In this paper we propose a generalized $f$-deformed Dicke model for the dynamics of an atomic Bose–Einstein condensate (BEC) in the presence of collisional interactions and Stark effect. The BEC contains $N$ two-level atoms and the nonlinear characteristics of quantized field originates from the $f$-deformation of the associated raising and lowering operators. After solving the time dependent Schrödinger equation corresponding to the model Hamiltonian, we investigate the dynamics of the system under various physical situations; in particular, two different initial states for the quantized field i.e., coherent and squeezed field. In this regard, at first, we obtain some analytical expressions correspond to the energy transfer and non-classical properties of the constituents of system and then proceed to analyze their dynamics, numerically. Our results show that the dynamical evolution of system can be governed by tuning the parameters describing the considered interactions. In particular, the energy levels can be controlled and shifted by changing the Stark effect. Collapse–revival phenomenon occurs in the patterns of atomic inversion, specially in the case of initial coherent state. However, with initial squeezed field typical revivals accompanied with short time collapses may be observed; moreover, the general behavior of atomic inversion shows irregular oscillatory manner. Short time squeezing takes place and can be exchanged between the field quadratures in the absence or presence of Stark effect. Also, the amount of entanglement depends on the nonlinearities which specify the interactions among the atoms in BEC and photons in the quantized field. Interestingly, the general pattern of Von Neumann entropy as a measure of entanglement is independent of the chosen initial states. However, the amplitude of entropy reduces in the case of squeezed state which means that the system possesses more separable states in this condition. In addition, the time evolution of Bloch sphere confirms irregular behavior of entanglement in the system.

在本文中，我们提出了一个广义的 $F$碰撞相互作用和斯塔克效应存在的情况下，用于原子玻色-爱因斯坦凝聚物（BEC）动力学的Dicke变形模型。BEC包含$ñ$ 两能级原子和量子化场的非线性特征源自 $F$-相关的升降操作员变形。在求解了与模型哈密顿量相对应的与时间相关的薛定ding方程后，我们研究了在各种物理情况下系统的动力学。特别地，对于量化场，两个不同的初始状态，即相干场和压缩场。在这方面，首先，我们获得一些与系统组成的能量传递和非经典特性相对应的解析表达式，然后进行数值动力学分析。我们的结果表明，可以通过调整描述所考虑相互作用的参数来控制系统的动态演化。特别地，可以通过改变斯塔克效应来控制和改变能级。坍塌-复兴现象以原子倒转的模式发生，特别是在初始相干状态下。然而，在最初的压缩场中，可以观察到典型的复兴并伴随着短暂的崩溃。此外，原子反转的一般行为表现出不规则的振荡方式。发生短时间压缩，并且可以在没有或没有斯塔克效应的情况下在场正交之间进行交换。同样，纠缠的量取决于非线性，该非线性规定了BEC中的原子与量子场中的光子之间的相互作用。有趣的是，冯·诺依曼熵的一般模式作为缠结的量度与所选初始状态无关。但是，在压缩状态下，熵的振幅会减小，这意味着系统在此条件下拥有更多可分离的状态。此外，