  We propose an experimental realization of the time-periodically modulated
Rabi frequency and suggest density-dependent hoppings of two species hardcore
bosons in a one-dimensional optical lattice. Distinct from the previous work
[Phys. Rev. Research {\bf 2}, 013275 (2020)], we study effects in the first
resonance region. In the effective Hamiltonian, the intra-species hopping
occurs only if the density discrepancy of the other species on these sites is
zero, while the inter-species one is allowed once the relevant density
discrepancy becomes nonzero. At integer-$1$ filling, the quantum phase diagram
of the effective Hamiltonian is determined by the perturbation analysis
together with numerical calculations. We find that in the limit of dominant
$J_{1}$, the system becomes a double-degenerate dimerized state, with
spontaneously breaking the translation symmetry. The interplay of $J_{0}$,
$J_{1}$ and the fixed ${\bar U}=1$ leads to three BKT transition lines and a
tricritical BKT point. Exact transition lines are obtained by the level
spectroscopic technique. Besides, general physical properties, including the
charge gap, neutral gap, superfluid density and dimerization strength, are
investigated as well.
