Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 11105087)
Received Date:15 December 2020
Accepted Date:09 January 2021
Available Online:13 May 2021
Published Online:20 May 2021
Abstract:Much attention has been paid to the dynamics of quantum correlation in an open quantum system coupled to a single-layered environment for a long time. However, the system can be influenced by the multilayer environment or hierarchical environment in realistic scenarios, which is attracting increasing interest at present. In this context, we explore in this paper the dynamics of quantum correlation for a quantum system consisting of three independent qubits, each being immersed in a single mode lossy cavity which is further connected to another cavity. The influences of cavity-cavity coupling strength Ω and the decay rate of cavity Γ1 on the measures of quantum correlation, including negativity, Bell non-locality as well as entanglement witness, are investigated in detail in a strong coupling regime and a weak coupling regime. It is shown that the phenomena of sudden death and sudden birth can happen to both Bell non-locality and entanglement witness. When the decay rate Γ1 = 0 is given, with the increase of Ω these measures eventually reach their stationary values over time after a short period of damping oscillations, in which these stationary values will become larger for the larger Ω. At the same time, the values or the survival times of quantum correlation considered by us in the weak coupling regime are better than in the strong coupling case. In addition, the non-zero Γ1 has a great negative effect on quantum correlation. Hence, in order to suppress the loss of quantum correlation better, the effective manipulation of quantum weak measurement and measurement reversal operator is considered further. Some interesting results are obtained. Keywords:quantum entanglement/ Bell non-locality/ entanglement witness/ weak measurement
图 3 Bell函数$\left| {\left\langle {{B}} \right\rangle } \right| - 1$在强耦合体系$g = 0.5\varGamma $ ((a)和(c))和弱耦合体系$g = 0.2\varGamma $((b)和(d))下随无量纲时间$\varGamma t$的变化曲线. 其他参数取值与图2相同 Figure3. The change of Bell function $\left| {\left\langle {{B}} \right\rangle } \right| - 1$ as a function of $\varGamma t$ in the strong coupling regime $g = 0.5\varGamma $((a) and (c)) and the weak coupling regime $g = 0.2\varGamma $((b) and (d)). The values of other parameters are the same as those in Fig. 2.
图 4 纠缠目击$ - {\rm{EWs}}$在强 ((a), (c))、弱((b), (d))耦合体系下的动力学行为. 其他参数取值与图2相同 Figure4. Dynamics of entanglement witnesses $ - {\rm{EWs}}$ in the strong ((a), (b)) and the weak ((c), (d)) coupling regimes. The values of other parameters are the same as those in Fig. 2(a).
图5为存在腔耗散${\varGamma _1} = 0.25\varGamma $、执行和未执行弱测量操作时量子关联随时间的演化行为, 参数$\varOmega = \varGamma $. 其中, 图5(a)和图5(c)为强耦合体系($g = 0.5\varGamma $), 而图5(b)和图5(d)为弱耦合体系($g = 0.2\varGamma $). 对比图1(b)和图5(a)可以发现, 一旦级联空腔${R_{i2}}$具有了耗散, ${N_3}$, Bell非定域性和$ - {\rm{EWs}}$将不再出现关联俘获现象. 具体来说, ${N_3}$经过阻尼震荡后随时间逐渐衰减, Bell非定域性会在短时间内直接猝死, 而$ - {\rm{EWs}}$在猝死后还会出现短暂的复苏现象. 同理, 图1(e)和图5(b)也说明, 非零耗散${\varGamma _1}$破坏了量子关联俘获, 致使它们都以阻尼震荡方式衰减. 图5(c)和图5(d)则说明, 较大的$m$会使得量子关联得到很大提高, 且不再发生猝死行为. 图 5 量子关联在强耦合体系$g = 0.5\varGamma $ ((a)和(c))和弱耦合体系$g = 0.2\varGamma $((b)和(d))下的变化曲线. 其中, (a)和(b)无弱测量操作, (c)和(d)有弱测量操作. 参数$\varOmega = \varGamma $和${\varGamma _1} = 0.25\varGamma $ Figure5. Change curves of quantum correlation in the strong coupling regime $g = 0.5\varGamma $((a) and (c)) and the weak coupling regime $g = 0.2\varGamma $((b) and (d)), where (a) and (b) are the cases without measurement, while (c) and (d) are the cases with measurement. The parameters $\varOmega $ and ${\varGamma _1}$ are set to $\varGamma $ and $0.25\varGamma $, respectively.