We obtain exact dynamics of a two-qubit central spin model (CSM) consisting of two interacting qubits homogeneously coupled to a spin bath via the $XXZ$-type coupling, with the bath initially prepared in linear superpositions of the symmetric Dicke states. Using the interaction picture Hamiltonian with respect to the non-spin-flipping part of the model, we derive a sequence of equations of motion within each magnetization sector satisfied by the probability amplitudes of the time-evolved state. These equations of motion admit analytical solutions for the single-qubit CSM in which one of the two central qubits decouples from the rest of the system. Based on this, we provide a quantitative interpretation to the observed collapse-revival phenomena in the single-qubit Rabi oscillations when the bath is prepared in the spin coherent state. We then study the disentanglement and coherence dynamics of two initially entangled noninteracting qubits when the two qubits interact with individual baths or with a common bath. For individual baths, the coherent dynamics is found to be positively correlated to the single-qubit purity dynamics, and entanglement sudden disappearance and revivals are observed in both cases. The entanglement creation of two initially separable qubits coupled to a common bath is also studied and collapse and revival behaviors in the entanglement dynamics are observed. Choosing the equally weighted state and the $W$-class states as the bath initial states, we finally study the dynamics of entanglement between two individual bath spins and demonstrate the entanglement sharing mechanism in such a system.

中文翻译：

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旋转对称对称迪克态制备的均质两量子位XXZ中心自旋模型的动力学

我们获得了一个由两个相互作用的量子位组成的两个量子位中心自旋模型（CSM）的精确动力学，这些相互作用的量子位均匀地耦合到一个自旋浴。 $XXž$型耦合，首先将浴以对称迪克状态的线性叠加形式制备。使用相对于模型的非自旋翻转部分的相互作用图片哈密顿量，我们得出了每个磁化扇区内的运动方程序列，这些运动方程由时间演化状态的概率幅度所满足。这些运动方程为单量子位CSM提供了解析解，其中两个中心量子位之一与系统的其余部分解耦。基于此，当浴以自旋相干状态制备时，我们对观察到的单量子位拉比振荡中的坍塌-恢复现象进行了定量解释。然后，我们研究当两个量子位与单个浴或公共浴相互作用时，两个初始纠缠的非交互量子位的解纠缠和相干动力学。对于单个浴，发现相干动力学与单量子位纯度动力学呈正相关，并且在两种情况下均观察到纠缠突然消失和复兴。还研究了耦合到公共浴池的两个最初可分离的量子位的纠缠创建，并观察了纠缠动力学中的崩溃和复兴行为。选择权重相等的状态和 还研究了耦合到公共浴池的两个最初可分离的量子位的纠缠创建，并观察了纠缠动力学中的崩溃和复兴行为。选择权重相等的状态和 还研究了耦合到公共浴池的两个最初可分离的量子位的纠缠创建，并观察了纠缠动力学中的崩溃和复兴行为。选择权重相等的状态和$\mathrm{w\; ^}$类状态作为浴的初始状态，我们最终研究了两个单独的浴自旋之间的纠缠动力学，并证明了这种系统中的纠缠共享机制。