  Following the Dirac-Frenkel time-dependent variational principle, transient
dynamics of a one-dimensional Holstein polaron with diagonal and off-diagonal
exciton-phonon coupling in an external electric field is studied by employing
the multi-D$_2$ {\it Ansatz}, also known as a superposition of the usual
Davydov D$_2$ trial states. Resultant polaron dynamics has significantly
enhanced accuracy, and is in perfect agreement with that derived from the
hierarchy equations of motion method. Starting from an initial broad wave
packet, the exciton undergoes typical Bloch oscillations. Adding weak
exciton-phonon coupling leads to a broadened exciton wave packet and a reduced
current amplitude. Using a narrow wave packet as the initial state, the bare
exciton oscillates in a symmetric breathing mode, but the symmetry is easily
broken by weak coupling to phonons, resulting in a non-zero exciton current.
For both scenarios, temporal periodicity is unchanged by exciton-phonon
coupling. In particular, at variance with the case of an infinite linear chain,
no steady state is found in a finite-sized ring within the anti-adiabatic
regime. For strong diagonal coupling, the multi-$\rm D_2$ {\it Anstaz} is found
to be highly accurate, and the phonon confinement gives rise to exciton
localization and decay of the Bloch oscillations.
