  We calculate non-perturbatively the inelastic effects on the conductance
through a conjugated molecular wire-metal heterojunction, including realistic
electron-phonon coupling. We show that at sub-band-gap energies the current is
dominated by quantum coherent transport of virtual polarons through the
molecule. In this regime, the tunneling current is strongly increased relative
to the case of elastic scattering. It is essential to describe the full quantum
coherence of the polaron formation and transport in order to obtain correct
physics. Our results are generally applicable to one-dimensional atomic or
molecular wires.
