  Quantum ratchets exhibit asymptotic currents when driven by a time-periodic
potential of zero mean if the proper spatio-temporal symmetries are broken.
There has been recent debate on whether directed currents may arise for
potentials which do not break these symmetries. We show here that, in the
presence of degeneracies in the quasienergy spectrum, long-lasting directed
currents can be induced, even if the time reversal symmetry is not broken. Our
model can be realized with ultracold atoms in optical lattices in the
tight-binding regime, and we show that the time scale of the average current
can be controlled by extremely weak fields.
