  We study the spatiotemporal Bloch states of a high-frequency driven
two-component Bose-Einstein condensate (BEC) with spin-orbit coupling (SOC) in
an optical lattice. By adopting the rotating-wave approximation (RWA) and
applying an exact trial-solution to the corresponding quasistationary system,
we establish a different method for tuning SOC via external field such that the
existence conditions of the exact particular solutions are fitted. Several
novel features related to the exact states are demonstrated, such as SOC leads
to spin-motion entanglement for the spatiotemporal Bloch states, SOC increases
the population imbalance of the two-component BEC and SOC can be applied to
manipulate the stable atomic flow which is conducive to control quantum
transport of the BEC for different application purposes.
