  In this work, we present a theoretical study of polaron states in a double
quantum dot system. We present realistic calculations which combine 8 band \kp
model, configuration interaction approach and collective modes method. We
investigate the dependence of polaron energy branches on axial electric field.
We show that coupling between carriers and longitudinal optical phonons via
Fr\"{o}hlich interaction leads to qualitative and quantitative reconstruction
of the optical spectra. In particular, we study the structure of resonances
between the states localized in different dots. We show that $p$-shell states
are strongly coupled to the phonon replicas of $s$-shell states, in contrast to
the weak direct $s$-$p$ coupling. We discuss also the dependence of the
phonon-assisted tunnel coupling strength on the separation between the dots.
