  Using the intertwining relation we construct a pseudosuperpartner for a
(non-Hermitian) Dirac-like Hamiltonian describing a two-level system
interacting in the rotating wave approximation with the electric component of
an electromagnetic field. The two pseudosuperpartners and pseudosupersymmetry
generators close a quadratic pseudosuperalgebra. A class of time dependent
electric fields for which the equation of motion for a two level system placed
in this field can be solved exactly is obtained. New interesting phenomenon is
observed. There exists such a time-dependent detuning of the field frequency
from the resonance value that the probability to populate the excited level
ceases to oscillate and becomes a monotonically growing function of time
tending to 3/4. It is shown that near this fixed excitation regime the
probability exhibits two kinds of oscillations. The oscillations with a small
amplitude and a frequency close to the Rabi frequency (fast oscillations) take
place at the background of the ones with a big amplitude and a small frequency
(slow oscillations). During the period of slow oscillations the minimal value
of the probability to populate the excited level may exceed 1/2 suggesting for
an ensemble of such two-level atoms the possibility to acquire the inverse
population and exhibit lasing properties.
