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Long-Range Non-Equilibrium Coherent Tunneling Induced by Fractional Vibronic Resonances

We study the influence of a linear energy bias on a non-equilibrium excitation on a chain of molecules coupled to local phonons (a tilted Holstein model) 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 homogeneous polaron dynamics. Remarkably, resonance between the phonon energy $\hbarω$ and the bias $δ_ε$ occurs not only at integer but also fractional ratios $δ_ε/(\hbarω) = \frac{m}{n}$, which effect long-range $n$-bond $m$-phonon tunneling. These observations are also reproduced in a model calculation of a recently demonstrated Cy3 system. Potential applications range from molecular electronics to optical lattices and artificial light harvesting via vibronic engineering of coherent quantum transport.