  We investigate wave transport properties of Parity-Time (PT) symmetric
lattices that are periodically modulated along the direction of propagation. We
demonstrate that in the regime of unbroken PT-symmetry the system Floquet-Bloch
modes may interfere constructively leading to either controlled oscillations or
linear power absorption and amplification occurring exactly at the phase
transition point. The differential power response is effected by the overlap of
the gain and loss system distribution with wave intensity pattern that is
formed through Rabi oscillations engaging the coupled Floquet-Bloch modes.
