  We investigate the topological properties of a resonantly shaken
one-dimensional optical lattice system, where the lattice position is
periodically driven with two harmonic frequencies to generate one- and
two-photon couplings between the two lowest orbitals. In a two-band
approximation, we numerically show that degenerate edge states appear under a
certain driving condition and that the corresponding topological phase is
protected by the chiral symmetry of the periodically driven system. The
system's micromotion is characterized with oscillating Zak phases and we find
that the Zak phases are quantized only at the time when the chiral symmetry
condition is explicitly satisfied. Finally, we describe the topological charge
pumping effect which arises when the driving parameters are slowly modulated
around a critical point, and investigate its adiabaticity for increasing the
modulation frequency.
