In this communication, we consider a pair of entangled quantum systems, each described by the su(1) Lie algebra, interacting with two two-level atoms. We discuss in detail the influence of the detuning terms on the system and derive from the Heisenberg equations of motion the expressions of various operators corresponding to the dynamics. Solving the associated Schrödinger equation, we obtain the general solution. Then we calculate and discuss in detail the expression of the von Neumann entropy for the two qubits and the radiation field. We examine the negativity index to gauge the degree of quantum entanglement between the su(1) quantum system and the atoms. Finally, we compare the results of the negativity and von Neumann entropy for some values of the initial state and the detuning parameter.

中文翻译：

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与两个两能级原子相互作用的su（1）量子系统的纠缠对

在此通信中，我们考虑一对纠缠的量子系统，每个系统都由su（1）Lie代数描述，它们与两个二级原子相互作用。我们详细讨论了失谐项对系统的影响，并从运动的海森堡方程中得出了与动力学相对应的各种算符的表达式。求解关联的薛定ding方程，我们获得了一般解。然后，我们计算并详细讨论了两个量子位和辐射场的冯诺依曼熵的表达式。我们研究了负性指数，以衡量su之间的量子纠缠程度（1）量子系统与原子。最后，我们比较了初始状态和失谐参数的某些值的负性和冯·诺依曼熵的结果。