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

TL;DR

This paper investigates how a harmonic oscillator coupled to a two-site quantum system affects its transition probability and coherence, highlighting quantum effects and the limitations of semiclassical approximations in long-term dynamics.

Contribution

It provides an exact diagonalization analysis of the coupled system and compares quantum and semiclassical approaches, revealing the importance of oscillator dynamics in coherence and transition behaviors.

Findings

Oscillator induces decoherence despite not being an extended bath.

Coherence degrades with increasing oscillator mass, affecting recoherence times.

Semiclassical methods capture short-term dynamics but fail to reproduce long-term quantum effects.

Abstract

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 intially displaced a coherent dynamics of change entangled with oscillator modes takes place. Coherency is however degraded as far as the oscillator mass increases producing a 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.