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摘要: 基于与各自的级联环境相互耦合的三个独立的量子比特系统, 详细考察了强、弱耦合体系下腔-腔耦合强度Ω和腔衰减率Γ1对负性纠缠度、Bell非定域性和纠缠目击的影响. 结果表明: Bell非定域性和纠缠目击都可以出现猝死和猝生现象; Γ1 = 0时, 随着Ω的增加, 三者在历经短时阻尼振荡后, 均会随时间达到各自的稳定值, 且该稳定值随着Ω的增大而增大. 同时, 三者在弱耦合体系的量值或存活时间都优于强耦合体系. 此外, 非零Γ1对量子关联有着很大的负面效应. 于是, 为了更好地抑制量子关联损失, 进一步分析了弱测量和测量反转操作的有效调控作用, 得到一些有趣的结果.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.
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Key words:
- quantum entanglement /
- Bell non-locality /
- entanglement witness /
- weak measurement
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图 1 耦合强度
$\varOmega $ 取不同值时, 负性纠缠度${N_3}$ 、Bell非定域性$\left| {\left\langle {{B}} \right\rangle } \right| - 1$ 和纠缠目击$ - {\rm{EWs}}$ 在强耦合体系$g = 0.5\varGamma $ ((a)—(c))和弱耦合体系$g = 0.2\varGamma $ ((d)—(f))下随无量纲时间$\varGamma t$ 的变化曲线. 其中,${\varGamma _1} = 0$ Figure 1. Time evolution of Negativity
${N_3}$ , Bell non-locality$\left| {\left\langle {{B}} \right\rangle } \right| - 1$ and entanglement witnesses$ - {\rm{EWs}}$ as the function of dimensionless time$\varGamma t$ for the different values of coupling strength$\varOmega $ in the strong coupling regime$g = 0.5\varGamma $ ((a)–(c)) and the weak coupling regime$g = 0.2\varGamma $ ((d)–(f)) with${\varGamma _1} = 0$ .
图 2 耦合强度
$\varOmega $ 和弱测量强度m取不同值时, 负性纠缠度$N_3$ 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. 其中,${\varGamma _1} = 0$ Figure 2. Negativity
$N_3$ versus dimensionless time$\varGamma t$ for the different values of coupling strength$\varOmega $ and the weak measurement strength$m$ in the strong coupling regime$g = 0.5\varGamma $ ((a) and (c)) and the weak coupling regime$g = 0.2\varGamma $ ((b) and (d)) with${\varGamma _1} = 0$ .
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Figure 3. 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 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 $ Figure 5. 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. -
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