  We investigate exciton transport through one-dimensional molecular aggregates
interacting strongly with a cavity mode. Unlike several prior theoretical
studies treating the monomers as simple two-level systems, exciton-vibration
coupling is explicitly included in the description of open quantum dynamics of
the system. In the framework of the Holstein-Tavis-Cummings model with
truncated vibrational space, we investigate the steady-state exciton transfer
through both a molecular dimer and longer molecular chains. For a molecular
dimer, we find that vibration-assisted exciton transfer occurs at strong
exciton-cavity coupling regime where the vacuum Rabi splitting matches the
frequency of a single vibrational quanta. Whereas for longer molecule chains,
vibration-assisted transfer is found to occur at the ultrastrong exciton-cavity
coupling limit. In addition, finite relaxation of vibrational modes induced by
the continuous phonon bath is found to further facilitate the exciton transport
in vibrational enhancement regimes.
