  We propose and discuss a method to engineer stroboscopically arbitrary
one-dimensional optical potentials with subwavelength resolution. Our approach
is based on subwavelength optical potential barriers for atoms in the dark
state in an optical \Lambda system, which we use as a stroboscopic drawing tool
by controlling their amplitude and position by changing the amplitude and the
phase of the control Rabi frequency in the \Lambda system. We demonstrate the
ability of the method to engineer both smooth and comb-like periodic potentials
for atoms in the dark state, and establish the range of stroboscopic
frequencies when the quasienergies of the stroboscopic Floquet system reproduce
the band structure of the time-averaged potentials. In contrast to usual
stroboscopic engineering which becomes increasingly accurate with increasing
the stroboscopic frequency, the presence of the bright states of the
\Lambda-system results in the upper bound on the frequency, above which the
dynamics strongly mixes the dark and the bright channels, and the description
in terms of a time-averaged potential fails. For frequencies below this bound,
the lowest Bloch band of quasienergies contains several avoided-crossing coming
from the coupling to high energy states, with widths decreasing with increasing
stroboscopic frequency. We analyze the influence of these avoided crossings on
the dynamics in the lowest band using Bloch oscillations as an example, and
establish the parameter regimes when the population transfer from the lowest
band into high bands is negligible. We also present protocols for loading atoms
into the lowest band of the painted potentials starting from atoms in the
lowest band of a standard optical lattice.
