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Chinese Physics Letters

Anomalous Temperature Effects of the Entanglement of Two Coupled Qubits in Independent Environments

Chuan-Jia Shan, Shuai Cao, Zheng‐Yuan Xue, Shi-Liang Zhu

Published Apr 1, 2012• 4 citations
Publisher

Abstract

We investigate the entanglement dynamical behavior of two coupled qubits via a Heisenberg XX interaction, which are connected with two independent finite temperature heat baths. By numerical simulations of the quantum master equation, it is found that the interesting phenomena of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. We also show that two critical temperatures T 1 (determining that the quantum state is entangled or separable) and T 2 (where maximal stationary entanglement can be observed) exist, and stationary entanglement exhibits a non-monotonic behavior as a function of the finite temperature noise strength. These results enlarge the domain of the reasonable experimental temperature where stationary entanglement can be observable.

DOI
10.1088/0256-307x/29/4/040301

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We investigate the entanglement dynamical behavior of two coupled qubits via a Heisenberg XX interaction, which are connected with two independent finite temperature heat baths. By numerical simulations of the quantum master equation, it is found that the interesting phenomena of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. We also show that two critical temperatures T 1 (determining that the quantum state is entangled or separable) and T 2 (where maximal stationary entanglement can be observed) exist, and stationary entanglement exhibits a non-monotonic behavior as a function of the finite temperature noise strength. These results enlarge the domain of the reasonable experimental temperature where stationary entanglement can be observable.
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We derive the master equation of a system of two coupled qubits by taking into account their interaction with two independent bosonic baths. Important features of the dynamics are brought to light, such as the structure of the stationary state at general temperatures and the behaviour of the entanglement at zero temperature, showing the phenomena of sudden death and sudden birth as well as the presence of stationary entanglement for long times. The model here presented is quite versatile and can be of interest in the study of both Josephson junction architectures and cavity-QED.
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 rrr between ω0ω_0ω0​ the characteristic frequency of the quantum system of interest, and ωcω_cωc​ 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 Cρ(t)\mathcal{C}_ρ(t)Cρ​(t) at temperature kBT=0k_BT=0kB​T=0 is different from the kBT>0k_BT>0kB​T>0 case. We find that "entanglement sudden death" (ESD) depends on the initial state when kBT=0k_BT=0kB​T=0, otherwise the concurrence always disappear at finite time when kBT>0k_BT>0kB​T>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 Cρ(t)\mathcal{C}_ρ(t)Cρ​(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.
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