Tunnelling system coupled to a harmonic oscillator: an analytical treatment

Charge transfer and coherence dynamics of a tunnelling system coupled to an harmonic oscillator

We study the transition probability and coherence of a two-site system, interacting with an oscillator. Both properties depend on the initial preparation. The oscillator is prepared in a thermal state and, even though it cannot be considered as an extended bath, it produces decoherence because of the large number of states involved in the dynamics. In the case in which the oscillator is initially displaced, a coherent dynamics of charge entangled with oscillator modes takes place. Coherency is, however, degraded as far as the oscillator mass increases, producing an increasingly large recoherence time. Calculations are carried on by exact diagonalization and compared with two semiclassical approximations. The role of the quantum effects are highlighted in the long time dynamics, where semiclassical approaches give rise to a dissipative behaviour. Moreover, we find that the oscillator dynamics has to be taken into account, even in a semiclassical approximation, in order to reproduce a thermally activated enhancement of the transition probability.