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We propose an experimental realization of the time-periodically modulatedRabi frequency and suggest density-dependent hoppings of two species hardcorebosons in a one-dimensional optical lattice. Distinct from the previous work[Phys. Rev. Research {\bf 2}, 013275 (2020)], we study effects in the firstresonance region. In the effective Hamiltonian, the intra-species hoppingoccurs only if the density discrepancy of the other species on these sites iszero, while the inter-species one is allowed once the relevant densitydiscrepancy becomes nonzero. At integer-$1$ filling, the quantum phase diagramof the effective Hamiltonian is determined by the perturbation analysistogether with numerical calculations. We find that in the limit of dominant$J_{1}$, the system becomes a double-degenerate dimerized state, withspontaneously breaking the translation symmetry. The interplay of $J_{0}$,$J_{1}$ and the fixed ${\bar U}=1$ leads to three BKT transition lines and atricritical BKT point. Exact transition lines are obtained by the levelspectroscopic technique. Besides, general physical properties, including thecharge gap, neutral gap, superfluid density and dimerization strength, areinvestigated as well.

Quantum phase diagram for two species hardcore bosons in one-dimensional optical lattices with the resonantly driven Rabi frequency