  We use numerical approach to study non-equilibrium transport of atomic gas in
a driven optical lattice atomtronic transistor. The shaken optical lattice
transistor displays a property of insulator within some regions of shaking
frequency and shaking strength. It is proved that appearance of the insulation
is directly connected to coherence of the system. Coherence of the system is
accompanied by coherent trapping of non-equilibrium atomic gas in one of the
optical wells, which stops atomic currents. Comparing with the effective
Hamiltonian approach in Floquet engineering, the time-dependent Hamiltonian
approach could be used in any frequency regime of periodically driven quantum
system.
