Decoherence of the two-level system coupled to a fermionic reservoir and the information transfer from it to the environment

We study the evolution of reduced density matrix of an impurity coupled to a Fermi sea after the coupling is switched on at time $t=0$. We find the non-diagonal elements of the reduced density matrix decay exponentially, and the decay constant is the impurity level width $\mathrm{\Gamma }$. And we study the information transfer rate between the impurity and the Fermi sea, which also decays exponentially. And the decay constant is $k\mathrm{\Gamma }$ with $k=2\sim 4$. Our results reveal the relation between information transfer rate and decoherence rate.