Title: The influence of dark excitons on the electroabsorption spectrum of polyacetylene

Abstract: This study revisits the electroabsorption (EA) spectrum of polyacetylene, as functions of the electric field strength, isomerization degree, and light polarization states. The EA spectrum of $cis$-$(CH)_x$ reveals an oscillatory feature that follows the Stark shift-related first derivative of the materials absorption spectrum that contains v(0-1) and v(0-2) sidebands of the excited $C=C$ stretching vibration that agrees well with the Raman spectrum. EA spectrum of $trans $-$(CH)_x$ does not match the first derivative of the materials absorption spectrum, and the phonon sideband frequency does not agree with the RS spectrum. EA spectrum of $trans $-$(CH)_x$ reveals a band below the first allowed $1B_u$ exciton. We interpret this feature as due to the electric field activated even-parity dark (forbidden) exciton, namely $mA_g$ ($m >1$), showing that the nonluminescent $trans $-$(CH)_x$ is due to the reverse order of the excited states, where a dark $mA_g$ exciton lies below the allowed $1B_u$ exciton. This agrees with the unusual phonon sideband in $trans $-$(CH)_x$ absorption, since the excited state attenuation caused by the fast internal conversion from $1B_u$ to $mA_g$ influences the apparent frequency that determines the phonon sideband. Consequently, from the EA and RS spectra we estimate the $1B_u$ lifetime in $trans $-$(CH)_x$ to be $\sim 30$ fs. Integrated EA spectrum of $trans $-$(CH)_x$ shows a traditional Huang-Rhys type series with a relaxation parameter, $S \sim 0.5$. This indicates that the EA spectrum of the $trans $ isomer is also determined by a Stark shift related to the first derivative of the absorption spectrum, but preferentially for the longest chains in the films chain lengths distribution. This is due to the $N^3$ response of the non-linear susceptibility, $\chi^{(3)}$ ($\sim$EA), dependence on the chain length having $N$ monomers.