Phase control during excitation of quantum oscillator by exponential pulse

The phase control of the excitation of a quantum oscillator without damping from the ground state under the influence of an exponential pulse of arbitrary duration and amplitude is studied analytically and numerically. Specific features of this process have been established, characteristic of an exponential pulse, different from the case of excitation by a pulse with a Gaussian envelope. It is shown that the phase modulation coefficient has maximum for ultrashort pulses, and for sufficiently long pulses it decreases as the pulse carrier frequency approaches the eigenfrequency of the oscillator.