We propose a simple analytical approach for description of energy transfer from ultra-short laser pulses to quantum oscillator in the thermal equilibrium based on approximate expression for oscillator spectral function. Formulas for the probability of energy transfer in the limits of high and low temperatures are derived and analyzed. The characteristic features of energy transfer to a quantum oscillator from unipolar pulses, wavelets and multi-cycle laser pulses are established.
Astapenko et al. (Sun,) studied this question.