  We investigate how collective behaviors of vibrations such as cooperativity
and interference can enhance energy transfer in a nontrivial way, focusing on
an example of a donor-bridge-acceptor trimeric chromophore system coupled to
two vibrational degrees of freedom. Employing parameters selected to provide an
overall uphill energy transfer from donor to acceptor, we use numerical
calculations of dynamics in a coupled exciton-vibration basis, together with
perturbation-based analytics and calculation of vibronic spectra, we identify
clear spectral features of single- and multi-phonon vibrationally-assisted
energy transfer (VAET) dynamics, where the latter include up to six-phonon
contributions. We identify signatures of vibrational cooperation and
interference that provide enhancement of energy transfer relative to that
obtained from VAET with a single vibrational mode. We observe a phononic
analogue of two-photon absorption, as well as a novel heteroexcitation
mechanism in which a single phonon gives rise to simultaneous excitation of
both the trimeric system and the vibrational degrees of freedom. The impact of
vibrations and of the one- and two-phonon VAET processes on the energy transfer
are seen to be quite different in the weak and strong site-vibration coupling
regimes. In the weak coupling regime, two-phonon processes dominate, whereas in
the strong coupling regime up to six-phonon VAET processes can be induced. The
VAET features are seen to be enhanced with increasing temperature and
site-vibration coupling strength, and are reduced in the presence of
dissipation. We analyze the dependence of these phenomena on the explicit form
of the chromophore-vibration couplings, with comparison of VAET spectra for
local and non-local couplings.
