Tunneling current-induced entanglement between electronic and vibrational modes in coupled molecules

The formation of entanglement between the electronic and vibrational subsystems of two interacting molecules localized between tunneling contact leads was theoretically analyzed using the Keldysh diagram technique. The time evolution of concurrence after 'switching on' the coupling between the molecules was investigated. It was revealed that non-zero concurrence can be present in the system in the resonant case, even if the molecules are connected by the leads. It was also shown that the stationary value of concurrence can be directly expressed by the stationary tunneling current. It reveals non-monotonic behavior with increasing coupling between the molecule's electronic states. In the regime of small tunneling rates between the molecules and the leads, 'switching on and off' the coupling between molecules multiple times, while detecting one of the molecules' charge states after each 'on' and 'off' cycle, results in the appearance of non-classical phonon statistics and opens the possibility of creating a vibrational mode in a Fock state.