  In a fixed spectral range, single- and half-cycle electromagnetic pulses have
the shortest duration. Half-cycle pulses are promising tools for ultrafast
control of quantum systems. Previously, the possibility of using a sequence of
single- and half-cycle attosecond pulses to generate and ultrafast control
light-induced population difference gratings has been demonstrated. However,
such studies have been carried out using different approximations. For example,
when the medium is modelled in the two-level approximation. In this paper,
based on the numerical solution of the system of Maxwell-Bloch equations, it is
shown that it is possible to generate and control population gratings in a
three-level medium without using the approximations used in previous studies.
It is shown that taking into account the additional level of the medium does
not lead to a violation of the effect of generating such gratings. This extends
the applicability of previous results.
