We investigate quantum Brownian motion in adiabatically rocked ratchet
systems. Above a crossover temperature T-c tunnelling events are rare
, yet they already substantially enhance the classical particle curren
t. Below T-c, quantum tunnelling prevails and the classical prediction
s grossly underestimate the transport. Upon approaching T=0 the quantu
m current exhibits a tunnelling induced reversal, and tends to a finit
e limit.