# Non-Markovianity of qubit evolution under the action of spin environment

## TL;DR

This paper investigates the non-Markovian behavior of a qubit interacting with a spin environment, analyzing how different coupling types and strengths influence the information flow and the transition between non-Markovian and Markovian dynamics.

## Contribution

It provides a detailed analysis of non-Markovianity in qubit evolution under various coupling conditions with a spin bath environment, including explicit Kraus operators.

## Key findings

- Time-independent and time-polynomial couplings induce non-Markovianity.
- Certain parameter values of time-exponential coupling also lead to non-Markovian behavior.
- Transition from non-Markovian to Markovian dynamics occurs as coupling strength varies.

## Abstract

The question, whether an open system dynamics is Markovian or non-Markovian can be answered by studying the direction of the information flow in the dynamics. In Markovian dynamics, information must always flow from the system to the environment. If the environment is interacting with only one of the subsystems of a bipartite system, the dynamics of the entanglement in the bipartite system can be used to identify the direction of information flow. Here we study the dynamics of a two-level system interacting with an environment, which is also a heat bath, and consists of a large number of two-level quantum systems. Our model can be seen as a close approximation to the `spin bath' model at low temperatures. We analyze the Markovian nature of the dynamics, as we change the coupling between the system and the environment. We find the Kraus operators of the dynamics for certain classes of couplings. We show that any form of time-independent or time-polynomial coupling gives rise to non-Markovianity. Also, we witness non-Markovianity for certain parameter values of time-exponential coupling. Moreover, we study the transition from non-Markovian to Markovian dynamics as we change the value of coupling strength.