  We show that the recently developed optical lattices with Peierls
substitution -- which can be modeled as a lattice with a complex tunneling
coefficient -- may be used to induce controllable quantum transport of
ultra-cold atoms. In particular, we show that by ramping up the phase of the
complex tunneling coefficient in a spatially uniform fashion, a finite quasi
steady-state current (QSSC) ensues from the exact dynamics of non-interacting
fermions. The direction and magnitude of the current can be controlled by the
overall phase difference but not the details of the ramp. The entanglement
entropy does not increase when the QSSC lasts. Due to different spin
statistics, condensed non-interacting bosons do not support a finite QSSC under
the same setup. We also find that an approximate form of the QSSC survives when
perturbative effects from interactions, weak harmonic background traps, and
finite-temperature are present, which suggests that our findings should be
observable with available experimental capabilities.
