In this paper, we propose a new transition scheme (Double Λ) for the interaction between a five-level atom and an electromagnetic field and study its dynamics in the presence of a cross Kerr-like medium in the exact-resonance case. The wave function is derived when the atom is initially prepared in its upper most state, and the field is initially prepared in the coherent state. We studied the atomic population inversion, the coherence degree by studying the second-order correlation function, Cauchy-Schwartz inequality (CSI) and the relation with P-function. Finally, we investigate the effect of Kerr-like medium on the evolution of Husimi Q-function of the considered system.

The Dynamics of a Five-level (Double Λ)-type Atom Interacting with Two-mode Field in a Cross Kerr-like Medium

/pdf/supersymmetry-as-an-algebraic-approach-to-the-jaynes-cumming-1garncy4.pdf

Supersymmetry as an Algebraic Approach to the Jaynes-Cumming Model with Stark Shift and Kerr-Like Medium

We have investigated numerically the dynamics of quantum Fisher information (QFI) and quantum entanglement (QE) for N-level atomic system interacting with a coherent field in the presence of Kerr (linear and non-linear medium) and Stark effects. It is observed that the Stark and Kerr effects play a prominent role during the time evolution of the quantum system. The evolving quantum Fisher information (QFI) is noted as time grows under the non-linear Kerr medium contrary to the QE for higher dimensional systems. The effect of non-linear Kerr medium is greater on the QE as we increase the value of Kerr parameter. However, QFI and QE maintain their periodic nature under atomic motion. On the other hand, linear Kerr medium has no prominent effects on the dynamics of N-level atomic system. Furthermore, it has been observed that QFI and QE decay soon under the influence of Stark effect. In short, the N-level atomic system is found prone to the change of the Kerr medium and Stark effect for higher dimensional systems.

/pdf/stark-and-kerr-effects-on-the-dynamics-of-moving-n-level-42cpp8hp44.pdf

Stark and Kerr Effects on the Dynamics of Moving N-Level Atomic System

We present an analytical solution for a quantum system characterized by a double $$\Lambda$$ five-level atom interacting with an intensity-dependent coupling regime, influenced by a nonlinear Kerr-like medium. We also derive the constants of motion through Heisenberg's equations. Furthermore, the dynamical evolution of the entanglement and quantum coherence between the atom and the field is discussed using linear entropy and $$l_{1}$$ -norm of coherence. Through a comprehensive examination of the quantum system, it is observed that both the detuning and the Kerr-like parameters exert a significant impact on the degree of entanglement and coherence. However, the impacts of detuning and the Kerr effect become less pronounced when the photon multiplicity is high. In addition, we conduct a comparison between the five-level atomic system and a four-level system, revealing that the number of energy levels has a profound impact on the behavior of entanglement and coherence. These findings highlight the importance of atomic structure and photon multiplicity in controlling and optimizing quantum processes, particularly in applications involving quantum communication and information processing. 

Dynamical evolution of a five-level atom interacting with an intensity-dependent coupling regime influenced by a nonlinear Kerr-like medium

We investigated numerically the dynamics of quantum Fisher information (QFI) and entanglement for three- and four-level atomic systems interacting with a coherent field under the effect of Stark shift and Kerr medium. It was observed that the Stark shift and Kerr-like medium play a prominent role during the time evolution of the quantum systems. The non-linear Kerr medium has a stronger effect on the dynamics of QFI as compared to the quantum entanglement (QE). QFI is heavily suppressed by increasing the value of Kerr parameter. This behavior was found comparable in the cases of three- and four-level atomic systems coupled with a non-linear Kerr medium. However, QFI and quantum entanglement (QE) maintain their periodic nature under atomic motion. On the other hand, the local maximum value of QFI and von Neumann entropy (VNE) decrease gradually under the Stark effect. Moreover, no prominent difference in the behavior of QFI and QE was observed for three- and four-level atoms while increasing the value of Stark parameter. However, three- and four-level atomic systems were found equally prone to the non-linear Kerr medium and Stark effect. Furthermore, three- and four-level atomic systems were found fully prone to the Kerr-like medium and Stark effect.

Entanglement Dynamics of Three and Four Level Atomic System under Stark Effect and Kerr-Like Medium

We study the interaction between a four-level atom (ladder type) in a momentum eigenstate with a single mode cavity field in the presence of non-linearities of both the field and the intensity-dependent coupling. The constants of motion and the wave function for the atomic system have been obtained. Special attention is given to discuss some statistical aspects of the considered atomic system such as momentum increment, momentum diffusion and high-order squeezing. The influence of the Kerr-like medium and the intensity dependent coupling on the momentum increment and the high-order squeezing are investigated numerically. It is found that addition of these parameters has an important effect on both the momentum increment and the squeezing phenomenon.

One-mode interaction with a four-level atom in a momentum eigenstate

We study the interaction between a one-mode electromagnetic field and a two-level atom in the presence of a Kerr-like medium when the atom is prepared initially in the momentum eigenstate. The wave function is calculated by using the Schrodinger equation for a coherent electromagnetic field and an atom in the excited state. The effects of the Kerr-like medium and the detuning parameters on the statistical aspects of the intensity-dependent-coupling Hamiltonian such as, atomic momentum increment, momentum diffusion, the radiation force, and the field entropy are calculated. We investigate the effect of the detuning, Kerr-like medium and photon number operator on the field entropy.

Influence of a Kerr-Like Medium and the Detuning Parameter on the Statistical Aspects of the Intensity-Dependent-Coupling Hamiltonian

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One-mode interaction with a four-level atom in a momentum eigenstate

Influence of a Kerr-Like Medium and the Detuning Parameter on the Statistical Aspects of the Intensity-Dependent-Coupling Hamiltonian