We develop an analytical solution of fractional Schrödinger equation to explain the interaction between a two-level atom and a single electromagnetic field mode inside a cavity. Based on this solution, two different cases are discussed; the first one reflects the standard Jaynes Cummings model, while the second solution gives rise to a wave equation for a dipole interacted with a field in semi-classical sense. By controlling different parameters inside cavity, the estimation degree in terms of quantum Fisher information is investigated. The obtained results show that the precision estimation increases as the detuning decreases and number of photons inside cavity increases. Moreover robust estimation is obtained for the standard Jaynes Cummings model. To measure the amount of information, a comparative study between von Neumann entropy and quantum Fisher information show the same behavior. As a result, we conclude that quantum Fisher information may detect entanglement of the interacted atom-field system.

中文翻译：

---

Quantum Fisher 信息：测量分数演化的探针

我们开发了分数阶薛定谔方程的解析解，以解释腔内两能级原子与单电磁场模式之间的相互作用。基于此解决方案，讨论了两种不同的情况；第一个反映了标准的 Jaynes Cummings 模型，而第二个解决方案产生了偶极子与半经典意义上的场相互作用的波动方程。通过控制腔内不同的参数，研究了量子Fisher信息的估计程度。所得结果表明，随着失谐减少和腔内光子数量增加，精度估计增加。此外，对于标准的 Jaynes Cummings 模型获得了稳健的估计。为了衡量信息量，冯诺依曼熵和量子费雪信息之间的比较研究显示出相同的行为。因此，我们得出结论，量子费雪信息可以检测相互作用的原子场系统的纠缠。