  We show theoretically that periodic density patterns are stabilized in two
counter-propagating Bose-Einstein condensates of atoms in different hyperfine
states under Rabi coupling. In the presence of coupling, the relative velocity
between two components is localized around density depressions in
quasi-one-dimensional systems. When the relative velocity is sufficiently
small, the periodic pattern reduces to a periodic array of topological solitons
as kinks of relative phase. According to our variational and numerical
analyses, the soliton solution is well characterized by the soliton width and
density depression. We demonstrate the dependence of the depression and width
on the Rabi frequency and the coupling constant of inter-component
density-density interactions. The periodic pattern of the relative phase
transforms continuously from a soliton array to a sinusoidal pattern as the
period becomes smaller than the soliton width. These patterns become unstable
when the localized relative velocity exceeds a critical value. The
stability-phase diagram of this system is evaluated with a stability analysis
of countersuperflow, by taking into account the finite-size-effect owing to the
density depression.
