In this paper, the problem of a three-level atom interacting with a single mode of the quantized electromagnetic cavity field is considered. The considered theoretical model describes the distinct configurations of a three-level atom. Also, this model includes a detuning and arbitrary forms of both the field and the intensity-dependent atom-field coupling. We obtain the general forms for both the constants of motion and the wavefunction when the atom is initially prepared in one of its states. We use this model for computing a number of statistical aspects of the three-level system. As an illustration, we use the model for studying the time evolution of the second-order correlation function when the atom is initially in an upper state and the field is considered in a coherent state.

We study the non-resonant interaction of a moving four-level N-type atom with cavity fields in the presence of a nonlinear Kerr-like medium. The exact solutions of the considered models are obtained when the atom is initially in an upper state, while the field is in a coherent state. We derive an expression for the occupation numbers of the photon state. Also, the momentum increment of the atomic system is obtained. The influence of the detuning parameters or the Kerr medium on the evolution time of the momentum increment is examined numerically. The existence of the detuning parameters leads to the retraction of the revivals for the three atomic systems. On the other hand, the presence of the Kerr medium is conducive to increasing the regularity and periodicity of the collapse–revival phenomenon for the one- and two-mode systems, while chaotic behaviour occurs for the three-mode system.

In this article, the problem of a double Ξ-type four-level atom interacting with a single-mode cavity field is considered. The considered model describes several distinct configurations of a four-level atom. Also, this model includes the detuning parameters of the atom-field system. We obtain the constants of motion and the wavefunction is derived when the atom is initially prepared in the upper state. We used this model for computing a number of the field aspects for the considered system. As an illustration, the model is used for studying the time evolution of the Mandel Q-parameter, amplitude-squared squeezing phenomenon and Q-function when the input field is considered in a coherent state. The results show that these phenomena are affected by the presence of detuning parameters.

In this paper, we investigate the collapse-revival phenomenon and the Poissonian statistics of a four-level N-configuration atom interacting with two-mode cavity fields. We assume that the transition between the upper level and the third level of an atom is coupled by the frequency of mode one, while the other transitions are coupled by the frequencies of the two modes or mode two. The interaction is a multi-photon process and a Kerr medium is taken into account in the non-resonant case. We solve the models when the atom is initially prepared in a coherent superposition of the upper and ground states and the field is considered in a coherent state. The effects of both the detuning and the Kerr medium on the temporal behaviour of some statistical aspects are analysed. The conclusions are reached and some features are given.

In this paper, we investigate the entanglement degree in the interaction of a two-level atom prepared in a momentum eigenstate with an additional Stark-shift. We use the quantum entropy as a measure of the entanglement degree. The constants of motion and the density matrix of the system are obtained. The effect of the detuning and the Stark-shift parameters when the atom is prepared initially in the upper state are investigated. It is found that the detuning and the Stark shift affected on the entanglement of the atomic system, and the influence of the center-of-mass motion play an important role in the entanglement degree.