Evaluating Wigner and Husimi Functions Using Fractional Multiphoton Jaynes–Cummings Model

One of the most significant physical models for characterizing the dynamics of robust-intensity and strong laser fields, has recently been solved using the so-called multiphoton Jaynes–Cummings model. This generalized model describes the interaction between a two-level atom and a field in the presence of multiple photons simultaneously. In the present study, we consider the generalized form of the equation, known as the fractional equation. An exact fractional solution of the multiphoton Jaynes–Cummings model is derived. Furthermore, the non-Gaussianity of the system is examined using the Wigner and Husimi quasiprobability distributions. Our main result can be summarized as follows: although the initial state is taken as a direct product of the atomic and coherent states, the system remains non-Gaussian when fractional dynamics is taken into account. The results show that the Wigner function consistently exhibits negative regions for small values of the fractional order, corresponding to strong fractional memory. Moreover, it is demonstrated that both the Wigner and Husimi functions are highly sensitive to variations in the parameters of the multiphoton Jaynes–Cummings model. In particular, localization of the quantum state is observed in both functions within a specific region of the phase plane.