Non-Markovian entanglement dynamics between two coupled qubits in the same environment

TL;DR

This paper investigates how non-Markovian environments influence entanglement dynamics between two qubits, revealing oscillatory behavior and temperature-dependent phenomena like entanglement sudden death, contrasting with Markovian decay.

Contribution

It provides a detailed analysis of non-Markovian entanglement dynamics, highlighting differences from Markovian cases and proposing temperature-based control strategies.

Findings

Non-Markovian entanglement oscillates, especially at high temperatures.

Entanglement sudden death depends on initial states at zero temperature.

Temperature influences whether entanglement decays smoothly or oscillates.

Abstract

We analyze the dynamics of the entanglement in two independent non-Markovian channels. In particular, we focus on the entanglement dynamics as a function of the initial states and the channel parameters like the temperature and the ratio $r$ between $\omega_0$ the characteristic frequency of the quantum system of interest, and $\omega_c$ the cut-off frequency of Ohmic reservoir. We give a stationary analysis of the concurrence and find that the dynamic of non-markovian entanglement concurrence $\mathcal{C}_{\rho}(t)$ at temperature $k_BT=0$ is different from the $k_BT>0$ case. We find that "entanglement sudden death" (ESD) depends on the initial state when $k_BT=0$, otherwise the concurrence always disappear at finite time when $k_BT>0$, which means that ESD must happen. The main result of this paper is that the non-Markovian entanglement dynamic is fundamentally different from the Markovian one. In the Markovian channel, entanglement decays exponentially and vanishes only asymptotically, but in the non-Markovian channel the concurrence $\mathcal{C}_{\rho}(t)$ oscillates, especially in the high temperature case. Then an open-loop controller adjusted by the temperature is proposed to control the entanglement and prolong the ESD time.