Pulsed excitation of a quantum oscillator: A model accounting for damping

This article proposes a model that accounts for damping of a quantum oscillator (QO) during pulsed excitation. Our model is based on the Schwinger formula, which calculates oscillator’s excitation probability through the energy of an associated classical damped oscillator. We utilize this model to describe the influence of damping on temporal and spectral dependences of QO excitation, induced by electromagnetic pulses with exponential and double exponential envelopes. The oscillator excitation is analyzed in terms of transition probability between stationary states after pulse termination. Here, we present an analytical description of these dependences, along with numerical results. Specifically, we derive analytical expressions that depict the saturation effect during pulsed excitation, taking into account the damping of a QO. The evolution of the temporal dependence of the excitation probability with a change in the damping constant is numerically traced. We demonstrate that the number of maxima in this dependence is determined by the values of pulse parameters and the damping constant.