Long-range non-equilibrium coherent tunneling induced by fractional vibronic resonances

We study the influence of a linear energy bias on a non-equilibrium particle on a chain with strong coupling to local phonons using both a random-walk rate kernel theory and a nonperturbative, massively parallelized adaptive-basis algorithm. We uncover structured and discrete vibronic resonance behavior fundamentally different from both linear response theory and unbiased-chain polaron dynamics. Remarkably, resonance between the phonon energy $\hbar\omega$ and the bias $\delta_\epsilon$ occurs not only at integer but also fractional ratios $\delta_\epsilon/(\hbar\omega) = \frac{m}{n}$, which effect long-range $n$-bond $m$-phonon tunneling. Potential applications range from molecular electronics to optical lattices and artificial light harvesting via vibronic engineering of coherent quantum transport.