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Quantum transport of double quantum dots coupled to an oscillator in arbitrary strong coupling regime

In this paper, we investigate the quantum transport of a double quantum dot coupled with a nanomechanical resonator at arbitrary strong electron-phonon coupling regimes. We employ the generalized quantum master equation to study full counting statistics of currents. We demonstrate the coherent phonon states method can be applied to decouple the electron-phonon interaction non-perturbatively. With the help of this non-perturbative treatment of electron-phonon couplings, we find that the phonon-assisted resonant tunneling emerges when the excess energy from the left quantum dot to the right one can excite integer number of phonons and multi-phonon excitations can enhance the transport in strong electron-phonon coupling regime. Moreover, we find that as the electron-phonon coupling increases, it first plays a constructive role to assist the transport, and then plays the role of scattering and strongly represses the transport.