  There are two types of two-photon transitions in molecular aggregates, that
is, non-local excitations of two monomers and local double excitations to some
higher excited intra-monomer electronic state. As a consequence of the
inter-monomer Coulomb interaction these different excitation states are coupled
to each other. Higher excited intra-monomer states are rather short-lived due
to efficient internal conversion of electronic into vibrational energy.
Combining both processes leads to the annihilation of an electronic excitation
state, which is a major loss channel for establishing high excitation densities
in molecular aggregates. Applying theoretical pulse optimization techniques to
a Frenkel exciton model it is shown that the dynamics of two-exciton states in
linear aggregates (dimer to tetramer) can be influenced by ultrafast shaped
laser pulses. In particular, it is studied to what extent the decay of the
two-exciton population by inter-band transitions can be transiently suppressed.
Intra-band dynamics is described by a dissipative hierarchy equation approach,
which takes into account strong exciton-vibrational coupling in the
non-Markovian regime.
