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

TL;DR

This paper investigates how a two-level impurity system loses coherence and transfers information to a fermionic environment, revealing exponential decay behaviors and their relation to impurity level width.

Contribution

It provides a detailed analysis of the decoherence process and quantifies the information transfer rate in a fermionic reservoir, highlighting their proportional relationship.

Findings

Non-diagonal density matrix elements decay exponentially with rate Γ.

Information transfer rate also decays exponentially, proportional to Γ.

Decay constant for information transfer is approximately 2 to 4 times Γ.

Abstract

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 $\Gamma$. And we study the information transfer rate between the impurity and the Fermi sea, which also decays exponentially. And the decay constant is $k\Gamma$ with $k=2\sim 4$. Our results reveal the relation between information transfer rate and decoherence rate.