  We investigate the optical response of a charge-transfer complex in a
condensed phase driven by an external laser field. Our model includes an
instantaneous short-range Coulomb interaction and a local optical vibrational
mode described by the Holstein-Hubbard (HH) model. Although characterization of
the HH model for a bulk system has typically been conducted using a complex
phase diagram, this approach is not sufficient for investigations of dynamical
behavior at finite temperature, in particular for studies of nonlinear optical
properties, where the time irreversibility of the dynamics that arises from the
environment becomes significant. We therefore include heat baths with infinite
heat capacity in the model to introduce thermal effects characterized by
fluctuation and dissipation to the system dynamics. By reducing the number of
degrees of freedom of the heat baths, we derive numerically "exact"
hierarchical equations of motion (HEOM) for the reduced density matrix of the
HH system. As demonstrations, we calculate the optical response of the system
in two- and four-site cases under external electric fields. The results
indicate that the effective strength of the system-bath coupling becomes large
as the number of sites increases. Excitation of electrons promotes the
conductivity when the Coulomb repulsion is equivalent to or dominates the
electron-phonon coupling, whereas excitation of optical vibrations always
suppresses the conductivity.
