  By using a propagation scheme for current matrices and an auxiliary mode
expansion method, we investigate the transient dynamics of a single molecular
junction coupled with a vibrational mode. Our approach is based on the
Anderson-Holstein model and the dressed tunneling approximation for the
electronic self-energy in the polaronic regime. The time-dependent currents
after a sudden switching on the tunneling to leads and an abrupt upward step
bias pulse are calculated. We show that the strong electron-phonon interaction
greatly influences the nonlinear response properties of the system, and gives
rise to interesting characteristics on the time traces of transient currents.
