes induced by few-cycle pulses.