We derive an analytical approximate solution of the time-dependent state vector in terms of material Bell states and coherent states of the field for a generalized two-atom Tavis-Cummings model with nonlinear intensity-dependent matter-field interaction. Using this solution, we obtain simple expressions for the atomic concurrence and purity in order to study the entanglement in the system at specific interaction times. We show how to implement entangling atomic operations through measurement of the field. We illustrate how these operations can lead to a complete Bell measurement. Furthermore, when considering two orthogonal states of the field as levels of a third qubit, it is possible to implement a unitary three-qubit gate capable of generating authentic tripartite entangled states such as the Greenberger-Horne-Zeilinger state and the $W$ state. As an example of the generic model, we present an ion-trap setting employing the quantized mode of the center-of-mass motion instead of the photonic field, showing that the implementation of realistic entangling operations from intrinsic nonlinear matter-field interactions is indeed possible.

中文翻译：

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非线性双原子 Tavis-Cummings 模型中的纠缠操作

对于具有非线性强度相关的物质场相互作用的广义双原子 Tavis-Cummings 模型，我们根据材料贝尔态和场的相干态推导出时间相关状态向量的解析近似解。使用这个解决方案，我们获得了原子并发和纯度的简单表达式，以研究特定交互时间系统中的纠缠。我们展示了如何通过对场的测量来实现纠缠原子操作。我们说明了这些操作如何导致完整的贝尔测量。此外，当考虑场的两个正交状态作为第三个量子位的能级时，可以实现一个单一的三量子位门，该门能够产生真实的三方纠缠态，例如格林伯格-霍恩-泽林格态和$宽$状态。作为通用模型的一个例子，我们提出了一个离子阱设置，它采用质心运动的量化模式而不是光子场，表明从内在非线性物质场相互作用中实现真实的纠缠操作确实是可能的。