在真實環境中糾纏動力學的非馬爾科夫效應

詹強+李銘仕+葉智婷+葉廣源+劉振考+王世洪+黃江

Abstract By considering the influence of the environmental disorder in the non-local decoherence system， the non-Markovian entanglement dynamics of two independent qubits was investigated. With the simulation of the environment noise as external entities， the preservation of entanglement depends on the environmental disorder was found. Its corresponding physical mechanism is also given.

Key words non-Markovian； entanglement； non-local

中圖分類號 O413.2 文獻標識碼 A 文章編號 1000-2537（2016）05-0065-05

摘 要 在非局域退相干系統中，研究了環境紊亂程度對兩體非馬爾科夫糾纏動力學的影響.通過模擬環境的噪聲，發現了糾纏保持依賴與環境的紊亂程度.并給出了相應的物理機制.

關鍵詞 非馬爾科夫；糾纏；非局域

All realistic quantum systems are unavoidable to interact with its environments that occurs the so-called dissipation and decoherence， the dissipation and decoherence quantum dynamics of quantum cavities have been studied for decades because it is the bases of quantum communication and information[1-5]. Taking into account the influence of the environment on the quantum dynamics evolution makes the systems more complicate and interesting[6-7]. We can mainly classify the quantum dynamical processes into Markovian processes with no memory effect and non-Markovian processes with memory effect， according to the environmental characters. Most of the studies are interested with the information between the system and reservoir， to investigate their characters. For memoryless Markovian open systems， the system information losses to the environment monotonically， and the last time is relatively short. So it has many limitation for further investigation. However， in the non-Markovian case， employing the memory effect， the lost information will return to the system at a later time during the interaction. This phenomenon arouses researchers much interest， and many works related with non-Markovian dynamics have been done[8-11]recently. Between the works， Breuer et al raised a theorem called the degree of non-Markovianity which can be used to study the non-Markovian dynamics quantitatively in Ref.[12]. They calculate the changing rate of trace distance as a criterion to distinguish the states. The increment is interpreted as the return back information flow form the reservoir to the system.

However， the realistic environment is not easy to control， and it will cause decoherence. In this paper， we import a system M to simulate the environment and use the amplitude damping channel to research its characteristic. The article is organized as follows： In Sec.2， we introduce our mode and build the initial states. Then the time-dependent evolution is calculated in Sec.3. In Sec.4 we use concurrence to study entanglement evolution and the analysis is given， too. At last， we conclude the paper simply.

1 The Model

First， we introduce our model： Consider a system of two identical non-interacting two-level atoms， each of them coupled with its own reservoir which is initially in the vacuum state. Due to the independence of each atom， we only need to discuss the problem of a single atom interacting with its corresponding reservoir. The Hamiltonian of the interaction between a single atom and N-mode reservoir under the rotating-wave approximation can be written as（h =1）：

4 Conclusion

In conclusion， we have investigated the behavior of non-local decoherence in this paper. We choose the not quite perfect Bell state as the initial condition and employ a system M to consider the effect of the environment. After the amplitude damping process， we trace off the external entities to get the reduced density matrix which has the X-style. Considering the concurrence of entanglement in the Markovian and non-Markovian regime， we find that the entanglement is greatly affected by the environmental disorder. The results are identical with Ref.[14]. The work provide a method to transfer entangled communication effectively.

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（編輯 CXM）