  The ground state polaron potential of 1D lattice of two-level molecules with
spinless electrons and two Einstein phonon modes with quantum phonon-assisted
transitions between the levels is found anharmonic in phonon displacements. The
potential shows a crossover from two nonequivalent broad minima to a single
narrow minimum corresponding to the level positions in the ground state.
Generalized variational approach implies prominent nonadiabatic effects:(i) In
the limit of the symmetric E-e Jahn- Teller situation they cause transition
between the regime of the predominantly one-level "heavy" polaron and a "light"
polaron oscillating between the levels due to phonon assistance with almost
vanishing polaron displacement. It implies enhancement of the electron transfer
due to decrease of the "heavy" polaron mass (undressing) at the point of the
transition. Pairing of "light" polarons due to exchange of virtual phonons
occurs. Continuous transition to new energy ground state close to the
transition from "heavy" polaron phase to "light" (bi)polaron phase occurs. In
the "heavy" phase, there occurs anomalous (anharmonic) enhancements of quantum
fluctuations of the phonon coordinate, momentum and their product as functions
of the effective coupling. (ii) Dependence of the polaron mass on the optical
phonon frequency appears.(iii) Rabi oscillations significantly enhance quantum
shift of the insulator-metal transition line to higher values of the critical
effective e-ph coupling supporting so the metallic phase. In the E-e JT case,
insulator-metal transition coincide with the transition between the "heavy" and
the "light" (bi)polaron phase at certain (strong) effective e-ph interaction.
