Formation of the stopped polarization pulse in a rectangular quantum well

The induced polarization oscillations in a one-dimensional rectangular quantum well are modeled by a numerical solution of the time-dependent Schroedinger equation. The finite-difference discretization over time is realized in the framework of the Crank-Nicolson algorithm, whereas over the spatial coordinate it is combined with the exterior complex-scaling technique. A formation of the harmonic oscillations of the dipole moment by an incident short unipolar pulse is shown. It is obtained that the frequency of oscillations is solely defined by the energy of the main resonant transition. Moreover, if two such short unipolar pulses are delayed by a half-period of the oscillation, then these oscillations can be abruptly induced and stopped. Thus, the so-called stopped polarization pulse is obtained. It is shown that both the amplitude and the duration of the incident unipolar pulse, contributing to the so-called electric pulse area, define the impact of the incident pulse on the quantum system.