Peculiarities of Excitation of a Harmonic Oscillator for Various Driving-Pulse Parameters

The dependence of energy transferred to a damped harmonic oscillator by a pulse of periodic force on pulse duration, carrier frequency, and shape of the pulse envelope is investugated. The cases of pulses with an exponential and Gaussian shape of the envelope are analyzed. Analytical expressions describing the process are obtained. It is established that the dependence of energy transferred to the oscillator on pulse duration in the case of an exponential pulse can have an inflection point, while extrema appear in the discussed dependence at sufficiently large offset of the pulse carrier frequency from the oscillator natural frequency in the case of a Gaussian pulse. It is demonstrated that the number of quanta and the amplitude of the average value of the coordinate operator upon excitation of a quantum oscillator are determined by the same dependences on the driving-pulse parameters as in the case of the classical oscillator.