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Advances in Mathematical Physics

Dynamical Features of Isolated Two- and Three-Level Atoms Interacting with a Cavity Field

Mahmoud Youssef Abd‐Rabbou, Eied Mahmoud Khalil, Fadhel Almalki

Published Jul 21, 2022• 3 citations
Publisher

Abstract

Some dynamical features of two- and three-level atoms interacting locally with an ideal cavity field are investigated. These dynamical features are introduced by employing the statistical atomic inversion, entropy squeezing, and tomographic entropy. Our results show that the initial setting states play an essential role in the temporal evolution of the three quantities. The sensitivity of the two-level atomic state is less than that depicted by the three-level atom. The initial state has a small impact on the two types of entropies for the two-level atom. However, it has an appreciable effect in the case of the three-level atom for different regulations of the initial atomic state.

DOI
10.1155/2022/5258035

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The behavior of the dipole moment of a three-level atom interacting with cavity fields of arbitrary detunings is investigated. The time evolution and squeezing conditions of the components and correlation function of the dipole moment are calculated for three cases: one-mode field and a \ensuremath{\Xi}-type atom initially in the upper state, two-mode field and a \ensuremath{\Lambda}-type atom initially in the upper state, and two-mode field and a \ensuremath{\Lambda}-type atom initially in one of the lower states. A number of interesting features are found and discussed.
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In this paper, we study the interaction between an effective two-level atom and a three-mode field. The atom and the field are initially in the excited state and finite dimensional trio-coherent state, respectively. For this sytem, we investigate the atomic inversion, the von Neumann entropy, and the atomic Wehrl entropy. We show that there is a connection between all of these quantities. Also, we prove that the atomic Wehrl entropy exhibits a temporal evolution similar to the von Neumann entropy. It is observed that the Stark shift parameter plays an important role on the evolution of these quantities.
We study the interaction of a three-level atom with two-mode cavity field containing a Kerr-like medium in this cavity. The atom is initially prepared in a momentum eigenstate and the field is in the squeezed state. The constants of motion and the wave function for the atomic system of Λ-configuration at any time t > 0 are obtained. Also, the momentum increment, the momentum diffusion and the field entropy are calculated. The analytic results are employed to perform some investigations of the temporal evolution of the momentum increment and the field entropy. The influence of the number operators, the detunings and/or the Kerr-like medium is analysed. It is shown that the addition of the Kerr medium and/or the detunings in the presence or absence of the number operators has an important effect on the properties of the momentum increment and of the field entropy. Finally, conclusions and some features and comments are given.
This paper delves into the influence of an external classical field on the statistical and dynamical properties of a four-level atom interacting with a cavity field. Leveraging mathematical transformations applied to the external classical field, the system?s wave function was derived. Subsequently, the impact of this external field and a detuning parameter on atomic inversion, Shannon-entropy, the Q-function, and relative coherence is explored. The analysis encompassed three distinct initial states for the atomic system. The results unveiled that the specific type of classical field employed acts as a control parameter, inducing squeezing within the system, as demonstrably evidenced by the Q-function analysis. Conversely, the influence of the detuning parameter exhibited dependence on the initial state of the atomic system. However, in broader terms, it appears to be responsible for driving the system towards chaotic behavior.